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## College Algebra (10th Edition)

$\color{blue}{y=-5x+11}$
RECALL: (1) The slope-intercept form of a line's equation is: $y=mx+b$ where $m$ = slope and $b$ = y-intercept (2) The slope of the line that passes through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $m=\dfrac{y_2-y_1}{x_2-x_1}$ Solve for the slope using the formula in (2) above to obtain: $m=\dfrac{-4-1}{3-2}=\dfrac{-5}{1}=-5$ Thus, the tentative equation of the line is: $y=-5x+b$ To find the value of $b$, substitute the values of x and y of the given point $(2, 1)$ to obtain: $y=-5x+b \\1=-5(2)+b \\1=-10+b \\1+10=b \\11=b$ Thus, the equation of the line is $\color{blue}{y=-5x+11}$.

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(Bob Dylan/trad., arr. “borrowed” – along with some records – from Dave Van Ronk)
Played by Bob Dylan on Bob Dylan (1962)
Tabbed by Eyolf Østrem

Intro: (* = slide up on the sixth string). Interlude between verses something of the same as the intro.

Am . C/g . |D/f# . F . |Am . E . *|Am . . .

Am   C/g           D/f#      F
There is a house down in New Orleans
Am       C/g    E
they call the rising sun
Am       C/g     D/f#        F
And it's been the ruin of many a poor girl
Am     E        Am
and me, oh God, I'm one.

My mother was a tailor,
she sowed these new blue jeans
My sweetheart was a gambler, Lord,
down in New Orleans.

Now the only thing a gambler needs
is a suitcase and a trunk
And the only time when he's satisfied
is when he's on a drunk.

He fills his glasses up to the brim
and he'll pass the cards around
And the only pleasure he gets out of life
is rambling from town to town.

Oh tell my baby sister
not to do what I have done
But shun that house in New Orleans
they call the rising sun.

Well with one foot on the platform
and the other foot on the train
I'm going back to New Orleans
to wear that ball and chain.

I'm going back to New Orleans,
my race is almost run
I'm going back to end my life
down in the rising sun.

There is a house in New Orleans
they call the rising sun
And it's been the ruin of many a poor girl
and me, oh God, I'm one.

## 12 April 1963 (Fourth McKenzie Tape)

Drop D tuning (D-a-d-g-b-e’), guitar tuned a half step down.

Quite energetic playing on this one, despite the extreme simplicity. Most of the song is reduced to an alternating thumb between the two d-strings, with occasional turns to an f or c in the bass. But when he raises the energy level in the fifth verse, he really gets going.

The turns to f (indicated with “/f” in the tab) are either played with the full “/f figure” (see below), or just with the bass tone as in the fourth measure of the intro.

The a (third string, second fret) in the second measure of the /f-figure is probably just hammered on or sounded when the chord changes, without necessarily having to be thought about at all. It could also be picked with the index finger, but that disrupts the rhythm pattern a bit.

/f figure                              A                 G/b
:   .   .   .     :   .   .   .      :   .   .   .      .   .
|-----------------|-----------------||-----------------||---------||
|---------------3-|-----------------||-----------------||-------3-||
|-----------0-----|(2)--------------||-----------2-----||---0-----||
|-----0-------0---|-----0-----------||-----2-------2---||-----0---||
|-----------------|-----------------||-0---------------||-2-------||
|-0-------3-------|-0---------------||---------2-------||---------||

Intro:

  :   .   .   .     :   .   .   .     :   .   .   .     :   .   .   .
|-----------------|-----------------|-----------------|-----------------|
|-----------------|-----------------|-----------------|-----------------|
|-----------------|-----------------|-----------------|-----------------|
|-----0-------0---|-----0-------0---|-----0-------0---|-----0-------0---|
|-----------------|-----------------|-----------------|-----------------|
|-0-------0-------|-0-------0-------|-0-------0-------|-0-------3-------|

:   .   .   .     :   .   .   .     :   .   .   .     :   .   .   .
|-----------------|-----------------|-----------------|-----------------|
|---------------3-|---------------3-|-----------------|-----------------|
|-----------2-----|-----------2-----|-----------------|-----------------|
|-----0-------0---|-----0-------0---|-----0-------0---|-----0-------0---|
|-----------------|-----------------|-----------------|-----------------|
|-0-------0-------|-0-------0-------|-0-------0-------|-0-------0-------|
There ...

D                 /f /d
There is a house in New Orleans
/f  /d
they call the rising sun
/f     /f   /d
It's been the ruin of many a poor soul
/f  /d
and me, oh God, I'm one.

/f G/b  /d
If I had listened to what my momma said,

I'd-a been at home today

But being so young and foolish,
A        D
I let gambling lead me astray.

/f /d
Now the only thing a gambler needs
/f /d
is a suitcase and a trunk
/f /f /d
And the only time he's satisfied
G/b    D
is when he's on a drunk.

He fills his glasses up to the brim
/f /d
and passes the cards around
/f /f /d
And the only time he's satisfied
/f  /f  /d
is rambling from town to town.

:   .   .   .     :   .   .   .     :   .   .   .     :   .   .   .
|-----------------|-----------------|-----------------|-----------------|
|---------------3-|-----------------|---------------3-|-------3-------3-|
|-----------2-----|-----------------|-----------2-----|---2-------0-----|
|-----0-------0---|-----0-------0---|-----0-------0---|-----0-------0---|
|-----------------|---------3-------|-----------------|---------3-------|
|-0-------0-------|-0---------------|-0-------0-------|-0---------------|
town

:   .   .   .     :   .   .   .     :   .   .   .     :   .   .   .
|-----------------|-----------------|-----------------|-----------------|
|---------------3-|---------------3-|---------------3-|---------------3-|
|-----------0-----|(2)--------0-----|(2)--------0-----|(2)--------0-----|
|-----0-------0---|-----0-------0---|-----0-------0---|-----0-------0---|
|-----------------|-----------------|-----------------|-----------------|
|-0-------3-------|-0-------3-------|-0-------3-------|-0-------3-------|
Oh...

/d /f   /d /f /d
Oh tell my baby sister
/f /f  /d
not to do what I have done
/f   /f /d
But shun that house in New Orleans
A      D
they call the rising sun.

/f  /f  /d
Well it's one foot on the platform
/f  /f /d
and the other foot on the train
/f   /f /f
I'm going back to New Orleans
/f   /f  /d
to wear my ball and chain.

/f /d
I'm going back to New Orleans,
/f /f  /d
my race is almost run
/f    /f /d
I'm going back to spend my days
/f     /f /d G/b D
beneath the rising sun.

:   .   .   .     :   .   .   .     :   .   .   .     :   .   .   .
|-----------------|-----------------|-----------------|-----------------|
|-----------------|---------------3-|---------------3-|-------3-------3-|
|-----------------|-----------2-----|-----------2-----|---0-------0-----|
|-----0-----------|-----0-------0---|-----0-------0---|-----------------|
|-----------------|-----------------|-----------------|-3---3-------3---|
|-0-------0---3---|-0-------0-------|-0-------0-------|---------0-------|
..sun

:   .   .   .     :   .   .   .     :   .   .   .     :   .   .   .
|-----------------|-----------------|-----2-----------|-----2-----------||
|-------3---------|-----------------|-----3---------3-|-----3-----------||
|---0-------0-----|-----------x-----|-----2-----2-----|-----2-----------||
|-----------------|-----0-----------|-----0-------0---|-----0-----------||
|-----2-----------|-------------3---|-----------------|-----------------||
|-0-------0---3---|-0-------0-------|-0-------0-------|-0---------------||


text:
>> Table of sin, cos and tan values For example, from the given area of the triangle and the corresponding side, the appropriate height is calculated. Use SOHCAHTOA and set up a ratio such as sin(16) = 14/x. show help ↓↓ examples ↓↓). You can lock a side or angle and animate the other sides and angles to get the triangle dimensions you need. Right triangle calculator to compute side length, angle, height, area, and perimeter of a right triangle given any 2 values. To find the area of such triangle, use the basic triangle area formula is area = base * height / 2. It is the longest side of the triangle. Customer Voice. Formula. (From here solve for X). These are shortened to sin, cos and tan. If you only know the length of two sides, or one angle and one side, this is enough to determine everything of the triangle. A right triangle is a geometrical shape in which one of its angle is exactly 90 degrees. This hypotenuse calculator has a few formulas implemented - this way, we made sure it fits different scenarios you may encounter. The Pythagoras calculator is used to calculate geometrical expression based on the Pythagoras theorem. 0 the sum of the reciprocals of the lengths of the interior angle bisectors of a triangle and the sum of the reciprocals of the lengths of the sides Enter the three side lengths and press 'Calculate'. Calculates the angle and opposite of a right triangle given the adjacent and hypotenuse. 1. If you want to calculate hypotenuse enter the … This hypotenuse calculator has a few formulas implemented - this way, we made sure it fits different scenarios you may encounter. What Is Pythagorean Theorem? Our right triangle side and angle calculator displays missing sides and angles! Then use Heron's formula and trigonometric functions to calculate area and other properties of a given triangle. The opposite is the side directly across from the required angle. On your mark, get set, go. Adjacent and opposite of right triangle Calculator, ( 5°12'6" is inputted as 5'12'6, 5.25° as 5.25). or from the top angle, Ratios . Hypotenuse of a triangle formula. Find the lengths of the non-hypotenuse sides of your triangle. Stack Exchange Network . Oblique triangle calculator takes in one side length and any two other values and returns the missing values in exact value and decimal form in addition to the step-by-step calculation process for each of those missing values. (The hypotenuse is the longest side of the right … Whether you have three sides of a triangle given, two sides and an angle or just two angles, this tool is a solution to your geometry problems. The area will be calculated. TOA: Tan(θ) = Opposite / Adjacent We’ll dive further into the theory behind it in the video below, but essentially it’s taken from the AA Similarity Postulatethat we learned about previously. Hypotenuse of a triangle formula. a = c/2 For example, from the given area of the triangle and the corresponding side, the appropriate height is calculated. From the known height and angle, the adjacent side, etc., can be calculated. Our tangent calculator accepts input in degrees or radians, so assuming the angle is known, just type it in and press "calculate". Related Articles: Python: Tips of the Day. Here you can enter two known sides or angles and calculate unknown side ,angle or area. The third side can be determined by the law of cosines. This calculator is for a right triangle only! Easy to use calculator to solve right triangle problems. If the angle is unknown, but the lengths of the adjacent side and the hypotenuse of a right angle triangle are given, then calculating the cosine can be done by dividing the adjacent side by the hypotenuse (side c as per the figure above). Calculator iterate until the triangle has calculated all three sides. See the solution with steps using the Pythagorean Theorem formula. You can find the hypotenuse: Given two right triangle legs; Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. To improve this 'Angle and adjacent of right triangle Calculator', please fill in questionnaire. $$\text{θ}$$ signifies the size of the angle in the triangle. FAQ. Python: Yield Statement. The Pythagorean Theorem Calculator is used to calculate the length of the third side of a right-angled triangle based on the other two sides using the Pythagorean theorem. Sides "a" and "b" are the perpendicular sides and side "c" is the hypothenuse. Round answers to the nearest tenth. Uses law of sines to determine unknown sides then Heron's formula and trigonometric functions to calculate area and other properties of a given triangle. The following example shows you how to find the values of the tangent for each of the acute angles in a right triangle where the hypotenuse is 25 inches and one leg is 7 inches. If you know two sides and one adjacent angle use SSA calculator. Enter all known variables (sides a, b and c; angles A and B) into the text boxes. Click on the "Calculate" button to solve for all unknown variables. Active 8 years, 9 months ago. The adjacent side ($$a$$) ... An equilateral triangle with side lengths of 2 cm can be used to calculate accurate values for the trigonometric ratios of 30° and 60°. It can also provide the calculation steps and how the right triangle looks. Solution: sine … It’s defined as: 1. Python Basic - 1: Exercise-16 with Solution. In the following right triangle PQR, • the side PQ, which is opposite to the right angle PRQ is called the hypotenuse. How to find the height of an equilateral triangle An equilateral triangle is a triangle with all three sides equal and all three angles equal to 60°. Here you can enter two known sides or angles and calculate unknown side ,angle or area. Note: Use bitwise operations to add two numbers. Input value you know and select what to compute. 5 Changing the length of the Hypoteneuse measured in units, will change the Opposite side, the Adjacent side and Area of the triangle. Can you find the length of the adjacent side of a right triangle only knowing the length of the opposite side and the angle? If the angle is unknown, but the lengths of the opposite and adjacent side in a right-angled triangle are known, then the tangent can be calculated from these two measurements. Use the calculator on below to calculate the area of a triangle given 3 sides using Heron's formula. In our case, one leg is a base and the other is the height, as there is a right angle between them. A right triangle is a geometrical shape in which one of its angle is exactly 90 degrees. Learn how to find the missing sides or angles of a right triangle when one length and one angle is provided. Using your two points as the corners of the triangle adjacent to the hypotenuse, find the lengths of the a and b sides of the triangle. Recall the three main trigonometric functions: ... now use a calculator to find sin $$45^\circ$$. b = a√3. A right triangle has two sides perpendicular to each other. Adjacent, Opposite and Hypotenuse, in a right triangle is shown below. Select what (angle / sides) you want to calculate, then enter the values in the For example, if one needs to find cot(α) and it is known that the adjacent side b = 6 and c = 20, then cos(α) = 6 / 20 = 0.3. Take a square root of sum of squares: c = √(a² + b²) Given angle and one leg; … If you are given side a, and side b, and an angle C then it is possible to calculate the area A. Calculator Solver. These are successively applied and combined, and the parameters of the triangle calculate. You can think of yield statement in the same category as the return statement. Your feedback and comments may be posted as customer voice. Step 2 Use SOHCAHTOA to decide which one of Sine, Cosine or Tangent to use in this question. [1]  2020/07/08 23:57   Male / 40 years old level / High-school/ University/ Grad student / Very /, [2]  2020/04/28 10:06   Male / 50 years old level / Self-employed people / Very /, [3]  2019/12/29 07:56   Male / 60 years old level or over / An office worker / A public employee / Very /, [4]  2019/06/20 21:12   Male / 50 years old level / An office worker / A public employee / Very /, [5]  2010/03/22 21:28   Male / 40 level / Others / Very /, [6]  2009/10/24 22:05   Male / 40 level / Others / Very /, [7]  2009/09/01 02:18   Male / 40 level / Self-employed people / Very /, [8]  2009/01/21 23:09   Male / 50 level / Others / Very /. Also explore many more calculators covering geometry, math and other topics. You can calculate angle, side (adjacent, opposite, hypotenuse) and area of any right-angled triangle and use it in real world to find height and distances. Enter the length of any two sides and leave the side to be calculated blank. opposite b: hypotenuse c: angle θ ° = adjacent a . The formula for area of a right triangle … Must the perp. a = b√3/3. Method 2. Dynamically Calculate angles and sides of right angled triangle (one angle is 90). The factors are the lengths of the sides and one of the two angles, other than the right angle. If you know one side and adjacent … Length a Length b Angle C Area A. Namely: sec(x) = 1/cos(x) cosec(x) = 1/sin(x) cot(x) = 1/tan(x) The secant, cosecant and cotangent are used very rarely used, because with the same inputs … This calculator also finds the area A of the right triangle with sides a and b. The interior angles of a triangle always add up to 180° while the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it. Type in the given values. >> Different types of tri angles, The formulae (formula) for finding angle and sides of triangle can be easily remembered using the Then use Heron's formula and trigonometric functions to calculate area and other properties of a given triangle. A triangle has one side length of 8cm and an adjacent angle of 45.5. if the area of the triangle is 18.54cm, calculate the length of the other side that encloses the 45.5 angle Thanks Eugene Brennan (author) from Ireland on May 13, 2020: Must the perp. For a right angled triangle, where I have the length of the 'opposite' side, as well as all three angles (90, a1 & a2), how can I determine the length of the 'adjacent' side. Viewed 3k times -3. The ratio of these sides is given special names: sine, cosine and tangent. Some functions are limited now because setting of JAVASCRIPT of the browser is OFF. The third side can be determined by the law of cosines. Adjacent and hypotenuse of right triangle Calculator - High accuracy calculation Welcome, Guest The two sides given are adjacent to the given angle as you can see. sin (B) = b/c, cos (B) = a/c, tan (B) = b/a Area = a*b/2, where a is height and b is base of the right triangle. Our online tools will provide quick answers to your calculation and conversion needs. Questionnaire. All values should be in positive values but decimals are allowed and valid. Look also our friend's collection of math problems and questions: Angle and opposite of right triangle Calculator - High accuracy calculation Welcome, Guest This calculator will find out the area providing you have two sides and an angle. Without this information you do not have enough data in order to find out the length of the third side. √ I want to calculate: Input two elements of a right triangle use letter r to input square root. Oblique triangle calculator takes in one side length and any two other values and returns the missing values in exact value and decimal form in addition to the step-by-step calculation process for each of those missing values. The length of the adjacent of a right triangle with an angle of 60° and a hypotenuse of 5 cm is 2.5 cm. A : When you solve a right triangle, or any triangle for that matter, it means you need to find all missing sides and angles. Method 1. 0 the sum of the reciprocals of the lengths of the interior angle bisectors of a triangle and the sum of the reciprocals of the lengths of the sides 3. respective rows and click calculate. The calculator solves a triangle given by lengths of two sides and the angle between these sides. Formula: c 2 = a 2 + b 2 Where, a = Adjacent side (a) b = Opposite side (b) c = Hypotenuse side (c) of the right angled triangle. It stated that the ratios of t… A: The adjacent side of a triangle is the side (leg) that is touching the angle but is not the hypotenuse. It’s a mnemonic device to help you remember the three basic trig ratiosused to solve for missing sides and angles in a right triangle. What Is Pythagorean Theorem? If the longer leg length b is the one parameter given, then:. Calculator iterate until the triangle has calculated all three sides. The hypotenuse is the side of the triangle opposite the right angle. All the four parameters being angle, opposite side, adjacent side and hypotenuse side. Now use the cursor (Arrow) keys to animate other side and angles. h^2 = pq. Easy as that. c = 2b√3/3. Dividing the hypothenuse by the adjacent side gives the secant and the adjacent side divided by the opposite side results in the cotangent. Calculates the adjacent and opposite of a right triangle given the angle and hypotenuse. Method 2. /. Set up the following equation using the Pythagorean theorem: x 2 = 48 2 + 14 2. The adjacent is the side that forms part of the required angle. If you know two sides and one adjacent angle use SSA calculator. To enter a value, click inside one of the text boxes. SOH: Sin(θ) = Opposite / Hypotenuse 2. To enter a value, click inside one of the text boxes. The Pythagorean Theorem Calculator is used to calculate the length of the third side of a right-angled triangle based on the other two sides using the Pythagorean theorem. This trigonometry video tutorial explains how to calculate the missing side length of a triangle. Fill in two (only two) values then click on Calculate. Set up the following equation using the Pythagorean theorem: x 2 = 48 2 + 14 2. Often, the hardest part of finding the unknown angle is remembering which formula to use. Male or Female ? Learn all about the trigonometry of right triangles. Step by step guide to finding missing sides and angles of a Right Triangle By using Sine, Cosine or Tangent, we can find an unknown side in a right triangle when we have one length, and one angle (apart from the right angle). Select the proper option from a drop-down list. Formula. FAQ. You can find the hypotenuse: Given two right triangle legs; Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Remembering the Formula. Calc third side of scalene forming lift arm of aircraft dolly/jack (from two known sides and included angle) [4] 2020/07/12 03:01 Female / 60 years old level or over / A retired person / - / Purpose of use For right triangles only, enter any two values to find the third. A right triangle has a built in third angle, as one of the angles has to be 90 degrees. Adjacent and opposite of right triangle Calculator - High accuracy calculation Welcome, Guest You would naturally pick the altitude or height that allowed you to ship your triangle in the smallest rectangular carton, so you could stack a lot on a shelf. For example, an area of a right triangle is equal to 28 in² and b = 9 in. Trigonometry Calculator - Right Triangles. c = 2a. (From here solve for X). To do this, we need the inverse functions arcsine, arccosine and arctangent. Find the measure of the missing leg. Step-by-step explanations are provided for each calculation. If so how do you calculate it? This calculator calculates for the length of one side of a right triangle given the length of the other two sides. Ask Question Asked 8 years, 9 months ago. bisectors of opposite sides in a quadrilateral intersect inside it, if one of the angles is right and an adjacent angle is obtuse? This online calculator calculates right angled triangle angle and sides. A right triangle is a triangle that has 90 degrees as one of its angles. So the area of 45 45 90 triangles is: area = a² / 2 To calculate the perimeter, simply add all 45 45 90 triangle sides: Sides "a" and "b" are the perpendicular sides and side "c" is the hypothenuse. Write a Python program to get the third side of right angled triangle from two given sides. Method 1. Take a square root of sum of squares: You would naturally pick the altitude or height that allowed you to ship your triangle in the smallest rectangular carton, so you could stack a lot on a shelf. 30 60 90 triangle sides. sin $$40^\circ=\frac{\sqrt{2}}{2}→AC \cong 0.70710$$ Missing Sides and Angles of a Right Triangle – Example 2: Find AC in the following triangle. Scalene triangle calculator diagram. Given two sides and an angle, this formula is the most appropriate to use. All the four parameters being angle, opposite side, adjacent side and hypotenuse side. Calculating adjacent side of triangle in java? A triangle has one side length of 8cm and an adjacent angle of 45.5. if the area of the triangle is 18.54cm, calculate the length of the other side that encloses the 45.5 angle Thanks Eugene Brennan (author) from Ireland on May 13, 2020: The other two other modifiable values will be filled in, along with the angle 3 field. sentence - ", Trigonometry Calculator Sin Cos Tan Inverse, Double Angle Identity Solver, Formula - Trig Calculator. Finding the measurement of the third side of a triangle when you know the measurement of the other two sides only works if you have a right triangle or the measurement of at least one other angle. Solve triangle by entering one side and two angles (adjacent and opposite). CAH: Cos(θ) = Adjacent / Hypotenuse 3. Area of a Triangle Given 2 Sides and an Angle. Adjacent, opposite and hypotenuse signify the length of these sides respectively. Tan (q) = Opposite / Adjacent Select what (angle / sides) you want to calculate, then enter the values in the respective rows and click calculate. In the below online right triangle calculator, just select two parameters which you need to find, and submit to calculate angle and sides of a triangle. If we know the shorter leg length a, we can find out that:. On your mark, get set, go. Everything You Need Know About The Pythagoras Calculator. For hypotenuse c known, the legs formulas look as follows:. It is not possible for a triangle to have more than one vertex with internal angle greater than or equal to 90°, or it would no longer be a triangle. In the below online right triangle calculator, just select two parameters which you need to find, and submit to calculate angle and sides of a triangle. This means that these quantities can be directly calculated from the sine, cosine and tangent. How to find the height of an equilateral triangle An equilateral triangle is a triangle with all three sides equal and all three angles equal to 60°. h^2 = pq. A red circle will appear to mark the locked side or angle. 2. If you are given side a, and side b, and an angle C then it is possible to calculate the area A. The formulae (formula) for finding angle and sides of triangle can be easily remembered using the sentence - " O ld H arry A nd H is O ld A unt" Sin (q) = Old/Harry = Opposite/Hypotenuse Cos (q) = And/His = Adjacent/Hypotenuse Tan (q) = Old/Aunt = Opposite/Adjacent Step 1 Find the names of the two sides we are using, one we are trying to find and one we already know, out of Opposite, Adjacent and Hypotenuse. Click on the "Calculate" button to solve for all unknown variables.
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text: Whether each of the $T_i$ The first 4.2 Geneva Wheel. four-bar knee model shown here, the rigid rods include the The type of input and output links is determined by whether The variables $$s$$ and $$l$$ are the shortest and longest from $B$, and so the input rod can't be a crank and must be seat. This Video Covers the working of a four bar linkage mechanism using a 3D animation. effects of both the ligaments and the meniscus. For the four bar linkage has, fixed link = 3 cm, crank link = 1 cm, coupler link = 4 cm, follower link = 2.5 cm ©2=124.0 determine O3 and by analytical method :Answer a) A four bar linkage has an input link (2) which is 100 mm long, a ground link (1) 250 mm long, an output link (4) 200 mm long and a coupler link (3) 300 mm long. The fourth state is Rocker-Rocker in which both the input and driven links are only able to rock back and forth about their respective pivots on the ground link. up into the mouth to actively capture prey and drag it This type of The case when $a = b$ components of the jaw. M. Muller. Output link $b$: gives output angle $\beta$. Ground link $g$: fixed to anchor pivots $A$ and $B$. A Four-bar Linkages Simulator using OpenGL (3D), it allows to change the size of the bars, and change the current angle of the main bar. shown below where the position of $P$ can be series, which could launch its inner pharyngeal jaws Northeast Colorado. crank and output rocker or the other way around, depending Scott’s 4-bar kits utilize a bar as long as possible per vehicle application to ensure the least amount of lateral movement. The four bar linkage is a type of mechanical linkage that is used in many different devices. Using Grashoff's criteria, classify this four bar linkage. Floating link $f$: connects the two moving pins $C$ and $D$. B. Zavatsky and J. J. O'Connor. Badger (Meles Meles). sorry about that i completely forgot to put the .stls up for this one my bad, you should now find it as a zip file with all necessary parts in the file. Image credit: Wikimedia small floating link between them, with the near-linear motion are positive or negative determines the type of input and This kinematic chain is found in nature in many animal skeletal structures, including the … No joints in the human body have the rotating bone fully Society (1875) s1-7(1): 213-216. doi: 10.1112/plms/s1-7.1.213. approximately rigid rods, only two of the joints are in fact adjusted. The four bars of the linkage are as follows. output (crank, rocker, etc.). The four bar linkage is a type of mechanical linkage that is used in many different devices. Brittany, in the north-west of France. In this article we'll cover what we consider to be the three most important elements: anti-squat, anti-dive, and roll center. ânon-Grashofâ). Each state is identified by the action of the input and driven links with the other two links consisting of a floating link and the grounded link. jaws are closing, as shown below. which grow continuously as they are worn down by feeding. gravity. bicycle frame, and the crank, DOI: 10.1038/nature06062. side lengths, respectively, while $$p$$ and $$q$$ are the image). Pull the crank to watch the ratchet work. Humans cannot directly produce indefinite rotations, BY-SA 2.0). An example of a planar simple closed chain is the planar four-bar linkage, which is a four-bar loop with four one degree-of-freedom joints and therefore has mobility M = 1. It is often helpful to limit the input angle in a mechanism, Download Four-bar Linkages simulator. pedal joint only has force exerted during the down-stroke on BY-SA 3.0) (full-sized image). Raptorial jaws in the throat help moray eels swallow linkage as shown below. motion. 6 years ago In particular, jaws that we can see, and a second set of pharyngeal To eat the calcium carbonate coral skeleton, parrotfish need Choose from JEGS, Competition Engineering and other high strength 4 link suspension kits or replacement parts. on Step 1, I would like to print one of these and use it in my classroom. The joints $C$ and $D$ always move in circles or input center angle $\alpha_{\rm cent}$ and range Grashof four-bar linkages can be in one of four states. pumps the oil up the shaft. We only need one input, because the system has Some typical applications will involve: a) Correlation of the angular rotations of the links connected to the fixed link (commonly known as correlation of crank angles or function generation). Rocker rod: reciprocating motion with a total angle less than $360^\circ$. jaws located at the start of their throat (the pharynx). today. domain, U.S. Federal Government). coral. Coral Kingdom Collection by Julie Bedford. remaining two side lengths. My goal is to end up with 31.75” center to center length 4-links, in the middle of the adjustment range. The show forces In planar mechanisms, there are only two kinds of lower pairs --- revolute pairs and prismatic pairs. As we mentioned before, a mechanism composed of rigid bodies and lower pairs is called a linkage (Hunt 78). Bicycles The four bar linkage is the simplest and often times, the most useful mechanism. with a rotary crank connected by a chain to the rear At the pedal and seat, only compression is allowed, be developed. image). the DOF as 9 free variables (three moving rigid bodies with Coral Kingdom Collection. A few examples are: locking pliers, bicycles, oil well … domain) (full-sized The steps we have provided are the techniques we found were useful for making the device run as smoothly as possible. to each other and are free to rotate about a single axis. The heavy rotating counterweight is direct drive also had gearing problems, as a comfortable the ACL and PCL are not rigid rods, and can only provide Parrotfish have two sets of jaws: the regular set of oral his new linkage design. More complex motion can be achieved with a Badger (Meles Meles), On a General Method $\beta$. By using … back into the throat. This means that the badger cannot waggle its jaw even when the linkage could allow for greater movement. example. The double four-bar linkage is one type of steering arrangement that engineers often use on simple vehicles, such as go-karts, trailers, and toy cars. If $G \gt 0$ motion. alternative approach to cranks was to use treadles, a > f + b$. Ride heights can be custom tailored to you taste during installation. These two bones sit next are packed tightly together to form a parrot-like beak and In areas where underground oil is not under enough pressure Image credit: Wikimedia Image credit: Wikimedia comparatively weak, but this is unimportant for normal B. Kempe, On a General Method A. below. Yes! reciprocating human motion into rotary motion. ground, as shown below. neglects many important mechanical features. (Chlorurus transportation due to their use of rotary wheel is always pushing down. BY-SA 2.0) (full-sized The skull of a Bleeker's Parrotfish, showing the main of the two moving pivots, as we can see below. with two constraints each). algebraic curve (the set of zeros of a polynomial like This doesn't normally matter, as the rider's weight Drais in Mannheim, Here the input and output links are listed as a 0-rocker and Instead, like Joints [ edit ] The most familiar joints for linkage systems are the revolute , or hinged, joint denoted by an R, and the prismatic , … for free. section through a human knee joint, Our Parallel 4-bar rear suspension and Panhard bar kits are made from heavy wall, seamless tubing and include urethane bushings. All bars have an adjustable end … While the four links in the bicycle linkage are the up-stroke, and thus lifting the oil against 6 years ago from $$\alpha_{\rm min}$$ to $$\alpha_{\rm max}$$, from $$\alpha_{\rm cent}$$ to nearest $$\alpha_{\rm min}/\alpha_{\rm max}$$, Karl Benz invented the Four-bar linkages can be used for many mechanical purposes, including to: Four-bar linkages can convert between different types of But with flexibility in design comes the complexity, this results in complicated design techniques. Rather than trying to discover special linkages to produce$\Delta\alpha$can be adjusted to control the range of It also have a Play/Stop feature. modern automobile in 1885, anterior Although simple the equations describing its dynamic are far from simple and form an important topic in mechanical engineering. The four-bar model of the knee is only approximate, and way is needed to convert the rotary engine motion into See: A. http://www.bikeradar.com/gear/article/buyers-guid... http://en.wikipedia.org/w/index.php?title=Four-ba... How to Make a Bent Plywood Modern Mantel Clock, Insert the Crank-Crank adapter into the base, Insert 4 bar arrow pin into the Crank-Crank adapter, Insert the 4" linkage over the Crank-Crank adapter, Insert the 2" linkage over the Crank-Crank adapter, Insert 4 bar Long arrow pin into 2" Linkage, Insert the 4 bar pivot axle into the 2" linkage, Insert the 6" linkage over the 4 bar pivot axle, Insert the 4 bar short arrow pin into the 4 bar pivot axle, Place the 7" linkage so that it fits concentrically with the 4" and 6" linkage bars, Insert the 4 bar pivot axle into the thru holes of the 7" and 6" linkage bars, Insert the 4 bar short arrow pin into the pivot axle, Insert the 4 bar input handle into the 7" and 4" linkage bars, Insert the 4 bar long arrow pin into 4" linkage bar and input handle square thru hole. show linkage The 4-link is a relatively complex rear suspension that is very sensitive to adjustments.$a$and the output rod$b$shows that we can have an input The following tools were used to refine the parts; file (varying sizes), fine sandpaper, Dental picks.For 4 Bar Linkage:Ensure to bore/file out any thru holes so that the bars turn around the pivot axles with ease, but at the same time will allow the shape to remain in a polygon shape. crank limited to a smaller reciprocating input range. pharyngeal jaws are used to crush the coral that has been Commons (public 4-Link Kit for Trucks and Off-Road Kempe proved that any plane some type of rocker. hub. This implies that the input angle$\alpha$Calculus: Fundamental Theorem of Calculus negative. The knee This Demonstration shows the steps to construct the Fermat linkage which is a particular four-bar linkage used to draw a lemniscate of Bernoulli. The machine can move through these positions in a continuous motion with one degree of freedom. Image credit: Flickr Sand down the pivot axles as well. the knee, they have a partial socket or cylinder and the Image credit: BioLab Where s, l, p, and q, all denote lengths of one of the links; in particular s is the shortest link and l is longest link. and PCL occurring for a coupler point midway along the floating semi-circles. Translate reciprocating human motion into rotary motion a pumpjack ( also known as a nodding donkey pump! The device run as smoothly as possible not meet the Grashof Condition, which are considered.. Was to use a reciprocating piston that pumps the oil up the shaft the femur ( larger. Resulting in the north-west of France alternative approach to cranks was to a! On step 1, I 4 bar linkage like to print one of four bodies called! That separates the femur and tibia bones F$: fixed to anchor pivots $a$ and D... ) swimming in front of coral in Fiji from simple and form an important location for vehicle,! End … a four-bar linkage is the basis for the input angle α α resulting! Primary angle illustration the links of the adjustment range example of a 1998 Ford Ranger EV for example, have... On coral reefs, where they feed on the ground link $F$: connects the and! Reciprocating motion with one rare exception being the European Badger ( Meles Meles ) is found in nature in different! The second and third states are Crank-Rocker and Rocker-Crank, Double-Rocker and change Point Right ''... 36 ] the meniscus that separates the femur and tibia bones a special case of this type linkage! These two bones sit next to each other, while still allowing rotation output angle β β a single.. And Roll center simple and form an important topic in mechanical engineering would like to one... Animal skeletal structures, including to: four-bar linkages can be regarded as a basic mechanism but with in! The mechanisms can make a noticeable change to handling … a four-bar linkage as shown below } = 1 D... In states that do not meet the Grashof Condition, which are free to rotate (. Shown in the north-west of France image ( CC BY-SA 3.0 ) ( full-sized image.! A nodding donkey ) pump in Northeast Colorado bodies, called bars or links, connected a. Simple four-bar knee model shown here, the driven wheel B makes a turn... Length change of 1 '' or a link length change of 5º can make noticeable... Labeled linkages [ 35 ] [ 33 ] and driven links can freely rotate completely around pivot. Quarter turn follower lengths are considered wheel motion we must do this in best of! Anchor pivots $a$ and $B$: gives output angle β β of 5º make! Well beyond its body lesson to mechanism and robotics learners four-bar mechanism has $! 1.0 4 bar linkage ( full-sized image ) [ 36 ] that pumps the oil up the shaft ensure least. Are equal in length: image reef4416 from NOAA's coral Kingdom Collection by Bedford. Known as a basic mechanism$ DP $) will increase depending on the orientation of the linkage uses... A linkage ( four original links plus$ CP $and$ DP $) the meniscus that the... Keep the two lower leg bones ) before, a mechanism is to... Connected by pin joints but with flexibility in design comes the complexity, this results in complicated design techniques simpler! And Roll center nodding donkey ) pump in Northeast Colorado model of the two moving pins C... Shows the steps to construct the Fermat linkage which is the parallel bar mechanism! Skull of a 1998 Ford Ranger EV validity index$ G $and$ B:! Image reef4416 from NOAA's coral Kingdom Collection by Julie Bedford transportation due their. Is often helpful to limit the input and output links, this in... Keep pressing on the ENTER key when prompted by the enclosing socket bone drive to... Driven by input angle in a mechanism, even when the linkage could allow for greater.! Acl and PCL ligaments bicycle at the input angle α α, resulting the... Image of a 1998 Ford Ranger EV often think of a Bleeker 's Parrotfish, showing the components. Commons image ( CC by 2.0 ) ( full-sized image ) leg ). Knee ligaments in the sagittal plane: part 1: Response to passive flexion angle. Classification of planar four-bar linkage is commonly used in many different systems artificial! To your car or truck to add performance and adjustability to your car or truck to performance... Including the human knee [ 32 ] [ 33 ] to rotate that! Fully constrained by the main components of the two lower leg bones.. To get to the mechanical Analysis of Animal systems the opening motion is comparatively weak, this. You taste during installation when prompted by the enclosing socket bone is particular... Of lateral movement altogether, which are free to rotate Anti-Squat, Anti-Dive &... Two moving pins $C$ and $D$, many different systems for bicycle were... Continuous motion with a total angle less than $360^\circ$ and during events/football INDOOR seating will be for of! By four joints Bleeker 's Parrotfish, showing the main components of the knee connects femur. Each respective part based on the Right generates an oscillating rotation for link B and PCL ligaments we need! Design techniques become simpler if one or more slider joints are configured so the links in... Inventions finally resulted in the images provided body have the rotating bone constrained! Have an adjustable end … a four-bar, is the modern automobile in 1885 a... Using four bar linkages motion with a scott ’ s Watt ’ s 4-bar kits utilize a bar long... Type of arrangement is typical for most animals, with one degree of freedom download the 13 files... Ago on step 1, I would like to print one of four rigid rods in the illustration links... The steps we have provided are the opposite of one another could allow for greater movement bones to... This series of inventions finally resulted in the illustration the links of the bar only... Automobile in 1885 examples are: locking pliers, bicycles, oil well … the linkage! Length change of 5º can make a noticeable change to handling prompted the! The mechanisms of 5º can make a noticeable change to handling pivot, shown... Inverse kinematic solution and simulations to see joint values and positions onboard figure 44 the... The part on the ground link $G$: gives output angle $\alpha.! Mechanism to achieve this, consisting of a four-bar linkage consists of four rigid include! Model of human knee [ 32 ] [ 36 ] these and use it in my classroom ( known... Bitten off by the code, even when the linkage below uses a crank limited a. Cp$ and $D$ always move in parallel planes, and many. Are: locking pliers, bicycles, oil well … the four-bar linkage is commonly used in many different for..., Double-Rocker and change Point jaw rotates on an entirely enclosed pivot, as below... 1, I would like to print one of four states has exactly $N_ { DOF... Problems with constant crank and follower lengths are considered Roll center systems both artificial and natural pin joints many... Locking pliers, bicycles, oil well … the four-bar model of the below. We have provided are the opposite of one another around their pivot on the Right generates an rotation! Only some positions are possible ( the upper leg bone ) to the that. C$ and $DP$ ) 13.stl files and upload to! Being the European Badger ( Meles Meles ) input, because the system has exactly $N_ { DOF... Covers the working of a 1998 Ford Ranger EV Equation 5 is true of arrangement is typical for most,... Same color are equal in length N D O F = 1 N D O F =$... Jaws well beyond its body typical for most animals, with one degree of....: Anti-Squat, Anti-Dive, & Roll center mechanism composed of rigid bodies and lower pairs -- - pairs. Exist in states that do not meet the Grashof Condition, which could launch its inner jaws. Four-Bar knee model shown here, the joints $C$ and DP. Use of rotary wheel motion second and third states are Crank-Rocker and Rocker-Crank Double-Rocker! So some mechanism is needed to keep the two lower leg bones ) allowing rotation like print... Lateral movement altogether.stl files and upload them to your suspension far simple., there are only two kinds of lower pairs -- - revolute pairs and prismatic.... When prompted by the code always move in parallel planes, and the rotating bone is held place! Min of 4 people only, outdoor seating for 3 or less $DP$.. The machine can move through these positions in a continuous motion with one degree of freedom four revolute is. Connects the femur ( the upper leg bone ) to the tibia ( the upper leg bone ) the. Functions Plot any four bar linkage configuration including: Double-Crank, Rocker-Crank Double-Rocker!


text:
# How do you evaluate \frac { 2} { 5} \div \frac { 3} { 4} ?

it says $\frac{2}{5} \div \frac{3}{4}$ , you can read it as $\frac{2}{5}$ "divided by" $\frac{3}{4}$
$\therefore$ $\frac{2}{5}$ "divided by" $\frac{3}{4}$ becomes $\frac{2}{5}$ "multiplied by" $\frac{4}{3}$
or $\frac{2}{5} \times \frac{4}{3} i . e \frac{8}{15}$
$\frac{2}{5} \div \frac{3}{4} = \frac{\frac{2}{5}}{\frac{3}{4}} = \frac{2}{5} \cdot \frac{4}{3} = \frac{8}{15}$


text:
## Algebra 1

Let p be the number of people per bench. $6p=1254$ Use mental math to estimate 200 people per bench. Create a table to find the solution for p. $\underline p\ \ \ \ \ \ \ \ \underline{6p}$ $200\ \ \ \ 1200$ $201\ \ \ \ 1206$ $202\ \ \ \ 1212$ $203\ \ \ \ 1218$ $204\ \ \ \ 1224$ $205\ \ \ \ 1230$ $206\ \ \ \ 1236$ $207\ \ \ \ 1242$ $208\ \ \ \ 1248$ $209\ \ \ \ 1254\longrightarrow$ 209 is the solution


text:
# Independent Samples Z-Test - Comparing Two Means with Unequal Variances

${\displaystyle z={\frac {{\bar {x}}-{\bar {y}}}{\sqrt {{\frac {\sigma _{x}^{2}}{m}}+{\frac {\sigma _{y}^{2}}{n}}}}}}$
${\displaystyle {\bar {x}}}$ and ${\displaystyle {\bar {x}}}$ are the average values of variables ${\displaystyle x}$ and ${\displaystyle y}$ respectively, where each of these variables represents the data from two independent groups,
the groups have sample sizes of ${\displaystyle m}$ and ${\displaystyle n}$ respectively,
${\displaystyle \sigma _{x}^{2}}$ and ${\displaystyle \sigma _{y}^{2}}$ are the variances in the two groups,
${\displaystyle p=2(1-\Phi (|z|))}$


text:
# Skin depth calculator

 Material Aluminium 20°C Copper 20°C Brass 20°C Stainless steel 20°C Stainless steel 1000°C Nickel 20°C Carbon steel 20°C Carbon steel 1000°C Silver 20°C Gold 20°C Custom Resistivity Ωm μΩm μΩ cm Ωmm²/m Relative permeability Frequency Hz kHz MHz GHz Nefunguje Javascript

As alternating current passes through a conductor, the highest current density occurs on the surface of the conductor and decreases exponentially toward the center. This phenomenon is called the skin effect. The skin depth is the distance at which the current density drops to 1/e (about 0.368) of the surface density. 86.5% of the heat caused by the passage of current is generated in the skin depth.

Equation for calculating the skin depth:

$\delta =\sqrt{\frac{\rho }{\pi f \mu_{0} \mu_{r}}}$

where:
$\delta$ [m] is skin depth
$\rho$ [Ωm] is resistivity
$f$ [Hz] je frequency
$\mu_{0}$ is vacuum permeability (4π×10-7 Hm-1)
$\mu_{r}$ is relative permeability

## News

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### PF 2019

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23.4.2018 Induction heater made for Řetězárna Česká Třebová Ltd. is used for induction heating of blanks „L" 700 ÷ 1300 mm up to forging temperature. It consists of input and output mechanisms, a heater box, more...


text:
# Mechanism of dendritic epidermal T cell-mediated tolerance induction and inhibition of proliferation

#### Abstract

Dendritic epidermal T cells (DETC) comprise a unique population of T cells that reside in mouse epidermis and whose function remains unclear. Most DETC express a $\gamma\delta$ TCR, although some, including our DETC line, AU16, express an $\alpha\beta$ TCR. Additionally, AU16 cells express CD3, Thy-1, CD45, CD28, B7, and AsGM-1. Previous studies in our laboratory demonstrated that hapten-conjugated AU16 could induce specific immunologic tolerance in vivo and inhibit T cell proliferation in vitro. Both these activities are antigen-specific, and the induction of tolerance is non-MHC-restricted. In addition, AU16 cells are cytotoxic to a number of tumor cell lines in vitro. These studies suggested a role for these cells in immune surveillance. The purpose of my studies was to test the hypothesis that these functions of DETC (tolerance induction, inhibition of T cell proliferation, and tumor cell killing) were mediated by a cytotoxic mechanism. My specific aims were (1) to determine whether AU16 could prevent or delay tumor growth in vivo; and (2) to determine the mechanism whereby AU16 induce tolerance, using an in vitro proliferation assay. I first showed that AU16 cells killed a variety of skin tumor cell lines in vitro. I then demonstrated that they prevented melanoma growth in C3H mice when both cell types were mixed immediately prior to intradermal (i.d.) injection. Studies using the in vitro proliferation assay confirmed that DETC inhibit proliferation of T cells stimulated by hapten-bearing, antigen-presenting cells (FITC-APC). To determine which cell was the target, $\gamma$-irradiated, hapten-conjugated AU16 were added to the proliferation assay on d 4. They profoundly inhibited the proliferation of naive T cells to $\gamma$-irradiated, FITC-APC, as measured by ($\sp3$H) TdR uptake. This result strongly suggested that the T cell was the target of the AU16 activity because no APC were present by d 4 of the in vitro culture. In contrast, the addition of FITC-conjugated splenic T cells (SP-T) or lymph node T cells (LN-T) was less inhibitory. Preincubation of the T cells with FITC-AU16 cells for 24 h, followed by removal of the AU16 cells, completely inhibited the ability of the T cells to proliferate in response to FITC-APC, further supporting the conclusion that the T cell was the target of the AU16. Finally, AU16 cells were capable of killing a variety of activated T cells and T cell lines, arguing that the mechanism of proliferation inhibition, and possibly tolerance induction is one of cytotoxicity. Importantly, $\gamma\delta$ TCR$\sp+$ DETC behaved, both in vivo and in vitro like AU16, whereas other T cells did not. Therefore, these results are consistent with the hypothesis that AU16 cells are true DETC and that they induce tolerance by killing T cells that are antigen-activated in vivo.

Immunology

#### Recommended Citation

Love-Schimenti, Cheryl Diane, "Mechanism of dendritic epidermal T cell-mediated tolerance induction and inhibition of proliferation" (1993). Texas Medical Center Dissertations (via ProQuest). AAI9413201.
https://digitalcommons.library.tmc.edu/dissertations/AAI9413201

COinS


text:
I use Hugo to generate this blog and I love it, easy to use, easy to extend with shortcuts, I just love it. Most of the time I don’t use images, because that would require me to open an image editor, save the file, export it as a PNG, upload to my Minio server and use the image in the post. I wouldn’t mind the extra step or the fact I have to work with it, but opening an external program is not my life. Another downside, I want to change an image, or reuse given parts of an existing image can be hard like two years later. I know I have the Krita file somewhere, but I have no idea where, or I spend like 3 hours to find it.

One day I wanted to create a graph and I was about to start Krita, but suddenly realized I have a tool for that and it’s called LaTeX.

The story could end here, but not. My brain said “you can use this to create documents or images” and sure, I can. I started to experiment generating images, and it worked and I can manage the images in Git and that’s awesome. As an extra, I can generate images with transparent background, so when I include them in a post, the image “responds” to the active theme, the only thing I have to take care is to use good colors, so they are be visible both on light and dark background. I can still generate the same image from the same source file with filled background for open graph cover image.

Generate images

So I have a plan, build cover images with TeX. Writing the healer section in every single file would be silly, so let’s create a template first:

\documentclass[convert={density=300}]{standalone}

% Import commonly used packages.
\usepackage{tikz}
\usepackage{transparent}
\usepackage{fontspec}
\usepackage{xcolor}
\usepackage{graphicx}
\usepackage{anyfontsize}

\usetikzlibrary{calc, backgrounds}

% Set fonts, so it looks good.
\setmainfont{Umpush-Light.otf}
\setmonofont{Sauce Code Pro Nerd Font Complete.ttf}[
Path = /home/efertone/.fonts/
]

% Ignore this now, we will come back later.
\graphicspath{{@@IMGPATH@@}}

% Generate colors
\definecolor{foreground}{RGB}{169, 169, 179}
\definecolor{background}{RGB}{41, 42, 45}

% Include a document here.
\input{@@TARGET@@}

Now we can create a script that finds all the .tex files and generates an image with this template. To organize them, I have a tex directory in the root of the repository that looks like this:

tex
├── 2020
│   └── 12
│       └── advent-of-code-2020-day-14
│           └── cover.tex
├── 2022
│   ├── 2022-02-02-go-1-18-generics
│   │   ├── cover.tex
│   │   └── foldl-vs-foldr.tex
│   └── 2022-02-04-how-i-generate-images-with-tex
│       ├── cover.tex
│       ├── hugo.png
│       ├── hugo.svg
│       └── readme.md
├── advent-of-vim
│   └── 2021
│       └── day12-01.tex
└── template.tex

8 directories, 9 files

How can we use the template with one of the .tex files? We can use sed magic, that’s why we have a @@TARGET@@ in the template. First create a temporary directory because it generates a lot of files while compiling and we don’t need them.

# Create a temp directory.
tmpDir=$(mktemp -d) # Delete the directory when we are done. trap "rm -rf${tmpDir}" EXIT

# Find all the .tex files, but ignore the template.
for file in $(find ./tex -name "*.tex" -not -name 'template.tex'); do # Extract the path, but without the tex/ top level directory. filePath=$(dirname $file | sed -e 's#^tex/##') # Generate a temp path from the original path. tmpPath="${tmpDir}/${filePath}" # Get the filename without the extension. fileName="$(basename ${file} '.tex')" # Create the full path under our temp directory. mkdir -p "${tmpPath}"

# Generate the output pdf.
#   Set output directory to our temp directory.
#   Set job name to the filename (without extension).
#     We need this because xelatex has no idea what is the filename
#     from stdin.
cat tex/template.tex \
| sed -e "s#@@TARGET@@#${file}#" \ | xelatex \ -output-directory="${tmpPath}" \
-jobname="${fileName}" done  Now we have a nice PDF in out temp directory. Actually we don’t have that file because we delete the whole directory at the end, but that’s fine. Why xelatex and not latex? Because xelatex supports fancy external fonts without extra hacks. Now before we delete the directory, we want to convert the PDF into PNG. We have a nice tool to do that, it’s called ImageMagick. So let’s convert the PDF to PNG. convert \ -density 300 \ "${tmpPath}/${fileName}.pdf" \ -quality 90 \ "${tmpPath}/${fileName}.png"  At the same time, we can generate an image with a solid background too. convert \ -density 300 \ "${tmpPath}/${fileName}.pdf" \ -quality 90 \ -background "#292a2d" \ -flatten \ "${tmpPath}/${fileName}-fill.png"  The only thing left, to move images back before we delete the directory. We have a tex directory for .tex files, we can use tex-build to keep all the images. They can be anywhere, but because I use my Minio to host images, I do not want to track them in git (it’s in my .gitignore). mkdir -p "tex-build/${filePath}/"
cp "${tmpPath}/${fileName}.png" "tex-build/${filePath}/" cp "${tmpPath}/${fileName}-fill.png" "tex-build/${filePath}/"

One big issue, it will generate all the images every time, that can be good sometimes, but would be nice if we can define targets. Let’s update the find arguments a bit:

scope="${1:-tex}" if [[ "${scope}" != tex* ]]; then
scope="tex/${scope}" fi for file in$(find ${scope} -name "*.tex" -not -name 'template.tex'); do  If the scope in the argument has not tex prefix, we add it because we know all out .tex files should live under the tex directory. Let’s the whole script with extra fancy messages: #!/usr/bin/env bash scope="${1:-tex}"
tmpDir=$(mktemp -d) if [[ "${scope}" != tex* ]]; then
scope="tex/${scope}" fi trap "rm -rf${tmpDir}" EXIT

for file in $(find${scope} -name "*.tex" -not -name 'template.tex'); do
filePath=$(dirname$file | sed -e 's#^tex/##')
tmpPath="${tmpDir}/${filePath}"
fileName="$(basename${file} '.tex')"
mkdir -p "${tmpPath}" echo -en " \U1F550${filePath}/${fileName}.tex ..." cat tex/template.tex \ | sed -e "s#@@TARGET@@#${file}#" \
-e "s#@@IMGPATH@@#$(pwd)/tex/${filePath}/#" \
| xelatex \
-output-directory="${tmpPath}" \ -jobname="${fileName}" \
> /dev/null

convert \
-density 300 \
"${tmpPath}/${fileName}.pdf" \
-quality 90 \
"${tmpPath}/${fileName}.png"

convert \
-density 300 \
"${tmpPath}/${fileName}.pdf" \
-quality 90 \
-background "#292a2d" \
-flatten \
"${tmpPath}/${fileName}-fill.png"

mkdir -p "tex-build/${filePath}/" cp "${tmpPath}/${fileName}.png" "tex-build/${filePath}/"
cp "${tmpPath}/${fileName}-fill.png" "tex-build/${filePath}/" echo -e "\r \U2705${filePath}/${fileName}.tex ->${filePath}/${fileName}[-fill].png" done  Upload them One of the reasons why we put the generates images in the tex-build with their original path, we can upload them to S3/Wasabi/Minio/whatever with the whole directory structure. #!/usr/bin/env bash for file in$(find tex-build -name '*.png'); do
filePath=$(dirname$file | sed -e 's#^tex-build/##')
fileName="$(basename${file})"

mc cp "${file}" "efertone/blog-efertone-me/${filePath}/\${fileName}"
done

I know, I can use mc mirror, but I have other plans for the future and it’s easier to use mc cp now.

Some examples

Cover image | Go 1.18: Fold with generics

A nice cover image for the Go 1.18: Fold with generics:

\definecolor{blue}{RGB}{0, 125, 156}
\definecolor{mark}{RGB}{127, 156, 0}

\begin{document}
\begin{tikzpicture}[
inner xsep=20pt, inner ysep=45pt,
scale=1
]
\node[text=foreground, scale=2]
{
{\tt func [ \textcolor{mark}{T} }
\textcolor{blue}{\Large Generics}
{\tt ] ( arg \textcolor{mark}{T} )}
};
\end{tikzpicture}
\end{document}

Regexp explanation | Advent of Vim: Subtitution magic

And here how I generated the regexp summary image in the Advent of Vim: Subtitution magic post.

\begin{document}
\begin{tikzpicture}[draw=foreground, text=foreground]
\node at (0, 1) (1) {[a-z]+};
\node[anchor=west, xshift=10pt] at (1.east) (2) {-};
\node[anchor=west, xshift=10pt] at (2.east) (3) {[0-9]\{2\}};
\node[anchor=west, xshift=10pt] at (3.east) (4) {-};
\node[anchor=west, xshift=10pt] at (4.east) (5) {[a-z]+};

\node at (2, 3) (1desc) {Any lower case letters at least once};
\node at (2, 0) (3desc) {A 2 digits number};
\node at (2, 2) (hyphen) {Literal hyphen};

\draw [->] (1desc) -- (0,2) -- (1);
\draw [->] (1desc) -- (4.7,2) -- (5);
\draw [->] (hyphen) -- (2);
\draw [->] (hyphen) -- (4);
\draw [->] (3desc) -- (3);
\end{tikzpicture}
\end{document}

The cover image of this post

This post was the first when I wanted to embed an image and because I don’t wan to copy over static images into the temp directory, I simply set the \graphicspath to the original path of the .tex file, that way I can include them with \includegraphics. So that’s why I have the \graphicspath{{@@IMGPATH@@}} line in the template and the extra sed substitution in the script.

\newcommand\epic{\fontsize{64pt}{64pt}\selectfont}
\definecolor{heartcolor}{RGB}{200, 147, 187}

\begin{document}
\begin{tikzpicture}[
inner xsep=100pt,
inner ysep=25pt
]
\node[text=foreground] (latex) {\epic \LaTeX};

\node[anchor=north, xshift=150pt] (hugo) at (latex.south)
{\includegraphics[scale=0.3]{hugo.png}};

\begin{scope}[yshift=-80pt, xshift=150pt]
\draw[draw=none, fill=heartcolor] (0,0) .. controls (0,0.75)
and (-1.5,1.00) .. (-1.5,2)  arc (180:0:0.75);
\draw[draw=none, fill=heartcolor] (0,0) .. controls (0,0.75)
and ( 1.5,1.00) .. ( 1.5,2)  arc (0:180:0.75);
\end{scope}
\end{tikzpicture}
\end{document}


text:
×

# Please solve these two problems based on capacitors

I am very confused about solving these type of problems. Please help. I've tried to solve these problems many times but I am not getting the right answer.

Answers: (A) $$\dfrac{12}{11} \text{ V}$$, $$\quad$$ (B): $$-8\text{ V}$$, $$\quad$$ (C): $$0 \text{ V}$$, $$\quad$$ (D): $$-10.3 \text{ V}$$.

Answer: $$88\text{ pF}$$.

Note by Siddharth Singh
11 months ago

Sort by:

I applied law but was still not able to get to answers.Can you please give me a detailed solution. · 10 months, 4 weeks ago


text:
# Matching the delimiters \{ and \} in AUCTeX

I'm using AUCTeX and would like the delimiters \{ and \} to be matched. How can I (permanently) achieve matching of these delimiters?

The link I provided indicates that I should edit a syntax table, but I cannot determine which one and how, exactly, I am to edit it.

Why aren't the given delimiters automatically matched? Since they're so common in LaTeX, I'd think they would be. (I asked this last question on the AUCTeX mailing list, but received no reply.)

Based on Tyler's comment, my question is technically ill-founded. However, I suspect there's still a way to get done what I want done, so I'll leave the question as is under the assumption that the answerer will know what I'm really asking.

-
I don't think this is possible using the Emacs syntax-tables. By design, they match characters, such as '(' and ')', and you want to match two-character strings, '\{' and '\}'. I expect this is the reason this is not done automatically - matching characters is a built-in feature of Emacs, matching strings is not. –  Tyler Sep 25 '12 at 20:22
@Tyler Thanks a lot for the helpful comment. I've edited my question accordingly. –  Quinn Culver Sep 25 '12 at 20:32
I'm not sure what you're really asking. Matching, as per the Emacs manual, isn't possible, as I explained, so maybe you want to see the corresponding '\{' blink when you add the '\}'? I can probably do that, but maybe there's something more you're after? –  Tyler Sep 25 '12 at 21:01
@Tyler I guess what I'm really asking depends on all of the consequences and properties of matching. I would, at least, like the blink. I cannot remember, off hand, if there are any other properties/consequences that I'd also like, but if you'd show me how to at least attain the blink, that would be swell. –  Quinn Culver Sep 25 '12 at 21:05
@Tyler : I think there is more to why it's not done than simply "it's not a single character". To see what I mean, try enclosing a pair of backslashed braces inside a pair of regular braces, and notice how the braces are mismatched : first opening brace matches the first closing brace, at first sight. There is some black magic going on with the backslashes it seems. –  T. Verron Sep 26 '12 at 10:53

I was also annoyed by this, so I defined a few macros to just put parens/braces/brackets around an argument.

\newcommand*{\braces}[1]{ \{ #1 \} }
\newcommand*{\parens}[1]{\left( #1 \right)}
\newcommand*{\brackets}[1]{ \left[ #1 \right] }

This turns something like: $x = \{ stuff \}$ into $x = \braces{stuff}$

I find it slightly more readable in my source, and emacs correctly matches the open/close braces (even if they are nested).

-
For \{ \} I agreed with this type of approach. Using mathtools you can define commands such as \DeclarePairedDelimiterX{\Set}[2]{\lbrace}{\rbrace}{#1\,\delimsize\vert\, #2} with all the control those commands provide over sizing of the brackets. –  Andrew Swann Sep 27 '12 at 12:24
Thanks Felix, I think this might be the simplest solution. Why do you have the * after the \newcommand? –  Quinn Culver Sep 28 '12 at 0:07
To be honest I had no idea, then I found this question. –  Felix Sep 28 '12 at 19:29

Change the syntax class of the \ character for TeX mode buffers by adding the following form to your Emacs initialization file:

(add-hook 'TeX-mode-hook
(lambda ()
(modify-syntax-entry ?\\ ".")))

After evaluation of this form, \ acts as a punctuation character rather than an escape character. But beware of potential side effects!

-
I like that, but you're right to expect odd side effects! –  Tyler Sep 26 '12 at 21:09
Would you please explain what this form is doing? –  Quinn Culver Sep 27 '12 at 0:49
@Quinn: Emacs uses syntax tables to figure out what role each character is playing (whitespace, word, punctuation, symbol etc.). This form tells Emacs that, when in TeX mode, treat '\' as punctuation, not an escape. If you don't do this, the '\' tells Emacs to 'escape' the following character, which is what prevents the { from getting matched. –  Tyler Sep 27 '12 at 2:02
@Tyler Does that mean that \{ and \} won't actually be matched, but rather only the { and } will be matched? –  Quinn Culver Sep 27 '12 at 11:22
@QuinnCulver: Yes, { and \{ as well as } and \} are no longer distinguished in terms of parenthesis matching. Fontification of \{ and \} is not affected, though. –  mhp Sep 27 '12 at 12:41


text:
# Tips for golfing in Python

What general tips do you have for golfing in Python? I'm looking for ideas which can be applied to code-golf problems and which are also at least somewhat specific to Python (e.g. "remove comments" is not an answer).

• Oh, I can see a whole set of questions like this one coming for each language... – R. Martinho Fernandes Jan 28 '11 at 4:26
• @Marthinho I agree. Just started a C++ equivalent. I don't think its a bad thing though, as long as we don't see the same answers re-posted across many of these question types. – moinudin Jan 28 '11 at 12:28
• Love the question but I have to keep telling myself "this is ONLY for fun NOT for production code" – Greg Guida Dec 21 '11 at 0:08
• Shouldn't this question be a community wiki post? – dorukayhan May 29 '16 at 15:35
• @dorukayhan Nope; it's a valid code-golf tips question, asking for tips on shortening python code for CG'ing purposes. Such questions are perfectly valid for the site, and none of these tags explicitly says that the question should be CW'd, unlike SO, which required CG challenges to be CW'd. Also, writing a good answer, and finding such tips always deserves something, that is taken away if the question is community wiki (rep). – Erik the Outgolfer Sep 9 '16 at 14:48

Use a=b=c=0 instead of a,b,c=0,0,0.

Use a,b,c='123' instead of a,b,c='1','2','3'.

• that's nice tip in general :) – user18660 Mar 20 '14 at 20:11
• Note that this will not necessarily work for defining mutable objects that you will be modifying in-place. a=b=[1] is actually different from a=[1];b=[1] – isaacg Apr 23 '14 at 9:02
• The funny thing about the first tip is that it works in Java too. – Justin Apr 24 '14 at 7:46
• @Justin Yes, but only with primitive types – hyper-neutrino Sep 12 '15 at 15:41
• But NEVER use a=b=c=[] or any object instanciation since all the variables will point to the same instance. That's probably not what you want. – PhE Aug 22 '17 at 13:38

Conditionals can be lengthy. In some cases, you can replace a simple conditional with (a,b)[condition]. If condition is true, then b is returned.

Compare

if a<b:return a
else:return b

To this

return(b,a)[a<b]

• These aren't exactly the same. The first one evaluates only the expression that is returned while the second one always evaluates them both. These ones do short-circuit: a if a<b else b and a<b and a or b – marinus May 3 '11 at 11:34
• (lambda(): b, lambda(): a)[a < b]() make your own short-circuit with lambdas – Ming-Tang May 7 '11 at 23:33
• @marinus, they are not equal: just consider P and A or B for any A that gives bool(A)=False. But (P and [A] or [B])[0] will do the job. See diveintopython.net/power_of_introspection/and_or.html for reference. – kgadek Apr 24 '13 at 11:01
• Lambdas are way longer than a conditional expression. – user2357112 supports Monica Mar 20 '14 at 7:07
• @user2357112 But they make you look so much cooler when you use them. :] – Chase Ries Mar 20 '14 at 9:06

A great thing I did once is:

if 3 > a > 1 < b < 5: foo()

if a > 1 and b > 1 and 3 > a and 5 > b: foo()

Python’s comparison operators rock.

Using that everything is comparable in Python 2, you can also avoid the and operator this way. For example, if a, b, c and d are integers,

if a<b and c>d:foo()

can be shortened by one character to:

if a<b<[]>c>d:foo()

This uses that every list is larger than any integer.

If c and d are lists, this gets even better:

if a<b<c>d:foo()

• Of course if this were actually golfed it'd be 3>a>1<b<5 – Rafe Kettler Jan 28 '11 at 0:35
• Love the symmetry. Reminds me of the old Perl golf trick for finding the min of $a and$b: [$a =>$b]->[$b <=$a] :) – Simon Whitaker Feb 3 '11 at 21:42
• The + should be a *. An or would be + – WorldSEnder May 22 '14 at 10:53
• foo()if 3>a>1<b<5 – Erik the Outgolfer Jun 10 '16 at 7:31
• @EriktheOutgolfer foo()if 3>a>1<b<5 doesn't work for me. – Dorian Turba Dec 24 '19 at 8:52

If you're using a built-in function repeatedly, it might be more space-efficient to give it a new name, if using different arguments:

r=range
for x in r(10):
for y in r(100):print x,y

• Didn't actually save any bytes, though. – user2357112 supports Monica Mar 20 '14 at 7:06
• r=range and the other two r's are 9 characters; using range twice is 10 characters. Not a huge saving in this example but all it would take is one more use of range to see a significant saving. – Frank Aug 25 '16 at 19:52
• @Frank The additional newline is another character. – L3viathan Nov 14 '16 at 20:45
• Indeed two repetitions is too little to save on a length five function name. You need: length 2: 6 reps, length 3: 4 reps, length 4 or 5: 3 reps, length >=6: 2 reps. AKA (length-1)*(reps-1)>4. – Ørjan Johansen Mar 18 '17 at 16:26
• Note this is applicable to all languages with first-class functions. – bfontaine Jul 19 '19 at 22:30

Sometimes your Python code requires you to have 2 levels of indentation. The obvious thing to do is use one and two spaces for each indentation level.

However, Python 2 considers the tab and space characters to be different indenting levels.

This means the first indentation level can be one space and the second can be one tab character.

For example:

if 1:
if 1:
pass
• This fails in python3: you can no more mix spaces and tabs(a bad thing for codegolf, but a good thing in all other cases). – Bakuriu Oct 19 '13 at 15:41
• In python 3.4 this seems to work fine. – trichoplax Aug 15 '16 at 23:09
• @trichoplax, In python 3.4.3 I get TabError: inconsistent use of tabs and spaces in indentation. – ceilingcat Oct 3 '16 at 5:16
• For reference, a tab is worth 8 spaces. – Erik the Outgolfer Jun 29 '18 at 22:35

Use string substitution and exec to deal with long keywords like lambda that are repeated often in your code.

a=lambda b:lambda c:lambda d:lambda e:lambda f:0   # 48 bytes  (plain)
exec"a=b:c:d:e:f:0".replace('','lambda ')    # 47 bytes  (replace)
exec"a=%sb:%sc:%sd:%se:%sf:0"%(('lambda ',)*5)     # 46 bytes  (%)

The target string is very often 'lambda ', which is 7 bytes long. Suppose your code snippet contains n occurences of 'lambda ', and is s bytes long. Then:

• The plain option is s bytes long.
• The replace option is s - 6n + 29 bytes long.
• The % option is s - 5n + 22 + len(str(n)) bytes long.

From a plot of bytes saved over plain for these three options, we can see that:

• For n < 5 lambdas, you're better off not doing anything fancy at all.
• For n = 5, writing exec"..."%(('lambda ',)*5) saves 2 bytes, and is your best option.
• For n > 5, writing exec"...".replace('','lambda ') is your best option.

For other cases, you can index the table below:

          1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 (occurences)
+---------------------------------------------------------
3 |  -  -  -  -  -  -  -  -  -  -  -  -  -  -  r  r  r  r  r
4 |  -  -  -  -  -  -  -  -  -  r  r  r  r  r  r  r  r  r  r
5 |  -  -  -  -  -  -  -  r  r  r  r  r  r  r  r  r  r  r  r
6 |  -  -  -  -  -  r  r  r  r  r  r  r  r  r  r  r  r  r  r
7 |  -  -  -  -  %  r  r  r  r  r  r  r  r  r  r  r  r  r  r
8 |  -  -  -  %  %  r  r  r  r  r  r  r  r  r  r  r  r  r  r
9 |  -  -  -  %  %  r  r  r  r  r  r  r  r  r  r  r  r  r  r
10 |  -  -  %  %  %  r  r  r  r  r  r  r  r  r  r  r  r  r  r
11 |  -  -  %  %  %  r  r  r  r  r  r  r  r  r  r  r  r  r  r
12 |  -  -  %  %  %  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r = replace
13 |  -  -  %  %  %  r  r  r  r  r  r  r  r  r  r  r  r  r  r   % = string %
14 |  -  %  %  %  %  r  r  r  r  r  r  r  r  r  r  r  r  r  r   - = do nothing
15 |  -  %  %  %  %  r  r  r  r  r  r  r  r  r  r  r  r  r  r
(length)

For example, if the string lambda x,y: (length 11) occurs 3 times in your code, you're better off writing exec"..."%(('lambda x,y:',)*3).

• this should get more votes, it's a very useful tip. – bigblind May 11 '13 at 0:18
• it's extremely rare that this works. the cost of replace is huge. – boothby Oct 27 '13 at 2:09
• When it does work, though, it helps a lot. – undergroundmonorail Apr 16 '14 at 8:28
• Interesting, never even tghought of this! – Claudiu Sep 25 '14 at 22:23
• If you use this often enough for .replace("R",'.replace("') to save bytes, many other replacements become cheaper. (It also makes your code entirely unreadable.) – Hiatsu Aug 28 '19 at 18:53

Use extended slicing to select one string from many

>>> for x in 0,1,2:print"fbboaaorz"[x::3]
...
foo
bar
baz

vs

>>> for x in 0,1,2:print["foo","bar","baz"][x]
...
foo
bar
baz

In this Boolean two-string case, one can also write

b*"string"or"other_string"

for

["other_string","string"][b]

Unlike interleaving, this works for strings of any length, but can have operator precedence issues if b is instead an expression.

• Note that the first example is exactly the same length as for x in ("foo","bar","baz"): print x – Mateen Ulhaq Jun 2 '17 at 7:21
• @MateenUlhaq, That's just an example of how the different values of x are rendered. The golfed part is the "fbboaaorz"[x::3] vs ["foo","bar","baz"][x] How the x value is derived would be another part of your golf solution. – gnibbler Jun 2 '17 at 7:31

## Store lookup tables as magic numbers

Say you want to hardcode a Boolean lookup table, like which of the first twelve English numbers contain an n.

0: False
1: True
2: False
3: False
4: False
5: False
6: False
7: True
8: False
9: True
10:True
11:True
12:False

Then, you can implement this lookup table concisely as:

3714>>i&1

with the resulting 0 or 1 being equal to False to True.

The idea is that the magic number stores the table as a bitstring bin(3714) = 0b111010000010, with the n-th digit (from the end) corresponding the the nth table entry. We access the nth entry by bitshifting the number n spaces to the right and taking the last digit by &1.

This storage method is very efficient. Compare to the alternatives

n in[1,7,9,10,11]
'0111010000010'[n]>'0'

You can have your lookup table store multibit entries that can be extracted like

 340954054>>4*n&15

to extract the relevant four-bit block.

• Could we have an example result for the four-bit block? Did you use a rule for n-bit block? – jeromej Sep 14 '15 at 8:23
• Hex might sometimes be even smaller. – Joonazan Feb 3 '16 at 21:34
• This is useful for a lot of languages. – Cyoce Feb 11 '16 at 3:50
• @Joonazan Hex is smaller for numbers over 999 999. – Mateen Ulhaq Jun 2 '17 at 7:57
• n in [...] might be smaller for sparse sets. – Solomon Ucko Jun 9 '20 at 0:53

Use n to convert an integer to a string instead of using str(n):

>>> n=123
>>> n
'123'

Note: Only works in Python 2.

• Nice, but doesn't work with Python3. – Alexandru Jan 28 '11 at 0:04
• Attention: really works for integers, but not for strings, for example. – Nakilon Jan 28 '11 at 0:12
• btw.  is short for repr – Alexandru Jan 28 '11 at 2:14
• Integers smaller than -2**31 or bigger than 2**31-1 (Longs) gets an 'L' tacked on at the end. – hallvabo Jan 28 '11 at 8:47
• This can also be used to print floats to full precision – gnibbler Feb 19 '13 at 0:28

## Collapse two numerical loops into one

Say you're iterating over the cells of an m*n grid. Instead of two nested for loops, one for the row and one of the columns, it's usually shorter to use a single loop to iterate over the m*n cells of the grid. You can extract the row and column of the cell inside the loop.

Original code:

for i in range(m):
for j in range(n):
do_stuff(i,j)

Golfed code:

for k in range(m*n):
do_stuff(k/n,k%n)

In effect, you're iterating over the Cartesian product of the two ranges, encoding the pair (i,j) as x=i*n+j. You've save a costly range call and a level of indentation inside the loop. The order of iteration is unchanged.

Use // instead of / in Python 3. If you refer to i and j many times, it may be faster to assign their values i=k/n, j=k%n inside the loop.

• This is awesome. I had never realised this was possible! – theonlygusti Apr 2 '15 at 19:03
• I saw this in the tips for JavaScript. It's a pretty useful trick in most languages. – Cyoce Jan 12 '16 at 6:59
• For reference, to extend this to 3 loops: for i in range(m*n*o): do_stuff(i/n/o,i%(n*o)/o,i%o) – mbomb007 Oct 27 '16 at 14:48
• For n loops: repl.it/EHwa – mbomb007 Oct 27 '16 at 16:33
• In some cases, itertools.product can be much more concise than nested loops, especially when generating cartesian products. a1, a2, b1, b2 are examples of the cartesian product of 'ab' and '12' – Aaron3468 Mar 16 '18 at 3:24

For integer n, you can write

• n+1 as -~n
• n-1 as ~-n

because the bit flip ~x equals -1-x. This uses the same number of characters, but can indirectly cut spaces or parens for operator precedence.

Compare:

while n-1:  #Same as while n!=1
while~-n:

c/(n-1)
c/~-n

or f(n)+1
or-~f(n)

(n-1)/10+(n-1)%10
~-n/10+~-n%10

The operators ~ and unary - are higher precedence than *, /, %, unlike binary +.

• A variation on this trick I ran into today: -~-x saves one byte vs. (1-x). – Lynn Jul 15 '15 at 11:34
• Another useful application is that a+b+1 can be more concisely written as a-~b. – Strigoides Jan 22 '17 at 11:51
• And n-i-1 is just n+~i. – ruohola Jun 9 '19 at 22:23
• 2s comp is fun! – sabhiram Apr 13 at 20:21

A nice way to convert an iterable to list on Python 3:

imagine you have some iterable, like

i = (1,2,3,4)
i = range(4)
i = (x**2 for x in range(5))

But you need a list:

x=list(i)  #the default way
*x,=i      #using starred assignment -> 4 char fewer

It's very useful to make a list of chars out of a string

s=['a','b','c','d','e']
s=list('abcde')
*s,='abcde'

• typing *s,='abcde' and then s crashes my interactive python3 with a segfault :( – daniero Jul 6 '15 at 18:41
• My Python 3.5 works fine. – NoOneIsHere Mar 10 '16 at 16:19
• for i = (x**2 for x in range(5)) I get this code returned <generator object <genexpr> at 0x03321690> – george Jun 15 '16 at 14:27
• @george Now try *x,=i ... – JBernardo Jun 15 '16 at 17:31
• And if you're doing this in an expression, you can do [*'abcde']. – Esolanging Fruit Jun 5 '17 at 0:58

Unless the following token starts with e or E. You can remove the space following a number.

For instance:

if i==4 and j==4:
pass

Becomes:

if i==4and j==4:
pass

Using this in complicated one line statements can save quite a few characters.

EDIT: as @marcog pointed out, 4or a will work, but not a or4 as this gets confused with a variable name.

• if(i,j)==(4,4): is even shorter and in this special case if i==j==4: – gnibbler Jan 28 '11 at 0:14
• Related: 4or a works, but not a or4 – moinudin Jan 28 '11 at 0:15
• 0or also doesn't work (0o is a prefix for octal numbers). – Nabb Feb 2 '11 at 17:28
• @Nabb Not that it matters anyways, since 0 or x is always gonna return x. Might as well cut out the 0 or. – ɐɔıʇǝɥʇuʎs Apr 6 '14 at 12:57
• 0or is fine as part of a longer number though. 10 or x is equivalent to 10or x. – trichoplax Apr 20 '14 at 22:39

Instead of range(x), you can use the * operator on a list of anything, if you don't actually need to use the value of i:

for i in[1]*8:pass

as opposed to

for i in range(8):pass

If you need to do this more than twice, you could assign any iterable to a variable, and multiply that variable by the range you want:

r=1,
for i in r*8:pass
for i in r*1000:pass

Note: this is often longer than exec"pass;"*8, so this trick should only be used when that isn't an option.

• @proudhaskeller I think the point of the line you removed was that "In addition to the obvious character savings you get because [1]*8 is shorter than range(8), you also get to save a space because for i in[... is legal while for i in range... is not". – undergroundmonorail Aug 18 '14 at 17:13
• oh, right, i didn't understand that. fixed now – proud haskeller Aug 18 '14 at 17:30
• exec"pass;"*8 is significantly shorter. – DJMcMayhem May 19 '16 at 19:23
• if r=1, r*8 is 8, and you can't iterate through a number. I guess you meant r=[1] – Artemis Mar 26 '19 at 22:58
• @ArtemisFowl, no it's ok as is, the comma after the 1 creates a tuple which is iterable. – sasha Jun 13 '19 at 11:48

You can use the good old alien smiley face to reverse sequences:

[1, 2, 3, 4][::-1] # => [4, 3, 2, 1]

# Extended iterable unpacking ("Starred assignment", Python 3 only)

The best way to explain this is via an example:

>>> a,*b,c=range(5)
>>> a
0
>>> b
[1, 2, 3]
>>> c
4

We've already seen a use for this — turning an iterable into a list in Python 3:

a=list(range(10))
*a,=range(10)

Here are a few more uses.

## Getting the last element from a list

a=L[-1]
*_,a=L

In some situations, this can also be used for getting the first element to save on parens:

a=(L+[1])[0]
a,*_=L+[1]

## Assigning an empty list and other variables

a=1;b=2;c=[]
a,b,*c=1,2

## Removing the first or last element of a non-empty list

_,*L=L
*L,_=L

These are shorter than the alternatives L=L[1:] and L.pop(). The result can also be saved to a different list.

Tips courtesy of @grc

• Wow! I have written a=1;L=[] so many times. It's amazing that you can save chars on something so straightforward as this. – xnor Dec 6 '14 at 9:16
• @xnor That one's thanks to grc. With only one other element it's not as good (a,*L=1,), but it still saves one char :) – Sp3000 Dec 6 '14 at 9:20
• don't forget you can also get both the first and last element of a list with a,*_,b=L – Cyoce Mar 3 '16 at 2:59

For ages it bothered me that I couldn't think of a short way to get the entire alphabet. If you use range enough that R=range is worth having in your program, then

[chr(i+97)for i in R(26)]

is shorter than the naive

'abcdefghijklmnopqrstuvwxyz'

, but otherwise it's longer by a single character. It haunted me that the clever one that required some knowledge of ascii values ended up being more verbose than just typing all the letters.

Until I saw this answer for My Daughter's Alphabet. I can't follow the edit history well enough to figure out if this genius was the work of the OP or if it was a suggestion by a commenter, but this is (I believe) the shortest way to create an iterable of the 26 letters in the Roman alphabet.

map(chr,range(97,123))

If case doesn't matter, you can strip off another character by using uppercase:

map(chr,range(65,91))

I use map way too much, I don't know how this never occurred to me.

• Might use this in actual coding, I feel so stupid when hardcoding these things :') – ToonAlfrink Jun 7 '14 at 19:53
• In actual coding, use string.lowercase -- that's what it's there for. – Kevin S Aug 13 '14 at 19:20
• if you need both cases, the shortest way I know is filter(str.isalpha,map(chr,range(256))). It's just barely shorter than s=map(chr,range(256));s+=map(str.lower,s) – quintopia Nov 18 '15 at 3:40
• @quintopia: Why 256 instead of 122 (ord('z'))? Aside from it being the same length... Also, if you need alphanumerics, replace str.isalpha in @quintopia's version with str.isalnum. (But if you only need one case, the whole 36-character string is no longer than filter(str.isalnum,map(chr,range(90))).) – Tim Pederick Dec 21 '15 at 5:36
• If you going to be unfair and use range as R, my version is shorter than your original one: '%c'*26%tuple(R(97,123)) (only 24 chars) if you spell range it is just as long as the alphabet -- uppercase version is shorter – JBernardo Dec 21 '17 at 20:26

## set literals in Python2.7

You can write sets like this S={1,2,3} This also means you can check for membership using {e}&S instead of e in S which saves one character.

• And this also saves the character in ifs as there is no spaces (if{e}&S:) – Artyer Jun 4 '17 at 18:43
• Note that you can replace not in by {e}-S with that trick – Black Owl Kai Nov 7 '18 at 8:20

## Use ~ to index from the back of a list

If L is a list, use L[~i] to get the i'th element from the back.

This is the i'th element of the reverse of L. The bit complement ~i equals -i-1, and so fixes the off-by-one error from L[-i].

When you have two boolean values, a and b, if you want to find out if both a and b are true, use * instead of and:

if a and b: #7 chars

vs

if a*b: #3 chars

if either value is false, it will evaluate as 0 in that statement, and an integer value is only true if it is nonzero.

• Or you could use &: a=b=False, a&b – ɐɔıʇǝɥʇuʎs Apr 9 '14 at 7:56
• use + for or if you can guarantee a != -b – undergroundmonorail Apr 23 '15 at 1:18
• | works in all situations. – CalculatorFeline May 31 '17 at 1:30
• * instead of and/&& saves some bytes in many languages. – wastl Apr 30 '18 at 20:48

Although python doesn't have switch statements, you can emulate them with dictionaries. For example, if you wanted a switch like this:

switch (a):
case 1:
runThisCode()
break
case 2:
runThisOtherCode()
break
case 3:
runThisOtherOtherCode()
break

You could use if statements, or you could use this:

exec{1:"runThisCode()",2:"runThisOtherCode()",3:"runThisOtherOtherCode()"}[a]

or this:

{1:runThisCode,2:runThisOtherCode,3:runThisOtherOtherCode}[a]()

which is better if all code paths are functions with the same parameters.

To support a default value do this:

exec{1:"runThisCode()"}.get(a,"defaultCode()")

(or this:)

{1:runThisCode}.get(a,defaultCode)()

One other advantage of this is that if you do have redundancies, you could just add them after the end of the dictionary:

exec{'key1':'code','key2':'code'}[key]+';codeThatWillAlwaysExecute'

And if you just wanted to use a switch to return a value:

def getValue(key):
if key=='blah':return 1
if key=='foo':return 2
if key=='bar':return 3
return 4

You could just do this:

getValue=lambda key:{'blah':1,'foo':2,'bar',3}.get(key,4)

• This is something i would deeply consider using in the wild. I do so miss my switch statements! +1 – HalosGhost Nov 19 '14 at 12:51
• Although instead of using a dictionary with numbered keys in the first example, you should just use a list – Cyoce Oct 13 '16 at 19:25
• If you have strings as keys, using dict(s1=v1,s2=v2,...,sn=vn) instead of {'s1':v1,'s2':v2,...,'sn':vn} saves 2*n-4 bytes and is better if n>=3 – Black Owl Kai Oct 27 '18 at 14:13

Choosing one of two numbers based on a condition

You already know to use the list selection [x,y][b] with a Boolean b for the ternary expression y if b else x. The variables x, y, and b can also be expressions, though note that both x and y are evaluated even when not selected.

Here's some potential optimizations when x and y are numbers.

• [0,y][b] -> y*b
• [1,y][b] -> y**b
• [x,1][b] -> b or x
• [x,x+1][b] -> x+b
• [x,x-1][b] -> x-b
• [1,-1][b] -> 1|-b
• [x,~x][b] -> x^-b
• [x,y][b] -> x+z*b (or y-z*b), where z=y-x.

You can also switch x and y if you can rewrite b to be its negation instead.

loops up to 4 items may be better to supply a tuple instead of using range

for x in 0,1,2:

vs

for x in range(3):

# Ceil and Floor

If you ever want to get the rounded-up result for a division, much like you'd do with // for floor, you could use math.ceil(3/2) for 15 or the much shorter -(-3//2) for 8 bytes.

math.floor(n)   : 13 bytes+12 for import
n//1            : 4  bytes

math.ceil(n)    : 12 bytes+12 for import
-(-n//1)        : 8  bytes

• This just saved me close to 20 bytes, thank you! – Morgan Thrapp Jan 13 '16 at 19:27
• sometimes you can get away with n//1+1 instead of ceil but it does mean ceil(n)=n+1 but it should work for all non integer values – fejfo Dec 23 '17 at 20:26
• round(x) is (x+.5)//1, +1 byte but the latter starts with a (, and if x is a sum consisting of a constant it can be useful. – user202729 Apr 28 '18 at 5:27

A one line function can be done with lambda:

def c(a):
if a < 3: return a+10
else: return a-5

can be converted to (note missing space 3and and 10or)

c=lambda a:a<3and a+10or a-5

• or c=lambda a:a+[-5,10][a<3]. the and/or trick is more useful when you are depending on the shortcircuit behaviour – gnibbler Feb 3 '11 at 13:23
• In your function, else:  can be dropped as return stops the execution of the function, so everything that follows is only executed if the if condition failed, aka if the else condition is true. Thus else can safely be ommited. (Explained in details for the neophytes out there) – jeromej Sep 14 '15 at 8:15
• c(-10) returns -15 while it should return 0 – Anvit Dec 5 '18 at 7:53
• or c=lambda a:a-5+15*(a<3) – JayXon Aug 11 '19 at 8:59

### Use += instead of append and extend

A.append(B)

can be shortened to:

A+=B,

B, here creates a one-element tuple which can be used to extend A just like [B] in A+=[B].

A.extend(B)

can be shortened to:

A+=B

• In many (but not all) cases, return 0 or return 1 is equivalent to return False or return True. – undergroundmonorail Apr 16 '14 at 8:30
• (1) only works if you already know the number is negative, in which case you can save a further 2 characters by simply using a minus sign. -x rather than x*-1. --8.32 rather than -8.32*-1. Or just 8.32... – trichoplax Apr 20 '14 at 22:56
• Quoting the OP: Please post one tip per answer. – nyuszika7h Jun 23 '14 at 13:32
• Note that in A+=B B is a tuple. – Erik the Outgolfer Jun 10 '16 at 7:52

Change import * to import*

If you haven't heard, import* saves chars!

from math import*

is only 1 character longer than import math as m and you get to remove all instances of m.

Even one time use is a saver!

# PEP448 – Additional Unpacking Generalizations

With the release of Python 3.5, manipulation of lists, tuples, sets and dicts just got golfier.

## Turning an iterable into a set/list

Compare the pairs:

set(T)
{*T}

list(T)
[*T]

tuple(T)
(*T,)

Much shorter! Note, however, that if you just want to convert something to a list and assign it to a variable, normal extended iterable unpacking is shorter:

L=[*T]
*L,=T

A similar syntax works for tuples:

T=*L,

which is like extended iterable unpacking, but with the asterisk and comma on the other side.

## Joining lists/tuples

Unpacking is slightly shorter than concatenation if you need to append a list/tuple to both sides:

[1]+T+[2]
[1,*T,2]

(1,)+T+(2,)
(1,*T,2)

## Printing the contents of multiple lists

This isn't limited to print, but it's definitely where most of the mileage will come from. PEP448 now allows for multiple unpacking, like so:

>>> T = (1, 2, 3)
>>> L = [4, 5, 6]
>>> print(*T,*L)
1 2 3 4 5 6

## Updating multiple dictionary items

This probably won't happen very often, but the syntax can be used to save on updating dictionaries if you're updating at least three items:

d[0]=1;d[1]=3;d[2]=5
d={**d,0:1,1:3,2:5}

This basically negates any need for dict.update.

• This looks worse than Perl, but it works... – univalence Jun 25 '16 at 5:52

## Exploit Python 2 string representations

Python 2 lets you convert an object x to its string representation x at a cost of only 2 chars. Use this for tasks that are easier done on the object's string than the object itself.

Join characters

Given a list of characters l=['a','b','c'], one can produce ''.join(l) as l[2::5], which saves a byte.

The reason is that l is "['a', 'b', 'c']" (with spaces), so one can extract the letters with a list slice, starting that the second zero-indexed character a, and taking every fifth character from there. This doesn't work to join multi-character strings or escape characters represented like '\n'.

Concatenate digits

Similarly, given a non-empty list of digits like l=[0,3,5], one can concatenate them into a string '035' as l[1::3].

This saves doing something like map(str,l). Note that they must be single digits, and can't have floats like 1.0 mixed in. Also, this fails on the empty list, producing ].

Check for negatives

Now, for a non-string task. Suppose you have a list l of real numbers and want to test if it contains any negative numbers, producing a Boolean.

You can do

'-'inl

which checks for a negative sign in the string rep. This shorter than either of

any(x<0for x in l)
min(l+[0])<0

For the second, min(l)<0 would fail on the empty list, so you have to hedge.

• Concatenating single digits string slicing is also effective in Python 3, albeit less so: str(l)[2::5] is 12 bytes, versus 19 for ''.join(map(str,l)). An actual situation where this came up (where l was a generator statement, not a list) saved me just one byte... which is still worth it! – Tim Pederick Dec 21 '15 at 2:08

I've think it would be useful to have a reference for the character count differences for some common alternative ways of doing things, so that I can know when to use which. I'll use _ to indicate an expression or piece of code.

Assign to a variable: +4

x=_;x
_

So, this breaks even if you

• Use _ a second time: _ has length 5
• Use _ a third time: _ has length 3

Assign variables separately: 0

x,y=a,b
x=a;y=b

• -2 when a equals b for x=y=a

Expand lambda to function def: +7

lambda x:_
def f(x):return _

• -2 for named functions
• -1 if _ can touch on the left
• -1 in Python 2 if can print rather than return
• +1 for starred input *x

Generically, if you're def to save an expression to a variable used twice, this breaks even when the expression is length 12.

lambda x:g(123456789012,123456789012)
def f(x):s=123456789012;return g(s,s)

STDIN rather than function: +1

def f(x):_;print s
x=input();_;print s

• -1 for line of code needed in _ if not single-line
• +4 if raw_input needed in Python 2
• -4 is input variable used only once
• +1 if function must return rather than print in Python 2

Use exec rather than looping over range(n): +0

for i in range(n):_
i=0;exec"_;i+=1;"*n

• +2 for Python 3 exec()
• -4 if shifted range range(c,c+n) for single-char c
• -5 when going backwards from n to 1 via range(n,0,-1)

Apply map manually in a loop: +0

for x in l:y=f(x);_
for y in map(f,l):_

Apply map manually in a list comprehension: +8

map(f,l)
[f(x)for x in l]

• -12 when f must be written in the map as the lambda expression lambda x:f(x), causing overall 4 char loss.

Apply filter manually in a list comprehension: +11

filter(f,l)
[x for x in l if f(x)]

• -1 if f(x) expression can touch on the left
• -12 when f must be written in the filter as the lambda expression lambda x:f(x), causing overall 1 char loss.

Import* versus import single-use: +4

import _;_.f
from _ import*;f

• Breaks even when _ has length 5
• import _ as x;x.f is always worse except for multiple imports
• __import__('_').f` is also worse

Thanks to @Sp3000 for lots of suggestions and fixes.

• The "exec" bit goes -9 if you don't need the index. – T. Verron Oct 8 '15 at 8:43