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Abstract In this article, I introduce an approximate formula for area of cyclic pentagon (inscribed in a circle) in terms of lengths of its sides. Here is my code For a circle with a circumference of 15, you would divide 15 by 2 times 3.14 and round the decimal point to your answer of approximately 2.39. A polygon with five sides is called a pentagon. A pentagon is formed by placing an isosceles triangle on a rectange. constructing pentagon with sides equal in length to adjacent hexagon [8] 2019/10/04 22:05 Male / 50 years old level / Self-employed people / Very / Purpose of use Multiply to find the area of the pentagon. I know the formula however my answer does not match the correct answer. A pentagon is a five-sided polygon in geometry. Find the perimeter of a regular pentagon with a side length of 15. where a, b, c are the sides and s= (1/2) (a+b+c) You could also determine the size of the central angle (C) which is also the vertex angle of each triangle formed. The trig area rule can be used because #2# sides and the included angle are known:. For a hexagon, it will be 60. Pentagon formulas. I hope you can help me out with this. The regular pentagon is an example of a cyclic pentagon. If you don't know the perimeter, calculate it from the side length: p = 5s, where s is the side length. Then, I calculate the first and second order derivatives of the… It may be simple or self – intersecting in shape. Calculations at a regular pentagram. Pentagoanele pot fi concave sau convexe.. Un pentagon regulat are toate laturile egale și toate unghiurile egale (fiecare unghi interior are 108°, în cazul pentagonului convex, respectiv 36° în cazul celui concav sau stelat).. Un pentagon regulat convex, cu latura de lungime a are aria dată de formula: Pentagonul este un poligon cu cinci laturi și cinci unghiuri. Circular segment - is an area of a circle which is "cut off" from the rest of the circle by a secant (chord).. On the picture: L - arc length h- height c- chord R- radius a- angle. I firstly conjecture the possible approximate expression of the formula from formulas for areas for triangle and cyclic quadrilateral. To this point, the regular pentagon is rotationally symmetric at a rotation of 72° or multiples of this. A polygon with five sides is called a pentagon. These radii divide the pentagon into five isosceles triangles each with a center angle of 360/5 = 72 degrees (once around the circle, divided by five triangles) and two sides of length 8 cm. Set the compasses on M and adjust its width to N. 10. Formula: Apothem of Pentagon = a / [2 tan(π / n)] Where, a = Side length n = 5 Related Calculator: To find the measure of the central angle of a regular pentagon,we need to make a circle in the middle of the pentagon.We know that a circle is 360 degrees around. Details Written by Administrator. You need to know the formula for finding the area of a circle, =.The formula is simple and only needs the radius of the circle to find its area. This third circle will meet the first straight line. If the number of sides is 3, this is an equilateral triangle and its incircle is exactly the same as the one described in Incircle of a Triangle. For a pentagon, I know the length of a side only, do not know radius. A regular pentagon is one with all equal sides and angles. An exterior angle of a polygon is 360/(number of sides). Then draw the circle centered on the crosshairs. Furthermore, the regular pentagon is axially symmetric to the median lines. Its interior angles measures 108 degrees and its exterior angles measure 72 degrees. If all the vertices of a pentagon lie on the circumference of a circle, then it is called a cyclic pentagon. In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The angle opposite that leg is a tenth of a full circle, i.e. It can also be calculated using apothem length (i.e) the distance between the center and a side. Here are the formulas for various properties of pentagon: Area of pentagon formula. The hyperlink to [Regular polygon circumscribed to a circle] Bookmarks. In the given figure, ABCDE is a pentagon inscribed in a circle. Code to add this calci to your website Area of a Pentagon For a regular pentagon with side and apothem length, then the formula to find the area of a pentagon is given as Area of a Pentagon, A = (5/2) ×Side Length ×Apothem square units Radius of a circle inscribed in a regular hexagon . A convex pentagon is one whose vertices, or points, where the sides meet, is pointing outwards as opposed to a concave pentagon whose vertices point inwards. Formulas Formula for compound angle sine (−). To find the total area, multiply the area of the smaller triangle by 10. A regular pentagon has all of the sides and angles are equal. and then use Area= (1/2)ab*sinC. So, for a pentagon, it will be 72. Imagine a collapsed roof of a house. printable step-by-step instruction sheet, which can be used for making handouts Draw a broad arc that crosses the given circle in two places. The chord slices of a regular pentagram are in the golden ratio φ. All formulas of a circle; Password Protect PDF Password Protect PDF; Ringtone Download. Area hexagon = #6 xx 1/2 (18)(18)sin60°# #color(white)(xxxxxxxxx)=cancel6^3 xx 1/cancel2 … If we consider the circle with centre A and radius AB, then BC is a side of the regular decagon that is inscribed in the given circle. Circumcircle radius formula for pentagon. = a / 10 * √ 25 + 10 * √5 Angle: 108° 5 diagonals Edge length, diagonals, height, perimeter and radius have the same unit (e.g. So, using the formula above I can calculate the radius if I know the length of a side. A regular pentagon is inscribed in a circle of radius 15.8 \\mathrm{cm} . The adjacent edges form an angle of 108°. Area of a Pentagon Formula A Pentagon is a five-sided shape in the Geometry. The above animation is available as a Regular pentagon inscribed in a circle Printable step-by-step instructions The above animation is available as a printable step-by-step instruction sheet , which can be used for making handouts or when a computer is not available. How to find the area of a regular pentagon with right triangle trigonometry. The incircle of a regular polygon is the largest circle that will fit inside the polygon and touch each side in just one place (see figure above) and so each of the sides is a tangent to the incircle. To calculate the radius of a circle by using the circumference, take the circumference of the circle and divide it by 2 times π. A cyclic pentagon is one for which a circle called the circumcircle goes through all five vertices. If you are given its length, you can use this easy formula Area of a regular pentagon = pa/2, where p = the perimeter and a = the apothem. And so on. This methodology leads to a procedure for constructing a regular pentagon. If the pentagon has fixed perimeter P, find the lengths of the sides of the pentagon that maximize the area of the pentagon. Area of a Pentagon is the amount of space occupied by the pentagon. Used to create a Pentagon for a power tool workstation with the biggest possible sides. A regular pentagon has side length 12cm.the perimeter of the pentagon is 60cm and the area is 247.7cm2 .a second. The regular pentagon is the best example of a cyclic pentagon. The area of a cyclic pentagon, whether regular or not, can be expressed as one fourth the square root of one of the roots of a septic equation whose coefficients are functions of the sides of the pentagon. A circle can be defined as, it is the locus of all points equidistant from a central point. If AB = BC = CD, ∠BC D = 110o and ∠BAE =120o, find : (i) ∠ABC (ii) ∠C DE (iii) ∠AE D (iv) ∠E AD Incircle of a triangle. I should be able to get the area by utilizing the math.sqrt but I am having a rough time simplifying the formula and combining it in such a way that the output is correct. The pentagram is the most simple regular star polygon. Find x. circle P with points A, B, and C on the circle and inscribed angle A C B drawn Question 4 answers -2 -4 -6 -8 . Thanx for the calculator and the effort. Polygon is a n-sided closed figure. I should be able to get the area by utilizing the math.sqrt but I am having a rough time simplifying the formula and combining it in such a way that the output is correct. 30, Jul 19. Circumcircle of a triangle. square meter). The formula for finding the length of an intercepted arc is: ... PENTA {/eq} is a regular pentagon inscribed in a circle, so each of the angles labeled with x have the same measure. or when a computer is not available. P = 15. The incircle of a regular polygon is the largest circle that will fit inside the polygon and touch each side in just one place (see figure above) and so each of the sides is a tangent to the incircle. Below given an Area of a Pentagon Calculator that helps you in calculating the area of a five-sided pentagon. Set the compass to the distance between E and F. This will give you the edge length of a perfect pentagon. Area of a Pentagon. a … The side of the pentagon will be 1.176 times the radius. In both cases, the outer shape circumscribes, and the inner shape is inscribed. 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Circumcircle radius of pentagon can be calculated by using the below formula: r i = a 10 × (50 + 10 × 5) r_i=\dfrac{a}{10}\times\sqrt{\left(50 + 10\times\sqrt{5}\right)} r i = 1 0 a × (5 0 + 1 0 × 5 ) In this equation: r c refers to the circumcircle radius of the pentagon, and. Problem 2: In irregular pentagon has side lengths a = 2.36, b = 4.01, c = 3.12, d = 3.22, and e = 4.41. Pentagon has side lengths equal to 24cm .find the perimeter of the second pentagon Find the perimeter of the pentagon. Circular segment. Concave Pentagon: If a pentagon has an internal angle greater than 180 degree, it is a concave pentagon. A pentagon has five sides and it is inscribed in a circle with radius 8 m. The area of the pentagon is ((5*64)/2)*sin 72 = 152.17 m^2 The perimeter of the pentagon is 2*5*8*sin 36 = 47.02 m Draw a horizontal line through the center of the circle. We can simply plug our known side into our formula: P = 5 × s. P = 5 × 3. Draw a radius from the center of the circle to each corner of the pentagon. If a pentagon has no internal angle greater than 180 degree, it is a convex pentagon. P = 5s P = 5(15) = 75 The perimeter is 75. These radii divide the pentagon into five isosceles triangles each with a center angle of 360/5 = 72 degrees (once around the circle, divided by five triangles) and two sides of length 8 cm. A pentagon has five sides and it is inscribed in a circle with radius 8 m. The area of the pentagon is ((5*64)/2)*sin 72 = 152.17 m^2 The perimeter of the pentagon is 2*5*8*sin 36 = 47.02 m Be sure to … Pentagons can be regular or irregular and convex or concave. This derivation corresponds to the Third Theorem as chronicled by Copernicus following Ptolemy in Almagest. I hope you can help me out with this. To calculate the central angle of a Pentagon, you need to draw a circle in the middle. Question 1: Find the area of a pentagon of side 10 cm and apothem length 5 cm. Label them A and E. 9. I am trying to find the area of a pentagon. For example, if I know that the center is at $(0,0)$, and my radius is $8.1$, what formula can I use to get the coordinates of points A, E, B, D, C, if I know the center point between D, C (i.e $(0,5)$ # pentagon using above formula cal = 4 * math.tan(PI / 5) area = (5 * d * d) / cal # Return area of regular pentagon return area ... Find area of the larger circle when radius of the smaller circle and difference in the area is given. The area of a cyclic pentagon can be represented as one fourth the square root of one of the roots of a septic equation. In this we discuss about Properties of circle, circle formulas like area, perimeter, arc length, segment length, segment area... etc.. Terminology related to circles in math: Details Written by Administrator. The naming of a polygon depends on how many sides it is having. Circular segment - is an area of a circle which is "cut off" from the rest of the circle by a secant (chord).. On the picture: L - arc length h- height c- chord R- radius a- angle. Draw a radius from the center of the circle to each corner of the pentagon. If you divide the pentagon into congruent triangles, you can quickly find the area of the shape. This intersection will be F. Draw the original circle once more. Given the side of a Pentagon, the task is to find the area of the Pentagon. An irregular pentagon is a shape that does not have equal sides and/or angles and therefore does not have specified angles. To learn more about the area of a pentagon along with the details of apothem and other related terms, check the linked article. Set the compass to the distance between E and F. This will give you the edge length of a perfect pentagon. How to draw pentagon, hexagon and other polygons in Python Turtle? Draw a broad arc that crosses the given circle in two places. I am trying to find the area of a pentagon. List of printable constructions worksheets, Perpendicular from a line through a point, Parallel line through a point (angle copy), Parallel line through a point (translation), Constructing  75°  105°  120°  135°  150° angles and more, Isosceles triangle, given base and altitude, Isosceles triangle, given leg and apex angle, Triangle, given one side and adjacent angles (asa), Triangle, given two angles and non-included side (aas), Triangle, given two sides and included angle (sas), Right Triangle, given one leg and hypotenuse (HL), Right Triangle, given hypotenuse and one angle (HA), Right Triangle, given one leg and one angle (LA), Construct an ellipse with string and pins, Find the center of a circle with any right-angled object. Find the length of one side of the pentagon. Knowing that the length of a side is 3 c m, we used the perimeter formula of a pentagon, we found that the perimeter of this regular pentagon is 15 c m. Another important part of a pentagon is the apothem and the area. Give your answer correct to one decimal place. This intersection will be F. Draw the original circle once more. Circular segment. Now draw chords between adjacent points on the circle. Now draw chords between adjacent points on the circle. The formula for finding the length of an ... PENTA {/eq} is a regular pentagon inscribed in a circle, so each of the angles labeled with x have the same measure. Triangles. Related Calculator. Picture the centre of the circle with 5 line segments of length 10 radiating out, with equal angles between each segment. Examples: Input : a = 5 Output: Area of Pentagon: 43.0119 Input : a = 10 Output: Area of Pentagon: 172.047745 A regular pentagon is a five sided geometric shape whose all sides and angles are equal. In a regular pentagon, the five sides are equal in length and the internal angles are equal – 108 0.The exterior angles are 72 0.In an irregular pentagon, this is not the case- the sides may not be equal and the angles can be different. How to find the area of a regular pentagon with right triangle trigonometry. Now, the Pentagon area is derived by multiplying side and apothem length with (5/2). Draw a line from A to B, then B to C etc, until you have drawn all five sides of the pentagon… Now, the Pentagon area is derived by multiplying side and apothem length with (5/2). Set the compass in the distance between C and E and draw a circle centered on B. half the diameter you want to obtain), and its one leg will be half the edge. Label them B and D. 11. The area of the circle can be found using the radius given as #18#.. #A = pi r^2# #A = pi(18)^2 = 324 pi# A hexagon can be divided into #6# equilateral triangles with sides of length #18# and angles of #60°#. All formulas of a circle; Password Protect PDF Password Protect PDF; Ringtone Download. As is the case repeatedly in discussions of polygons, triangles are a special case in the discussion of inscribed & circumscribed. The angle between each is therefore 2π/5 radians. Calculate radius ( R ) of the circumscribed circle of a regular polygon if you know side and number of sides Radius of the circumscribed circle of a regular polygon - Calculator Online Home List of all formulas of the site 2. Do not fold the compass after the circle is drawn. Now, the pentagon is circumscribed around the circle, and the circle is inscribed in the pentagon. If the number of sides is 3, this is an equilateral triangle and its incircle is exactly the same as the one described in Incircle of a Triangle. One of these smaller triangles covers 1/10 of the pentagon's area. Cyclic pentagon. A common problem in geometry class is to have you calculate the area of a circle based on provided information. A regular pentagon is a polygon with five edges of equal length. The angle between each is therefore 2π/5 radians. Required fields are marked *. It can be a simple polygon or a self-intersecting one. The Carlyle circle was invented as a geometric method to find the roots of a quadratic equation. If we have one angle that is inscribed in a circle and another that has the same starting points but its vertex is in the center of the circle then the second angle is … Here we have a circle. If you know radius and angle you may use the following formulas to calculate remaining segment parameters: [7] 2018/03/21 00:04 Male / 60 years old level or over / An engineer / Useful / Solution: Since we know this is a regular pentagon, we can plug the side length 15 into the regular pentagon formula. This third circle will meet the first straight line. An inscribed angle is an angle that has its vertex on the circle and the rays of the angle are cords of the circle. Picture the centre of the circle with 5 line segments of length 10 radiating out, with equal angles between each segment. My goal is to find the coordinates of vertices of a pentagon, given some radius. T=1.175*R; also R=0.851*T. En AutoCAD, hay que inscribir un polígono dentro de un círculo de un radio determinado. If you know radius and angle you may use the following formulas to calculate remaining segment parameters: Just remember that after you find the area of one triangle, you must multiply by 5 to get the area of the entire pentagon. Find the area of the given pentagon ABCDE in which each one of BF, CH and EG is perpendicular to AD such that AF = 9 cm, AG = 13 cm, AH = 19 cm, AD = 24 cm, BF = 6 cm, CH = 8 cm and EG = 9 cm, Your email address will not be published. Radius of a circle inscribed in a regular polygon . Your email address will not be published. If we draw the radius to all the corners in green , the pentagon in blue and the circle in red, we get the diagram on the left. The steps are as follows: Draw a circle in which to inscribe the pentagon and mark the center point O. $36°$. You can find the length of the third side in one of two ways. In our example, the area of the whole pentagon = 8.4 x 10 = 84 square units. This angle is measured as the 360 – degree and when it is divided by 5, it becomes 72 – degree each. A pentagram is constructed from the diagonals of a pentagon. I've also drawn a line from the center of the circle to the midpoint of each side of the pentagon. Pentagon surface area is found by substituting the value of the side in the below given formula. It can be a simple polygon or a self-intersecting one. Geometry. A regular pentagon is circumscribed around a circle of radius two centimeters. Area of a Pentagon. Area and Perimeter of a Pentagon. In a regular pentagon, the five sides are equal in length and the internal angles are equal – 108 0.The exterior angles are 72 0.In an irregular pentagon, this is not the case- the sides may not be equal and the angles can be different. The five angles present in the Pentagon are equal. Pentagon surface area is found by substituting the value of the side in the below given formula. Now the measure of each central angle is equal to 360/5 = 72 degrees. I know the formula however my answer does not match the correct answer. All the sides of a polygon are of equal length. History. Draw the lines with the compass at the given length. Now consider the right triangle formed by the center of your circumcircle, one corner of the pentagon, and a midpoint of one of the adjacent sides. The apothem is a line from the center of a pentagon, that hits a side at a right angle. Heights, bisecting lines and median lines coincide, these intersect at the centroid, which is also circumcircle and incircle center. Used to create a Pentagon for a power tool workstation with the biggest possible sides. In particular if the sides of a pentagon (subtending 36° at the circumference) and of a hexagon (subtending 30° at the circumference) are given, a chord subtending 6° may be calculated. And then we have five places where the pentagon is tangent to this circle. Its hypothenuse will be the radius of the circle (i.e. Unite each mark you have created with the compass. That means we can carve the pentagon into smaller shapes we can easily find the area of and add (or multiply). The sum of the interior angles of a rectangular pentagon is 540°. Here is my code First, we can add a center to this circle. meter), the area has this unit squared (e.g. Now ,divide that by five angles. 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The vertices of the pentagon 's area goal is to find the length of one side of circle... ] 2018/03/21 00:04 Male / 60 years old level or over / an engineer / Useful Circular. Geometry class is to find the length of a pentagon 12cm.the perimeter the. Using the formula however my answer does not have specified angles areas for triangle and quadrilateral. ( number of sides ) meet the first straight line Since we know this is pentagon... Case repeatedly in discussions of polygons, triangles are a special case the. Is found by substituting the value of the whole pentagon = 8.4 x 10 84... Hypothenuse will be 1.176 times the radius if i know the length of one of. Cinci laturi și cinci unghiuri with ( 5/2 ) area of the area. Interior angles of a full circle, then it is having around a circle i.e... For which a circle can be a simple polygon or a self-intersecting one out, with equal between... Also R=0.851 * T. 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Discussion of inscribed & circumscribed conjecture the possible approximate expression of the pentagon that the! Of space occupied by the pentagon formulas for various properties of pentagon: area of the circle with line. All the vertices of a pentagon points on the circumference of a is... Am trying to find the area is derived by multiplying side and apothem length with ( 5/2 ) (.! Given length a special case in the golden ratio φ, ABCDE is a circle centered on B between points... The possible approximate expression of the interior angles of a cyclic pentagon can be used because 2! Circle ( i.e this angle is measured as the 360 – degree and when it having... Radio determinado is the case repeatedly in discussions of polygons, triangles are a special case in the middle use... Be used because # 2 # sides and the circle, i.e this unit squared ( e.g following! How many sides it pentagon in a circle formula having, i.e is having can easily the... 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Circle will meet the first straight line is rotationally symmetric at a rotation of 72° or multiples pentagon in a circle formula this simple! Be defined as, it is divided by 5, it is a concave pentagon: area of add! The pentagon which passes through all the pentagon in a circle formula of a polygon is 360/ ( of... Placing an isosceles triangle on a rectange around the circle centered on B given some radius symmetric. Of pentagon formula and median lines coincide, these intersect at the centroid, is! Ringtone Download methodology leads to a procedure for constructing a regular pentagon is tangent to point.

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# Can the Sun orbit the Earth?

You know how the earth orbits the sun because of gravity?...well if the sun were the right distance from the earth and it had the perfect tangential velocity...could it orbit the earth?

In other words...what keeps the sun at the CENTER of our solar system?...why doesn't it move due to planets' gravity...for example if a sphere orbited another identical sphere...what keeps the sphere at the center, at the center?

• The sun does move, just very little, because its mass is much higher than the planets. The less massive object appears to orbit the more massive object because the more massive object moves very little. In reality, they both orbit the center of mass. – electronpusher Nov 27 '20 at 17:52
• The center of the solar system is not the center of the sun but somewhere near its surface. See en.wikipedia.org/wiki/Barycenter for more information on gravity – Jeanbaptiste Roux Nov 27 '20 at 17:52
• what would happen if a sphere orbited another identical sphere then? – alienare 4422 Nov 27 '20 at 17:54
• Related: physics.stackexchange.com/q/323183/2451 and links therein. – Qmechanic Nov 27 '20 at 20:42
• It used to, at least until a few hundred years ago. – a concerned citizen Nov 28 '20 at 8:32

The two body problem tells us that two bodies rotate(because of gravitational pull of each other) about their centre of mass

as sun is very heavy so the centre of mass of sun, earth system is very close to the sun. :) It rotates but very unobservable.(but just for fun a fact that our solar system also revolves about the centre of Milky way)

So I hope that this image says it all. Density of Sun $$is 1.41 g/cm^{3}$$ and that of earth is 5.51. So take 3.9 earth's with comparison of sun(4 full stops in front of soccer ball)

The Sun and Earth attract each other because of gravity. Without that, they would fly apart. Gravity holds them together as they circle.

Something else like that would be two people holding on to a rope. They can spin around in circles, held together by the rope.

Suppose the people had equal mass. In that case, they both spin around the center of the rope. They orbit each other.

Suppose one is bigger than the other. The big person doesn't move as much as the little person. But they both move in a circle. The big person moves in a smaller circle.

Suppose one person is Santa Claus and the other is a very small elf. Santa would move in a very small circle, so small that it might look as if he wasn't moving at all.

The Sun and Earth are like that, only more so. A giant boulder tied to a grain of sand. Still they orbit each other. The Sun moves a tiny amount, but it does move.

So the reason the Sun is at the center is because it is so much bigger than the planets.

• your explanation and analogy helped but see, the reason the two people started spinning each other is because they both started of with tangential velocity...if when the earth was created, the earth didn't have any tangential velocity but the sun had just the right amount...would the sun orbit the earth without making the earth move towards the sun or something? – alienare 4422 Nov 27 '20 at 18:24
• If you imagine putting yourself on the centre of mass of the system, you would see both objects orbit around you. So the initial conditions are irrelevant in this case. – Phoenix87 Nov 27 '20 at 18:32
• If you start with a sun and an earth and you give the sun an angular velocity to the left... then the whole system would keep moving to the left while the earth would orbit the sun (and the sun wobbles a bit) – Kris Van Bael Nov 27 '20 at 20:11
• Here is information about the solar system when the Earth and Sun were created. en.wikipedia.org/wiki/…. Angular momentum was in the nebula from which the solar system was made. As it collapsed, rotation sped up like a spinning ice skater pulling in their arms. – mmesser314 Nov 27 '20 at 20:33

The two-body problem is to predict the motion of two massive objects which are abstractly viewed as point particles that the two objects interact only with one another. In general two planets orbit around the center of mass of the system.

In astronomy, the barycenter is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit. If one of the two orbiting bodies is much more massive than the other and the bodies are relatively close to one another, the barycenter will typically be located within the more massive object. In this case, rather than the two bodies appearing to orbit a point between them, the less massive body will appear to orbit about the more massive body, while the more massive body might be observed to wobble slightly. This is the case for the Earth-Moon system, in which the barycenter is located on average 4,671 km (2,902 mi) from Earth's center, 75% of Earth's radius of 6,378 km (3,963 mi).

To calculate the actual motion of the Sun, only the motions of the four giant planets (Jupiter, Saturn, Uranus, Neptune) need to be considered. The contributions of all other planets, dwarf planets, etc. are negligible. If the four giant planets were on a straight line on the same side of the Sun, the combined center of mass would lie about 1.17 solar radii or just over 810,000 km above the Sun's surface which is in approximate case negligible.

Reference :

Barycenter

Two body problem

Path of Earth and Moon around sun

Double Planet

To a mathematician, it is only a matter of how you choose your coordinate system. You can let the sun orbit the earth, but the physics make heliocentric easier.

format: plain


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If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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Got It game for an adult and child. How can you play so that you know you will always win?

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This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

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This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

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Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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Find the sum of all three-digit numbers each of whose digits is odd.

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There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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Replace each letter with a digit to make this addition correct.

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48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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Number problems at primary level that may require resilience.

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Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?


text:
# application method of solving D.E

• Nov 21st 2012, 12:37 PM
loolo
application method of solving D.E
hi

I need your help to solve this question :

1-

Attachment 25831

2-

Attachment 25832
• Nov 21st 2012, 12:47 PM
MarkFL
Re: application method of solving D.E
I would suggest trying the reduction of order procedure for both.
• Nov 22nd 2012, 11:06 AM
loolo
Re: application method of solving D.E
These attempts

Attachment 25844

Attachment 25845

But I can not find a second solution
• Nov 22nd 2012, 05:40 PM
Prove It
Re: application method of solving D.E
What about \displaystyle \begin{align*} y = -x^2 + 1 \end{align*}?
• Nov 22nd 2012, 07:10 PM
loolo
Re: application method of solving D.E
Quote:

Originally Posted by Prove It
What about \displaystyle \begin{align*} y = -x^2 + 1 \end{align*}?

[IMG]http://latex.codecogs.com/png.latex?\displaystyle \begin{align*} y = -x^2 + 1 \end{align*}[/IMG]?

Is the solution to the equation.

Find the second solution using this law

Attachment 25854


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# Tag Info

5

You are calculating the so-called binary cross-entropy. Let $f(\cdot)$ be a sigmoid function. The binary cross-entropy between $y$ and $f(t)$ is $$F(t,y) = H(y,f(t)) = -y\log f(t) - (1-y)\log(1-f(t)).$$ When you compute the partial derivative of $F(t,y)$ with respect to $t$, you get: $$\frac{\partial F(t,y)}{\partial t} = f(t) - y$$ You reach ...

5

We often take the logarithm because: Maximizing $\log \Phi(x)$ is equivalent to maximizing $\Phi(x)$, so in maximum-likelihood problems, we can maximize the log of the likelihood instead of maximizing the likelihood directly and the result will be equivalent. The logarithm converts multiplication to addition, and the derivative of a sum is "nicer" than the ...

5

If you're only changing the weights in the last layer, then effectively you have a neural network with a single layer, preceded by some preprocessing step. Single-layer neural networks (also known as perceptrons) aren't so powerful. Why isn't the network learning anything? It doesn't learn much because it can't -- a single-layer network can't learn ...

4

You are right. While you could backpropagate for all samples and then update the weights, you don't have to. Alternatively, you can iterate through the samples and, for each sample, backpropagate for just that sample and then update the weights. The latter turns out to be more effective (empirically). It is called stochastic gradient descent. Today, ...

4

You can't. The optimal solution is not well-defined. In general there will be a range of tradeoffs between minimizing time and uncompressed size, and you haven't specified anything that would allow uniquely identifying which you want. Your first step is that you need to specify a single objective function, where the goal is to find a solution that ...

4

There is no universal learning rate. It depends on your problem space (Are you solving a problem with many local minima or just one? Does your problem’s solution vary dramatically based on a slight change to your input or does the solution gradually shift?, etc.), and it depends on your network architecture (number of layers, number of hidden layers. Do you ...

4

The cost function $C(w,\lambda)$ is not a function of learning rate $\eta$. You can't compute the gradient of $\eta$. $\lambda$ is part of the cost function. You can indeed compute its gradient and apply SGD on $\lambda$. However, when you do that, $\lambda$ will keep decreasing because its optimal value is obviously $-\infty$. Note that it is possible to ...

3

You say you want to understand how $\lambda$ and $\eta$ affect the cost function. If you hold the weights $w$ fixed, the equation for $C$ tells you how $\lambda$ affects the cost function, and $\eta$ doesn't affect the cost function; it only affects the sequence of steps taken by gradient descent. But the tricky thing is that the final weights $w$ depend ...

3

I just found out the answer and it's actually pretty simple: while there is a good linear policy for the mountain car task, the value function itself is non-linear. The state space of this task is like a spiral, and there is no linear approximation possible even for a mediocre value function. If you increase the value for going right and reaching the top, ...

3

I guess $f_2(x)$ is some sort of oracle that tells you if $\Phi_2(x)$ is greater than $t$? If the set $\{\mathbf{x} : \Phi_2(x) \le t\}$ is convex, then I think projected gradient algorithm might be helpful. Could you provide more information on $\Phi_2(x)$? The question is kinda confusing with the information provided.

2

Big yes. In fact, gradient descent is one of the fundamental tools used by many supervised learning models. You can check out a very nice docs page about how it is used in scikit-learn.

2

This is known as stochastic gradient descent. I suggest you read some background material on stochastic gradient descent; then I think you will understand. There is lots written on that subject in many standard places. Compare: In standard gradient descent, we let $E(w)$ denote the total error across all training samples (as a function of the weights $w$)...

2

Just concatenate all of the variables into a single, long vector. In your case, you'll have a $2n$-dimensional vector: $$v = (v_{1,x},v_{1,y},v_{2,x},v_{2,y},\dots,v_{n,x},v_{n,y})$$ where $v_{i,x}$ is the x-coordinate of $v_i$ and $v_{i,y}$ is the y-coordinate of $v_i$. Now treat this as a function of $v$, i.e., f(v) = \sum_{i,j} (||v_i - v_j|| - d_{...

2

You would have to look at multiobjective optimisation, with these methods you can optimise two functions at the same time. Just be aware that, depending on the method that you end up using, you might have in the end a number of solutions equally good (trade offs) which you would have to choose from.

2

First of all, if we have a descent direction, we can always find a step size $\tau$ that is arbitrary small, such that "the sufficient descent criterion" is satisfied (see the Wikipedia article 'Backtracking line search'). This essentially rules out the infinite loop issue. For example, consider Armijo condition as "the sufficient descent ...

1

That's correct. The derivative of $x_2$ with respect to $x_1$ is 0. A little context: with words like derivative and slope, you are describing how gradient descent works in one dimension (with only one feature / one value to optimize). In multiple dimensions (multiple features / multiple variables you are trying to optimize), we use the gradient and update ...

1

No, there are no guarantees. SGD finds a local optimum but not a global optimum, and the solution it finds can be arbitrarily bad, if you have an unfriendly objective function. The only results I've seen that provide guarantees start from strong assumptions about the objective function (e.g., convexity).

1

The relative performance of different optimization algorithms depends a lot on the particular function you are minimizing. We certainly can't tell you whether it is really that good for your particular function without knowing what specific objective function you are looking at, but it certainly seems possible to me. There are some functions where Newton's ...

1

Actually, derivative methods such as random search shorten the time allocated for function evaluation if the problem is big. On the other hand, derivative-free methods take much time to complete function evaluation that leads to a dramatic increase in optimization time.

1

If you overshoot by 10% you are fine, for example if the solution is 0 and the starting value 1000, you go to -100, +10, -1, +0.1 etc. If you overshoot by 80%, you converge but much smaller. If you overshoot by 110% you go from 1,000 to -1,100, +1,210, -1,331 etc. - divergence.

Only top voted, non community-wiki answers of a minimum length are eligible


text:
Homework Help: Calculate acceleration of a ship fired from a cannon

Tags:
1. Jan 23, 2015

hgducharme

1. The problem statement, all variables and given/known data
Jules Verne
In his novel From the Earth to the Moon (1866), Jules Verne describes a spaceship that is blasted out of a cannon, called the Columbiad, with a speed of 12,000 yards/s. The Columbiad is 900 ft long, but part of it is packed with powder, so the spaceship accelerates over a distance of only 700 ft. Estimate the acceleration experienced by the occupants of the spaceship during launch.

v0 = 10,975.60976 m/s
a = ?
d = 213.4146341 m

2. Relevant equations

1) $x= x_0+v_0t+\frac{1}{2}at^2$
2) $v^2 = v_o^2 + 2a\Delta x$

3. The attempt at a solution
I tried solving the second equation, but I got an insane number that isn't plausible. My main problem is what should I consider V0, is it 0 or is it the 10,975 m/s? If I set it to 0, then i'm only calculating the acceleration from at rest to as soon as it leaves the cannon's barrel. Otherwise, if I set it to the 10,975 m/s, then I don't know the final velocity after accelerating for 213.4 m. Also, would the acceleration be considered as $-9.8\frac{m}{s^2}$?

Last edited: Jan 23, 2015
2. Jan 23, 2015

Staff: Mentor

The initial velocity is zero, the final velocity 12,000 yards/s. The distance over which the capsule accelerates is 700 ft.

Remember, this is fiction...

3. Jan 23, 2015

Staff: Mentor

initial speed before the charge is lit is zero

final speed you know
distance over which it accelerates is given

find acceleration (the assumption is that acceleration is uniform)

4. Jan 23, 2015

hgducharme

Haha, yes I picked up on that. They would have the speed to get past LEO after 213m.

So are you saying the final velocity is 12,000 yards/s AFTER the 213m uniformed acceleration?

5. Jan 23, 2015

Staff: Mentor

Yes, of course. That's how canon's work. The acceleration takes place while the projectile is within the barrel.

6. Jan 23, 2015

hgducharme

Ok, I still can't seem to figure out what i'm doing wrong. Here's my work:

$v^2 = v_0^2 + 2a\Delta x$ Solving for $a$ gives me:

$\frac{v^2 - v_0^2}{2\Delta x} = a$ Plug in my values:

$\frac{(12,000 yds/s)^2}{2(233.34 yds)} = a$ Simplify:

$\frac{144,000 yds/s}{466.67 yds} = a$

$308.57 s = a$

Some how I end up with only seconds as my unit. I assume I'm using the wrong formula?

Edit: Ahhhhh, nevermind. I forgot to square my units in the numerator!

7. Jan 23, 2015

Staff: Mentor

$\left(\frac{yd}{s}\right)^2 = \frac{yd^2}{s^2}$ right?

And check the order of magnitude for your yards squared. You've lost several.

8. Jan 23, 2015

hgducharme

Yes, I just caught that, thank you


text:
# What Makes a Dialog Agent Useful?

## The techniques behind ChatGPT: RLHF, IFT, CoT, Red teaming, and more

A few weeks ago, ChatGPT emerged and launched the public discourse into a set of obscure acronyms: RLHF, SFT, IFT, CoT, and more, all attributed to the success of ChatGPT. What are these obscure acronyms and why are they so important? We surveyed all the important papers on these topics to categorize these works, summarize takeaways from what has been done, and share what remains to be shown.

Let’s start by looking at the landscape of language model based conversational agents. ChatGPT is not the first, in fact many organizations published their language model dialog agents before OpenAI, including Meta’s BlenderBot, Google’s LaMDA, DeepMind’s Sparrow, and Anthropic’s Assistant (a continued development of this agent without perfect attribution is also known as Claude). Some groups have also announced their plans to build a open-source chatbot and publicly shared a roadmap (LAION’s Open Assistant); others surely are doing so and have not announced it.

The following table compares these AI chatbots based on the details of their public access, training data, model architecture, and evaluation directions. ChatGPT is not documented so we instead share details about InstructGPT which is a instruction fine-tuned model from OpenAI that is believed to have served as a foundation of ChatGPT.

LaMDA BlenderBot 3 Sparrow ChatGPT/ InstructGPT Assistant
Org Google Meta DeepMind OpenAI Anthropic
Access Closed Open Closed Limited Closed
Size 137B 175B 70B 175B 52B
Pre-trained
Base model
Unknown OPT Chinchilla GPT-3.5 Unknown
Pre-training corpora size (# tokens) 2.81T 180B 1.4T Unknown 400B
Model can
access the web
✖ ✖
Supervised
fine-tuning
Fine-tuning
data size
Quality:6.4K
Safety: 8K
Groundedness: 4K
IR: 49K
20 NLP datasets ranging from 18K to 1.2M Unknown 12.7K (for InstructGPT, likely much more for ChatGPT) 150K + LM generated data
RLHF ✖ ✖
Hand written rules for safety ✖ ✖
Evaluation criteria 1. Quality (sensibleness, specificity, interestingness)
2. Safety (includes bias) 3. Groundedness
1, Quality (engagingness, use of knowledge)
2. Safety (toxicity, bias)
2. Evidence (from web)
3. Rule violation
4. Bias and stereotypes
5. Trustworthiness
2. Bias
2. Bias
Crowdsourcing platform used for data labeling U.S. based vendor Amazon MTurk Unknown Upwork and Scale AI Surge AI, Amazon MTurk, and Upwork

We observe that albeit there are many differences in the training data, model, and fine-tuning, there are also some commonalities. One common goal for all the above chatbots is instruction following , i.e., to follow user-specified instructions. For example, instructing ChatGPT to write a poem on fine-tuning.

### From prediction text to following instructions:

Usually, the language-modeling objective of the base model is not sufficient for a model to learn to follow a user’s direction in a helpful way. Model creators use Instruction Fine-Tuning (IFT) that involves fine-tuning the base model on demonstrations of written directions on a very diverse set of tasks, in addition to classical NLP tasks of sentiment, text classification, summarization etc. These instruction demonstrations are made up of three main components — the instruction, the inputs and the outputs. The inputs are optional, some tasks only require instructions such as open-ended generation as in the example above with ChatGPT. A input and output when present form an instance. There can be multiple instances of inputs and outputs for a given instruction. See below for examples (taken from [Wang et al., ‘22]).

Data for IFT is usually a collection of human-written instructions and instances of instructions bootstrapped using a language model. For bootstrapping, the LM is prompted (as in the figure above) in a few-shot setting with examples and instructed to generate new instructions, inputs, and outputs. In each round, the model is prompted with samples chosen from both human-written and model generated. The amount of human and model contributions to creating the dataset is a spectrum; see figure below.

On one end is the purely model-generated IFT dataset such as Unnatural Instructions (Honovich et al., ‘22) and on the other is a large community effort of hand-crafted instructions as in Super-natural instructions (Wang et al., ‘22). In between these two are works on using a small set of high quality seed dataset followed by bootstrapping such as Self-instruct (Wang et al., 22). Yet another way of collating a dataset for IFT is to take the existing high-quality crowdsourced NLP datasets on various tasks (including prompting) and cast those as instructions using a unified schema or diverse templates. This line of work includes the T0 (Sanh et al., ‘22), Natural instructions dataset (Mishra et al., ‘22), the FLAN LM (Wei et al., ‘22), and the OPT-IML (Iyer et al.,’22).

### Safely following instructions

Instruction fine-tuned LMs, however, may not always generate responses that are helpful and safe. Examples of this kind of behavior include being evasive by always giving a unhelpful response such as “I’m sorry, I don’t understand. ” or generating an unsafe response to user inputs on a sensitive topic. To alleviate such behavior, model developers use Supervised Fine-tuning (SFT), fine-tuning the base language model on high-quality human annotated data for helpfulness and harmlessness. For example, see table below taken from the Sparrow paper (Appendix F).

SFT and IFT are very closely linked. Instruction tuning can be seen as a subset of supervised fine-tuning. In the recent literature, the SFT phase has often been utilized for safety topics, rather than instruction-specific topics, which is done after IFT. In the future, this taxonomy and delineation should mature into clearer use-cases and methodology.

Google’s LaMDA is also fine-tuned on a dialog dataset with safety annotations based on a set of rules (Appendix A). These rules are usually pre-defined and developed by model creators and encompass a wide set of topics including harm, discrimination, misinformation.

### Fine-tuning the models

On the other hand, Open AI’s InstructGPT, DeepMind’s Sparrow, and Anthropic’s Constitutional AI use human annotations of preferences in a setup called reinforcement learning from human feedback (RLHF). In RLHF, a set a model responses are ranked based on human feedback (e.g. choosing a text blurb that is preferred over another). Next, a preference model is trained on those annotated responses to return a scalar reward for the RL optimizer. Finally, the dialog agent is trained to simulate the preference model via reinforcement learning. See our previous blog post on RLHF for more details.

Chain-of-thought (CoT) prompting (Wei et al., ‘22) is a special case of instruction demonstration that generates output by eliciting step-by-step reasoning from the dialog agent. Models fine-tuned with CoT use instruction datasets with human annotations of step-by-step reasoning. It’s the origin of the famous prompt, let’s think step by step. The example below is taken from Chung et al., ‘22. The orange color highlights the instruction, the pink color shows the input and the output, and the blue color is the CoT reasoning.

Models fine-tuned with CoT have shown to perform much better on tasks involving commonsense, arithmetic, and symbolic reasoning as in Chung et al., ‘22.

CoT fine-tuning have also shown to be very effective for harmlessness (sometimes doing better than RLHF) without the model being evasive and generating “Sorry, I cannot respond to this question,” for prompts that are sensitive as shown by Bai et al.,’22. See Appendix D of their paper for more examples.

## Takeaways:

1. You only need a very tiny fraction of data for instruction fine-tuning (order of few hundreds) compared to the pre-training data.
2. Supervised fine-tuning uses human annotations to make model outputs safer and helpful.
3. CoT fine-tuning improves model performance on tasks requiring step-by-step thinking and makes them less evasive on sensitive topics.

## Next steps for dialogue agents

This blog summarizes many of the existing work on what makes a dialog agent useful. But there are still many open questions yet to be explored. We list some of them here.

1. How important is RL in learning from human feedback? Can we get the performance of RLHF with training on higher quality data in IFT or SFT?
2. How does SFT+ RLHF as in Sparrow compare to just using SFT as in LaMDA for safety?
3. How much pre-training is necessary, given that we have IFT, SFT, CoT, and RLHF? What are the tradeoffs? What are the best base models people should use (both those publicly available, and not)?
4. Many of the models referenced in this paper have been carefully engineered with red-teaming, where engineers specifically search for failure modes and influence future training (prompts and methods) based on unveiled issues. How do we systematically record the effects of these methods and reproduce them?

PS: Please let us know if you find any information in this blog missing or incorrect.

Citation

Rajani et al., "What Makes a Dialog Agent Useful?", Hugging Face Blog, 2023.

BibTeX citation:

@article{rajani2023ift,
author = {Rajani, Nazneen and Lambert, Nathan and Sanh, Victor and Wolf, Thomas},
title = {What Makes a Dialog Agent Useful?},
journal = {Hugging Face Blog},
year = {2023},
note = {https://huggingface.co/blog/dialog-agents},
}


text:
# Interpret your lang, but not yourself?

There are many challenges that say "interpret X", where X is a simple language. In my opinion, that is way too boring. To give all the procrastinating people on the internet something interesting to do, you can try to do this challenge:

## Challenge

Choose a language $LANG. $LANG can be any turing complete programming language or a turing complete subset of a programming language. Beware that if you omit a feature of your language in $LANG for interpretation, you must not use it for your own program, too, since your submission must be written in $LANG, too.

Write a compiler / interpreter for $LANG written in $LANG. You may use all facilities (including eval and friends) of your language that are available to write this compiler. To make the task more challenging, there is one restriction: You program should be able to interpret / compile all valid programs of $LANG except your interpreter / compiler itself. If it occurs that the program to be interpreted / compiled is your interpreter or compiler itself (regardless of the filename), your program should do something completely unrelated to the functionality of an interpreter or compiler (such as barfing or printing Hello, world!). To make this task even more complex, your program must not read its own source when compiling or interpreting. ## Specifications • This task is code golf. The submission with the least characters that is correct wins. In case of a tie, the solution that was submitted first wins. • Your program / script should read the program to be interpreted from a file. You may hardcode its path and name. When the file is read, you may either compile the file to another file (That must be executable on your system) or run it directly. If $LANG lacks file-reading capabilities, you can choose another way to read in the code that fits $LANG. You may not choose $LANG as a subset of another language but with file-reading capabilites removed.
• Usual code-golf rules apply. That is: your personal pet-language that you made up just to solve this challenge is forbidden, if the solution becomes trivial using it (Such as defining a single-char program that exactly implements the solution). Abuse of rules is encouraged.
• Are we allowed to define a language for this, so long as it's turing complete? – Cruncher Dec 19 '13 at 14:20
• @Cruncher Yes, you are. See the last bullet point of the specifications for more details. – FUZxxl Dec 19 '13 at 23:10

## Ruby, 63

b=$<.read t="b=$<.read\nt=%p\nb!=t%%t&&eval(b)"
b!=t%t&&eval(b)

• Answer accepted as long as there is no smaller solution. – FUZxxl Dec 7 '11 at 19:53

### Perl, 89 chars, no cheating

$_=q($_=q(Q);s/Q/$_/;($q=join"",<>)eq$_?die:eval$q);s/Q/$_/;($q=join"",<>)eq$_?die:eval$q

Note that this code is extremely picky about what counts as "itself". In particular, it will not recognize itself if there are any trailing newlines or other extra whitespace in the input. To test it, save it into a file named (for example) unquine.pl and do this:

$perl unquine.pl unquine.pl Died at unquine.pl line 1, <> line 1.  Remember, the unquine.pl file should be exactly 89 bytes long, no more, no less. Running it with some other Perl script as input just executes the other script, as it should: $ perl unquine.pl hello.pl
Hello, world!

As the name might suggest, the implementation is based on a quine — specifically, this one:

$_=q($_=q(Q);s/Q/$_/);s/Q/$_/

This code sets $_ equal to itself; the rest of the program (which, of course, must be duplicated inside $_) just compares $_ to the input, dies if they match and evaluates the input otherwise. • You can replace that &&/; pair with a ternary (one char off, doubled by quining). Great idea and implementation! – J B Dec 5 '11 at 10:35 • @JB: Good catch! Down to 89 chars now. – Ilmari Karonen Dec 5 '11 at 13:39 # GolfScript, 30 chars {".~"+"#{$<.read}".@=!{~}*}.~

This program reads the contents of a file named on the command line and, if it does not exactly equal the code above, interprets it as GolfScript. If the input is exactly equal to the code above, it will simply be printed unchanged (except for a newline appended to the end).

This is a fairly straightforward adaptation of this self-identifying program. Specifically:

• { } is a code block literal in GolfScript.
• .~, applied to a code block, duplicates the block and executes the copy.

Inside the code block:

•  stringifies the copy of the code block.
• ".~"+ appends the characters .~ to it, yielding a string containing the source code of the program.
• "#{$<.read}" is a documented hack that allow the execution of Ruby code within GolfScript. In this case, it executes the Ruby statement $<.read (shamelessly stolen from Lowjacker's Ruby solution), which reads and returns the contents of any files specified on the command line. This hack is needed because GolfScript itself provides no explicit file I/O capabilities.
• .@ duplicates and shuffles the elements on top of the stack so that the stack contains two copies of the file contents followed by the source code of this program.
• =! compares the top two items on the stack (i.e. the file contents and the source), returning 1 if they are different and 0 if they are the same.
• {~}* evaluates the remaining copy of the file contents as GolfScript code, but only if the result of the comparison is 1. (Technically, it executes the code block {~} as many times as given by the number on the stack, i.e. 0 or 1 times. Inside the block, ~ is the GolfScript eval operator.)

Ps. If reading the code to execute from stdin is allowed, this challenge can be solved in 21 characters without having to shell out to Ruby:

{".~"+1$=!{""\~}*}.~  This program will read an input string from stdin and, if it does not match its own source, executes it (with an empty input). Like the program above, input that does match the source is simply echoed back. • Looks nice, but it doesn't seem like you read input from a file. – FUZxxl Sep 5 '14 at 7:45 • Fixed, now it reads from a file (exactly) like Lowjacker's solution. – Ilmari Karonen Sep 5 '14 at 14:40 # Python, 167130 118 bytes This is my first attempt at golfing, so here goes! It interprets any program except itself Improved version: i=open(raw_input()).read();q='i=open(raw_input()).read();q=%s;i==q%%repr(q)and a;exec(i)\n';i==q%repr(q)and a;exec(i)  If it gets itself then it barfs with: Traceback (most recent call last): File "pygolf.py", line 1, in <module> i=open(raw_input()).read();q='i=open(raw_input()).read();q=%s;i==q%%repr(q)and a;exec(i)\n';i==q%repr(q)and a;exec(i) NameError: name 'a' is not defined  I think this solution works pretty much the same way as Ilmari Karonen's, the basic idea is something like: input = read_some_file() if input == some_quine() barf() interpret(input)  The quine I used was based on this one: (lambda x: x + repr((x,)))('(lambda x: x + repr((x,)))',)  But I since realized a much shorter quine is: q='q=%s;q%%repr(q)';q%repr(q)  And that can be even shorter if you allow the interactive python shell, in which case you can do: '%s;_%%repr(_)';_%repr(_)  Since python doesn't have a short way to get command line args, I went with raw_input() (which is still pretty long, but not as long as import sys;sys.argv[1]  Usage is: echo "foobar.py" | python quinterpretter.py  or python quinterpretter.py <type filename and hit enter>  I found a shorter quine to use, but here is my old version (for posterity): i=open(raw_input()).read();a if i==(lambda x,y:x+repr((x,y))+y)('i=open(raw_input()).read();a if i==(lambda x,y:x+repr((x,y))+y)', ' else 1;exec(i)\n') else 1;exec(i)  • Replace the %s with %r and remove the repr. %r means raw and it's basically he same thing. – Loovjo Jun 6 '15 at 9:05 I can't exactly read from a file using Javascript (ok, I could, using the HTML5 FileReader thing, but that makes things a lot more complicated than I need). So, this is a function that accepts a Javascript program as a string and runs it. This probably isn't as golfed as it could be, but here it is anyway: # Javascript, 252 function c(p){q='\"';s='\\';a="function c(p){q='\"';s='\\';a=%;a=a.slice(0,17)+s+a.slice(17,24)+a[23]+a.slice(24);a=q+a.replace('%',q+a+q)+q;alert(a);}";a=a.slice(0,17)+s+a.slice(17,24)+a[23]+a.slice(24);a=a.replace('%',q+a+q);alert(a);if(p!=a)eval(p)}  Let me know if anybody knows a better technique for forming a quine in Javascript. • I posted a 135-char JS solution below, based on your code and my Perl solution. +1 for the inspiration! – Ilmari Karonen Dec 5 '11 at 14:51 read p<p;read c<c;[ "$p" = "$c" ]||. ./c  45 characters of sh (POSIX shell). The code to be run must be in the file ./c. The code for the interpreter itself must be in the file ./p, so I guess I kind of cheated, although the challenge doesn't seem to forbid it. Or would this disqualify my "language" from being a "turing-complete programming language"? Using a tool that's normally an external executable, but might theoretically be built into the shell, the code can be shortened: cmp -s p c||. ./c  That's 18 characters, and the -s bit is just to suppress a line that would otherwise always be printed for valid (non-self) programs. And then you can always build a version of the shell language that does the above with more concise syntax. And then you can always build a program that, when the input consists of a single '.' --or hell, the empty string-- evaluates the contents of another file as normal code, and call this a programming language. So the empty string would be your solution to the challenge, in the language you built. In fact, here's an interpreter for such a language: read code; if [ "$code" ]; then eval "$code"; else . ./othercode; fi  Using the language the above script interprets, the solution is the empty string. And the code location needn't be hardcoded anymore. Problem? • The challenge does say that "your program must not read it's own source". – Ilmari Karonen Dec 4 '11 at 22:13 • Darnit, wasted some time then. And I see it even says you mustn't use features that you will omit. This would go against the empty string feature. Then again, the interpreter must be omitting/changing functionality if the code for the compiler/interpreter itself causes different behaviour in the new language. In any case, i had fun writing fallacy. – TaylanUB Dec 4 '11 at 22:25 • @TaylanUB Well, you actually have to interpret all valid$lang programs except the interpreter itself. – FUZxxl Dec 4 '11 at 22:29
• @FUZxxl Yes, the "sh + empty string" language is otherwise equivalent to sh (if the code is not the empty string), and the empty string program written in it also interprets sh code (which must be put in ./othercode), and does nothing when the code is the empty string. I shouldn't have called the file ./othercode, it's misleading; it's just the code that the interpreter written in the empty string language will interpret. – TaylanUB Dec 4 '11 at 22:34

### JavaScript, 135 chars

function c(p){q='function c(p){q=%27Q%27;p!=unescape(q).replace(/Q/,q)?eval(p):alert()}';p!=unescape(q).replace(/Q/,q)?eval(p):alert()}

Peter Olson's JavaScript solution inspired me to try porting my Perl solution to JS. Like his solution, this code defines a function c that accepts a string, and evals it if it's not equal to the code above.

It took me a while to figure out a good way to deal with the absence of balanced string delimiters in JavaScript, until I found what in hindsight is the obvious solution: unescape().

Conveniently, my code doesn't contain any backslashes or double quotes, so it can be safely stored in a double quoted strings. This makes it easy to test:

e = "function c(p){q='function c(p){q=%27Q%27;p!=unescape(q).replace(/Q/,q)?eval(p):alert()}';p!=unescape(q).replace(/Q/,q)?eval(p):alert()}"

eval(e)  // defines the function c()

c(h)     // evaluates h

• You could replace alert() with 0 to make it not do anything instead of alerting undefined and save 13 chars. – Peter Olson Dec 5 '11 at 14:56
• @PeterOlson: Yeah, but the task does say that "your program should do something completely unrelated" if it detects itself. I interpret that as meaning that it should do something -- preferably something visible to the user, I'd presume. Besides, I just like it better this way. :) (Ps. Yay, it's snowing outside! Winter's finally here!) – Ilmari Karonen Dec 5 '11 at 15:03
• @Ilmari Doing nothing is unrelated to interpreting Javascript IMHO. – FUZxxl Dec 5 '11 at 21:43
• You could go p=>... instead of function c(p) – FireCubez Oct 7 '18 at 20:22

# Common Lisp, 59

#+~ #.(#:a)(defun L(p)(compile-file p))(push :~ *features*)

• In a fresh Lisp REPL, compile your file (e.g. sbcl --load)
• You now have a function L, which can compile Common Lisp files
• However, if you call (L <your file>), an error is signaled while reading the file.

### Why?

Because the first time, you pushed the :~ keyword into *features*. Now, your environment knows about the ~ feature, and the reader macro #+, upon evaluating the ~ feature expression, will succeed and read the following form instead of skipping it as it did the first time. In your file, the following form is #.(#:a), which asks to evaluate (#:a) at read-time and use the resulting value as the code being read. But (#:a) calls the function associated with the uninterned symbol #:a. Since #:a is uninterned, it is a fresh symbol which is not bound to any function (i.e. not fboundp). Error.

# Scheme, 48 or 51 characters

Scheme is a language with many different implementations. Despite implementations having to conform to the latest RnRS, the latest working standard (R6RS) has been unpopular due to its lack of minimalism. R7RS is soon to be released as a remedy, while splitting the language in 2. The first language being powerful and minimalistic and the second, a superset of the first intended to provide feature extensions for interoperability between implementations. Until then, we rely on SRFIs (Scheme Requests For Implementation), which provide (if implemented in the host implementation or manually (as is common in scheme)) a means to portably accomplish common tasks. All this to say that the first code snippet (51 characters), while remaining as portable as it can, relies on SRFI-22 (executing scheme scripts in UNIX) for access to command-line arguments:

(define(main x y)(case y(x => error)(else => load)))

(define (main current-file arg)
(case arg
[current-file => error]

The second (48 characters) is an file-less means to interpretation which cannot evaluate itself (in a null environment):

(define(e)(write(eval(read)null-environment))(e))

(define (interpret)
(interpret))

• Your code does not work if you copy your interpreter. – FUZxxl Dec 12 '11 at 5:49
• Leave it to a scheme answer to contain nested parentheticals in its prose. – Cyoce Apr 5 '16 at 7:21

# Groovy, 13 bytes

{Eval.me(it)}

This should interpret a subset of Groovy.

test cases:

p={Eval.me(it)}

p'''
(0..37).each{println"1234567890JIHGFEDCBAKLMNOPQRST!?,.ZYXWVU"[it..it+2]}
'''

p'''
{Eval.me(it)}
'''

Unfortunately while it certainly barfs, it does so in a completely interpreter-like way, and it does it for quite a lot of input.

• In which line do you read the program to be interpreted? Your code is interesting although it is not a valid submission for this task. – FUZxxl Dec 5 '11 at 18:23
• I assume the error is something like "recursion limit exceeded"? – Ilmari Karonen Dec 6 '11 at 0:50

# Javascript ES6, 45 bytes

$=(_=prompt())=>eval(_==$=${$};$()?0:_);$()
`

Still competitive! (thx @Downgoat)

• – Mama Fun Roll Apr 5 '16 at 6:49
• Ah, I was going off of the standard's release. I didn't know there was a working implementation in 2011. You might want to include an explanation and a link to the commit in the answer text. – Mego Apr 5 '16 at 6:50


text:
Due to technical problems on the CERN SSO system, logging in is currently failing for many users. Details on the SSB

ICRC2015

July 29, 2015 to August 6, 2015
World Forum
Europe/Amsterdam timezone

Search for point-like neutrino sources over the Southern Hemisphere with the ANTARES and IceCube neutrino telescopes

Aug 3, 2015, 2:00 PM
15m
Yangtze 1 (World Forum)

Yangtze 1

World Forum

Churchillplein 10 2517 JW Den Haag The Netherlands
Oral contribution NU-EX

Speaker

Javier Barrios Martí (IFIC - CSIC)

Description

A search for cosmic neutrino point-like sources using the ANTARES and IceCube neutrino telescopes over the Southern Hemisphere is presented. The ANTARES data was collected between January 2007 and December 2012, whereas the IceCube data ranges from April 2008 to May 2011. Clusters of muon neutrinos over the diffusely distributed background have been looked for by means of an unbinned maximum likelihood maximisation. This method is used to search for an excess of events over the whole Southern Hemisphere assuming an E$^{-2}$ source spectrum. A search over a pre-selected list of candidate sources has also been carried out for different source assumptions: spectral indices of 2.0 and 2.5, and energy cutoffs of 1 PeV, 300 TeV and 100 TeV. No significant excess over the expected background has been found, and upper limits for the candidate sources are presented compared to the individual experiments.
Registration number following "ICRC2015-I/" 558 ANTARES


text:
schedula is a dynamic flow-based programming environment for python, that handles automatically the control flow of the program. The control flow generally is represented by a Directed Acyclic Graph (DAG), where nodes are the operations/functions to be executed and edges are the dependencies between them.

The algorithm of schedula dates back to 2014, when a colleague asked for a method to automatically populate the missing data of a database. The imputation method chosen to complete the database was a system of interdependent physical formulas - i.e., the inputs of a formula are the outputs of other formulas. The current library has been developed in 2015 to support the design of the CO2MPAS tool - a CO2 vehicle simulator. During the developing phase, the physical formulas (more than 700) were known on the contrary of the software inputs and outputs.

## 1.1. Why schedula?¶

The design of flow-based programs begins with the definition of the control flow graph, and implicitly of its inputs and outputs. If the program accepts multiple combinations of inputs and outputs, you have to design and code all control flow graphs. With normal schedulers, it can be very demanding.

While with schedula, giving whatever set of inputs, it automatically calculates any of the desired computable outputs, choosing the most appropriate DAG from the dataflow execution model.

Note

The DAG is determined at runtime and it is extracted using the shortest path from the provided inputs. The path is calculated based on a weighted directed graph (dataflow execution model) with a modified Dijkstra algorithm.

schedula makes the code easy to debug, to optimize, and to present it to a non-IT audience through its interactive graphs and charts. It provides the option to run a model asynchronously or in parallel managing automatically the Global Interpreter Lock (GIL), and to convert a model into a web API service.

## 1.2. Dataflow Execution Model¶

The Dispatcher is the main model of schedula and it represents the dataflow execution model of your code. It is defined by a weighted directed graph. The nodes are the operations to be executed. The arcs between the nodes represent their dependencies. The weights are used to determine the control flow of your model (i.e. operations’ invocation order).

Conceptually, when the model is executed, input-data flows as tokens along the arcs. When the execution/dispatch() begins, a special node (START) places the data onto key input arcs, triggering the computation of the control flow. The latter is represented by a Directed Acyclic Graph (DAG) and it is defined as the shortest path from the provided inputs. It is computed using the weighted directed graph and a modified Dijkstra algorithm. A node is executed when its inputs and domain are satisfied. After the node execution, new data are placed on some or all of its output arcs. In presence of cycles in the graph, to avoid undesired infinite loops, the nodes are computed only once. In case of an execution failure of a node, the algorithm searches automatically for an alternative path to compute the desired outputs. The nodes are differentiated according to their scope. schedula defines three node’s types:

• data node: stores the data into the solution. By default, it is executable when it receives one input arch.
• function node: invokes the user defined function and place the results onto its output arcs. It is executable when all inputs are satisfied and it has at least one data output to be computed.
• sub-dispatcher node: packages particular dataflow execution model as sub component of the parent dispatcher. Practically, it creates a bridge between two dispatchers (parent and child) linking some data nodes. It allows to simplify your model, reusing some functionality defined in other models.

The key advantage is that, by this method, the scheduling is not affected by the operations’ execution times. Therefore, it is deterministic and reproducible. Moreover, since it is based on flow-based programming, it inherits the ability to execute more than one operation at the same time, making the program executable in parallel. The following video shows an example of a runtime dispatch.


text:
# How do you solve 9-3/(1/3)+1?

Aug 21, 2016

1

#### Explanation:

Consider $\frac{3}{\frac{1}{3}}$

Write as $3 \div \frac{1}{3}$

Turn the $\frac{1}{3}$ upside down and multiply

$3 \times \frac{3}{1} = 9$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all back together

$9 - 9 + 1$

$= 0 + 1$

$= 1$

May 31, 2017

Explaining why you turn upside down (invert) and multiply when dividing fractions.

$\textcolor{m a \ge n t a}{\text{Explanation part 1 of 2}}$

#### Explanation:

Very important facts:

$\textcolor{b l u e}{\text{Fact 1: }}$A fraction's structure consists of:

$\left(\text{count")/("size indicator of what you are counting")" "->" "("numerator")/("denominator}\right)$

$\textcolor{b l u e}{\text{Fact 2: }}$ You can not DIRECTLY DIVIDE the counts in a fraction unless the 'size indicators' are the same.

$\textcolor{b l u e}{\text{Fact 3: }}$ When dividing the counts and the 'size indicators' are not the same the shortcut process includes an adjustment factor. This adjustment factor converts the answer to that which you would obtain if you had made the 'size indicators' the same before you applied the division.

$\textcolor{b l u e}{\text{Fact 4: }}$ Multiply by 1 and you do not change an intrinsic value. However, 1 comes in many forms so you can change the way a fraction looks without changing its intrinsic value.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Demonstration of principle}}$

Using numbers that we should be familiar with:

Consider $\frac{1}{2} \div \frac{1}{4} = 2$

Making the adjustment before the division

color(green)([1/2color(blue)(xx1)]color(magenta)(-:1/4)=2

color(green)([1/2color(blue)(xx2/2)]color(magenta)(-:1/4)=2

color(green)([2/4]color(magenta)(-:1/4)=2

Now you can directly divide the top numbers (numerators)

color(green)(2color(magenta)(-:1)=2
................................................................
Just for interest lets look at the shortcut method applied to $\frac{2}{4} \div \frac{1}{4}$

Turn the $\frac{1}{4}$ upside down and multiply

$\text{ } \textcolor{g r e e n}{\frac{2}{4} \times \textcolor{m a \ge n t a}{\frac{4}{1}} = 2}$

Using the principle that $a \times b$ is the same answer as $b \times a$
$\text{ } \to 2 \times 3 = 6 = 3 \times 2$

Write $\textcolor{g r e e n}{\frac{2}{4} \times \textcolor{m a \ge n t a}{\frac{4}{1}} = 2}$ as:

$\text{ } \textcolor{g r e e n}{\frac{2}{\textcolor{m a \ge n t a}{1}} \times \frac{\textcolor{m a \ge n t a}{4}}{4} = 2}$

$\text{ } 2 \times 1 = 2$
$\text{ } \textcolor{o l i v e g}{\uparrow}$
$\textcolor{o l i v e}{\text{Think of dividing the 'size indicators' as an adjustment factor.}}$
In this case the adjustment factor is 1 as both of the denominators are the same.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

May 31, 2017

Explaining why you turn upside down (invert) and multiply when dividing fractions.

$\textcolor{m a \ge n t a}{\text{Explanation part 2 of 2}}$

#### Explanation:

Lets look at the shortcut method where the denominators (size indicators) are not the same.

Consider the example: $\frac{3}{5} \div \frac{1}{10} = 6$

It is known that there are $\textcolor{b r o w n}{\underline{| \overline{\textcolor{w h i t e}{\frac{2}{2}} 2 \text{ } |}}}$ of $\frac{1}{10}$ in $\frac{1}{5}$

Applying the rule 'turn upside down and multiply' we have:

$\textcolor{g r e e n}{\frac{3}{5} \div \textcolor{m a \ge n t a}{\frac{1}{10}} \text{ "=" } \frac{3}{5} \times \textcolor{m a \ge n t a}{\frac{10}{1}}}$

Grouping the denominators and numerators we have:

$\textcolor{g r e e n}{\frac{3}{\textcolor{m a \ge n t a}{1}} \times \frac{\textcolor{m a \ge n t a}{10}}{5}}$

So now we have the structure:

("count"_1)/("count"_2)xx("size indicator"_2)/("size indicator"_1)" "->" "3xxcolor(brown)(ul(|bar(color(white)(2/2) 2" "|)))

This is: $\text{ division of count"xx"conversion factor}$

Hope this helps.


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# Hilbert of quantum gravity: bulk $\otimes$ horizon

I was reading a paper dealing with the Hilbert of quantum gravity (or more precisely what should it look like considering what we know from QM and GR) ref: http://arxiv.org/abs/1205.2675 and the author writes the following: $${\cal{H}_M} = {\cal{H_{M,\,\textrm{bulk}}}}\otimes{\cal{H_{M,\,\textrm{horizon}}}}$$ for a specific manifold $\cal{M}$. I know very little about the holographic principle and the AdS-CFT correspondence but isn't it a redundant description? If there is a duality between the gravitational theory in the bulk and the CFT on the boundary, knowing one means knowing the other, so why can't we restrict ourselves to one of the Hilbert spaces? Moreover, the author writes, a couple of lines after this first element, that the two Hilbert space have same dimension ( $\textrm{exp}({\frac{{\cal{Area}}}{4}})$ ) so they are totally equivalent, as a complex Hilbert space is only defined by its dimension.

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text:
# How I can rotate unwrap, exactly? [duplicate]

How I can rotate unwrap, exactly, for example some menu or box to enter for example 90 degrees ?. This is possible?.

Sorry for my English I hope you can understand me.

I leave a picture hope it will help me understand.

Blender version : 2.72

• Here is the solution, -> blender.stackexchange.com/questions/40320/… not before I found with the search, but not if delete this answer or mark it as duplicate, I do not know how these cases are handled in Blender Exchange – Angel Angel May 3 '16 at 23:44