text:
50g multiple output
12-03-2021, 03:43 PM
Post: #1
 oierpa Junior Member Posts: 12 Joined: Dec 2021
50g multiple output
Hi all.
I'm new in this forum and quite a new HP calculator user.
When I discovered HP world (at university) I was fascinating on it, but during ’90 years I had not a lot of money to change calculator and HP was really expensive. My first programmable calculator (in fact) was an old CASIO FX850-P, I still have it since 1989 and still work, this calculator had a BASIC programming interface, really simple.
During lockdown I bought a 50g and I tried to start programming it and I found really difficult. I also have a HP 35s bought to keep it in office, with this calculator I understood RPN mode, I like it and I started to program this calculator, I found it really simple and intuitive, so I decided to move to an upgrade, the 50g.
I’m sure that my difficult are due to difference between a basic like language (typical of Casio calculator) and User RPL, but I found this language so strange that it’s extremely difficult for me find some solution.

One of my tipical problem is this:
I’m approaching with a simple financial formula to calculate a periodical amount of a loan, formula is simple: ( I can solve it with a simple formula in the equation editor, but I would solve it with a program to made some practice.
I had no problem to input initial data: amount of a loan, interest rate, number or yearly period (12 in this case), number of years.
I need to calculate:
• montly amount;
• total amount;
• interest.
Formula I use (is not important now), is R=C+((t/100/12)/(1-(1+t/100/12)^(-A*12)), where:
• R: montly amount;
• t: annual interest rate;
• A: number of years.
My problem is to calculate the three quantities above and show them in the display. I can only calculate one (montly amount, or total amount, or interest), but not the other because I can’t recall intermediate calculation and display it correctly.
I'm locked in this kind of problem, I'm sure that is stupid, but I've no idea to unlok my mind now.
Thanks in advance for any help.
12-03-2021, 09:44 PM
Post: #2
 DA74254 Member Posts: 164 Joined: Sep 2017
RE: 50g multiple output
I do not have my 50g with me here at work, but there is already a finacial module in the calc that works. Don't remember where it is but it should be in a menu by one of the shift keys and one of the number keys. Look for "financial" on your keypad.

Esben
28s, 35s, 49G+, 50G, Prime G1 HW A, Prime G2 HW D, SwissMicros DM42
Elektronika MK-52 & MK-61
12-03-2021, 10:42 PM (This post was last modified: 12-04-2021 04:46 AM by Joe Horn.)
Post: #3
 Joe Horn Senior Member Posts: 1,892 Joined: Dec 2013
RE: 50g multiple output
(12-03-2021 09:44 PM)DA74254 Wrote:  I do not have my 50g with me here at work, but there is already a finacial module in the calc that works. Don't remember where it is but it should be in a menu by one of the shift keys and one of the number keys. Look for "financial" on your keypad.

Left-shift 9 launches the built-in Finance input form & solver. If you prefer the soft-menu finance app from the HP 48, it's available in the 50g by typing 80 MENU. Press NXT if you need to change BEGIN/END mode or the number of payments per year.

EDIT: Oops, I forgot about the 50g's built-in key path to the 48-style finance solver: Press and hold down Right-shift, then press 7 and release both. Then press the TVM menu key, then the SOLVR menu key.

<0|ɸ|0>
-Joe-
12-04-2021, 08:13 AM
Post: #4
 oierpa Junior Member Posts: 12 Joined: Dec 2021
RE: 50g multiple output
Hi .
Thnks but program I'm try to made is only an example. I saw that there is a lot of financial functions.
Then I forget to write my simple code:
<<"insert C t a"
{":C:
:t:
:A:"
{1 0 } V} INPUT OBJ-> -> C t A 'C*(t/100/12/(1-(1+t/100/12)^(-A*12)))' -> NUM "R" -> TAG>>

If I try to calculate also total amount due (with formula M=R*A*12) nothing works.

I modified program like this:

<<"insert C t a"
{":C:
:t:
:A:"
{1 0 } V} INPUT OBJ-> -> C t A 'C*(t/100/12/(1-(1+t/100/12)^(-A*12)))' -> NUM "R" -> TAG 'R*A*12' -> NUM "M" -> TAG>>
but ressult it's wrong.
I'm sure is a syntax problem but I don' understand where.
Can someone help me?
12-05-2021, 02:35 PM (This post was last modified: 12-05-2021 03:20 PM by nlj.)
Post: #5
 nlj Junior Member Posts: 32 Joined: Apr 2015
RE: 50g multiple output
(12-04-2021 08:13 AM)oierpa Wrote:  If I try to calculate also total amount due (with formula M=R*A*12) nothing works.
...
<<"insert C t a"
{":C:
:t:
:A:"
{1 0 } V} INPUT OBJ-> -> C t A 'C*(t/100/12/(1-(1+t/100/12)^(-A*12)))' -> NUM "R" -> TAG 'R*A*12' -> NUM "M" -> TAG>>
but ressult it's wrong.
I'm sure is a syntax problem but I don' understand where.
Can someone help me?

Two apparent errors that immediately jump out from the code above are these:

1) The -> command creates local variables whose scope is limited to the following algebraic or program object. So by the time you get to the 'R*A*12' algebraic your local variables are gone and the A here refers to a global variable A.

2) You haven't assigned a value to R in your program. Presumably you intend R to to refer to the value you put on the stack that you labelled "R" with the TAG command, but the calculator doesn't know what you intend. (And again in 'R*A*12', R refers to a global variable R.)

You can fix Problem 1 by wrapping everything in a program object (with << and >>) from just before your first algebraic to the the end of the program.

I hope this helps.

N.

[Edited with slightly better English.]
12-05-2021, 06:23 PM
Post: #6
 oierpa Junior Member Posts: 12 Joined: Dec 2021
RE: 50g multiple output
Hi Nlj.
Thanks a lot for your help.
Can you suggest me some readings, article, manual or website that explain a little more how variables are used inside program?
I would finish this simple program by myself (I've several other program to made), I understood that syntax I used is really wrong, I assumed that calculator has same variables handlig of other environment (like basic that is more familiar for me).
12-06-2021, 12:39 PM
Post: #7
 John Keith Senior Member Posts: 840 Joined: Dec 2013
RE: 50g multiple output
(12-05-2021 06:23 PM)oierpa Wrote:  Can you suggest me some readings, article, manual or website that explain a little more how variables are used inside program?

One very good source is https://literature.hpcalc.org/. Nearly every HP manual is available there, as well as many third party manuals. Even better is the Museum thumb drive which has even more manuals and literature in a convenient form.

Specifically, the Programming section in the HP 50g advanced user's reference has the info you are looking for. The 50g users manual is somewhat infuriating to use because every example has both RPN and algebraic versions. The HP48G user's manual is more readable but obviously doesn't cover features of newer calculators. William Wickes' HP48 Insights (GX Version) is also a valuable reference. It is on the thumb drive but not on hpcalc.org.

RPL is an unusual programming language, especially compared to BASIC which is used on many other scientific calculators. Some people love it, others hate it or just never get it. RPL is based primarily on LISP and FORTH so familiarity with those languages is helpful. The local variable structure that you are having trouble with is similar to lambda expressions as you would find in LISP, Python or Haskell.
12-06-2021, 02:36 PM
Post: #8
 oierpa Junior Member Posts: 12 Joined: Dec 2021
RE: 50g multiple output
Hi all.
I made some test and I understood something more.
Here there is my program list:
Code:
<<"Ins C t A n" {     ":C:      :t:      :A:      :n:" {1 0} V} INPUT OBJ-> -> C t A n      << t 100 / 'n' RCL / DUP 1+ 'n' RCL       'A' RCL * NEG ^ NEG 1 + / 'C' RCL *       'R' STO>>       'n' RCL 'A' RCL *       'R' RCL * "M" -> TAG        ->STR "       " ->STR + 'R' RCL "R" -> TAG        ->STR +       MSGBOX 'R' PURGE        >>
With this syntax I can calculate and display 2 different result (obtained with the same input data). I used RPN and not Algebraic because when I try use this notation variables are changing.
Thanks to all that read and can suggest me something to do better programs.
12-06-2021, 05:59 PM
Post: #9
 nlj Junior Member Posts: 32 Joined: Apr 2015
RE: 50g multiple output
Hi oierpa,

(12-05-2021 06:23 PM)oierpa Wrote:  ... Can you suggest me some readings, article, manual or website that explain a little more how variables are used inside program? ...

My answer to this was going to be very similar to the one from John Keith above, although his is more detailed.

If you want to limit the amount of reading you need to do initially, I would say that the "Chapter 1: RPL Programming" and possibly "Chapter 2: Programming Examples" in the "HP 50g / 49g+ / 48gii Graphing Calculator Advanced User's Reference Manual" are essential reading.

I agree with John that the "HP 50g Graphing Calculator User's Manual" [and also the "HP 50g Graphing Calculator User's Guide"] are somewhat infuriating and that going back to a manual to a less evolved calculator in the line can be better. But rather than the manuals for the 48G, I would suggest that the manuals for the 48SX cannot be beaten for clarity and simplicity even though the calculator is less similar to the 50g.

(12-05-2021 06:23 PM)oierpa Wrote:  ... I understood that syntax I used is really wrong. ...

Not "really" wrong. I'd say you are more than 90% of the way there.

(12-06-2021 02:36 PM)oierpa Wrote:  Hi all.
I made some test and I understood something more.
Here there is my program list:
Code:
<<"Ins C t A n" {     ":C:      :t:      :A:      :n:" {1 0} V} INPUT OBJ-> -> C t A n      << t 100 / 'n' RCL / DUP 1+ 'n' RCL       'A' RCL * NEG ^ NEG 1 + / 'C' RCL *       'R' STO>>       'n' RCL 'A' RCL *       'R' RCL * "M" -> TAG        ->STR "       " ->STR + 'R' RCL "R" -> TAG        ->STR +       MSGBOX 'R' PURGE        >>
With this syntax I can calculate and display 2 different result (obtained with the same input data). I used RPN and not Algebraic because when I try use this notation variables are changing.
Thanks to all that read and can suggest me something to do better programs.

* You don't need all those RCL statements. Instead of 'n' RCL just use n. ('n' (with quotes) evaluates to the name of the object and n (without quotes) evaluates to the value of the object.)

* You can still use your algebraic objects if you like. In a formula an algebraic can sometimes be more readable. Just remember that the scope of local variables is the following algebraic or program object so if you want the scope of you local variables to extend beyond one algebraic then you need an enclosing program object. Along these lines:

[NOTE: The calculator sadly does not support comments in programs, but I have sprinkled comments here introduced by semicolon characters.]

Code:
<< ; This section is usually used to set up the stack so that the local variables can be assigned from it. -> a b c <<     ; Your local variables a, b, and c are defined here.     'some-algebraic'         ; Your local variables are still defined inside your algebraic.     ; And they're still defined here.     'another-algebraic'      ; And they're defined inside this algebraic too.     ' And they're still defined here. >> ; End of scope of local variables a, b, and c. >> ; End of program

* You can avoid having 'R' being a global variable (which might overwrite an existing variable 'R' that you have outside your program) by introducing a new (inner) local variable scope for 'R'.

Code:
<< ; Get C, t, A, and n on the stack by whatever means (e.g. by your INPUT OBJ-> approach). -> C t A n <<     ; Code calculating R, using an algebraic or otherwise.     -> R <<         ; Code using C, t, A, n, and R goes here.     >> End of scope of local variable R. >> ; End of scope of local variables C, t, A, and n. >> ; End of program

Or more simply, put a dummy value for R on the stack (such as 0) and create R in your initial set of local variables,

Code:
<< ; Get C, t, A, and n on the stack by whatever means (e.g. by your INPUT OBJ-> approach). 0                              ; Dummy value for R -> C t A n R <<     ; Code calculating R, using an algebraic or otherwise.     'R' STO                    ; Replace value of the local variable R     ; Code using C, t, A, n, and R. >>  ; End of scope of local variables C, t, A, n, and R. >>  ; End of program

N.
12-10-2021, 06:53 PM
Post: #10
 oierpa Junior Member Posts: 12 Joined: Dec 2021
RE: 50g multiple output
Hi Nlj.
Excuse me if I reply only now, wednesday was national holiday here (Italy) and when I come back to work I had a lot of things to do.

First of all, thank you so much, in few words I understood more than reading manual, I agree with you, sometimes is hard to understand. I think that my biggest problem is entering understanding logic of User RPL.

Anyway I make few test and of course it works.
Now last running version is:
Code:
<<"Ins C t A n" {     ":C:      :t:      :A:      :n:" {1 0} V} INPUT OBJ-> -> C t A n      << t 100 / n / DUP 1+ n        A * NEG ^ NEG 1 + / C *       'R' STO>>       n A *       R * "M" -> TAG        ->STR "       " ->STR + 'R' RCL "R" -> TAG        ->STR +       MSGBOX 'R' PURGE        >>
This work fine, so I tried some new versions using your suggestions.
Version with algebraic formula:
Code:
 <<"Ins C t A n" {     ":C:      :t:      :A:      :n:" {1 0} V} INPUT OBJ-> -> C t A n      << C t A n 'C* (t/100/n)/(1-(1+t/100/n)^(-n*a))' EVAL      'R' STO 'R*n*A' EVAL >> 'M' RCL "M" -> TAG       -> STR " " -> STR + 'R' RCL "R" ->TAG -> STR +       MSGBOX 'R' PURGE 'M' PURGE        >>
Calculation time over a minute and an error occurred (insufficient memory)

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12-11-2021, 02:18 AM (This post was last modified: 12-11-2021 04:23 AM by nlj.)
Post: #11
 nlj Junior Member Posts: 32 Joined: Apr 2015
RE: 50g multiple output
Hi oierpa,

(12-10-2021 06:53 PM)oierpa Wrote:  I think that my biggest problem is entering understanding logic of User RPL.

I feel that you are maybe making it more complicated for yourself than it need be. With the exception of a few control flow constructs almost everything in UserRPL is exactly the same as the RPN you use when using the calculator interactively*.

The only thing you really need to wrap your mind around is the simple idea that commands take zero or more arguments off the bottom of the stack and return zero or more results there.

[* If you normally use the calculator in algebraic mode, I suggest you switch it RPN mode at least to get yourself in the right mindset for programming the calculator.]

(12-10-2021 06:53 PM)oierpa Wrote:  Anyway I make few test and of course it works.
Now last running version is:
Code:
<<"Ins C t A n" {     ":C:      :t:      :A:      :n:" {1 0} V} INPUT OBJ-> -> C t A n      << t 100 / n / DUP 1+ n        A * NEG ^ NEG 1 + / C *       'R' STO>>       n A *       R * "M" -> TAG        ->STR "       " ->STR + 'R' RCL "R" -> TAG        ->STR +       MSGBOX 'R' PURGE        >>
This work fine, so I tried some new versions using your suggestions.

I don't think that is actually working the way you intend because the n A *' expression is not using your local variables n and A but whatever values you happen to have stored in them globally.

(12-10-2021 06:53 PM)oierpa Wrote:  Version with algebraic formula:
Code:
 <<"Ins C t A n" {     ":C:      :t:      :A:      :n:" {1 0} V} INPUT OBJ-> -> C t A n      << C t A n 'C* (t/100/n)/(1-(1+t/100/n)^(-n*a))' EVAL      'R' STO 'R*n*A' EVAL >> 'M' RCL "M" -> TAG       -> STR " " -> STR + 'R' RCL "R" ->TAG -> STR +       MSGBOX 'R' PURGE 'M' PURGE        >>
Calculation time over a minute and an error occurred (insufficient memory)

Ah, now you have gotten in quite a tangle!

One thing that jumps out at me is that you haven't defined the lower case a' in your long algebraic so that will be accessing an arbitrary global variable if you have one defined -- and if you haven't you're asking the CAS to evaluate an expression with an unknown.

To get back on track I suggest you re-read Chapter 1 on the Advanced User's Reference Manual slowly, and try little bits of your program interactively.

Also consider this simpler code which expects to get values for C, t, A and n off the stack and returns R and M to the stack (appropriately tagged). [To avoid for now your long algebraic expression, in this example R is the sum of C, t, A, and n.]

Code:
 << 0 0 -> C t A n R M     << 'C + t + A + n' ->NUM 'R' STO         'R * n * A' ->NUM 'M' STO          R "R" ->TAG         M "M" ->TAG     >> >>

I hope this helps a bit!

[Edit: Replacing EVAL with ->NUM, otherwise the calculator needs to be in Numeric Results Mode (unless an exact rational result is desired, but calculating that here is very slow).]
12-11-2021, 02:45 PM
Post: #12
 DavidM Senior Member Posts: 906 Joined: Dec 2013
RE: 50g multiple output
You're getting some great advice here from multiple sources. I'll add my take on a couple of specific issues.

nlj has hinted at something in one of his responses that I'd like to emphasize: everything in RPL is case-sensitive. So variable 'a' is not the same variable as 'A' (globally or locally). I suspect you probably already know that, but I just wanted to emphasize it because it can definitely make bug-finding more difficult if you've mixed the case of variable names in different parts of the program.

The User RPL concept of local variables (and the mechanics of using them) takes a little time to understand. The syntax used to define them isn't as "RPN-ish" as many would like, but I suspect was chosen in an effort to improve readability more than to fit into the traditional RPN "operand(s) first then operator" model. Just keep in mind that there are 4 distinct parts to any UserRPL local variable context:

1: objects on the stack that define the initial values of the named locals
2: the "→" operator
3: a sequence of local variable names
4: a single object that will be executed/evaluated using the named locals

That single object in item 4 above has to be one of two things: a program (enclosed in brackets « »), or an algebraic (enclosed in tic marks ' ').

The local variable names listed in item 3 above only exist for that last object. Anything following that object in your program won't ever know that they even existed, and will treat any references to those names as global variables instead. So the context of the locals both begins and ends within that single object defined in part 4.

Consider some examples. In this situation, I have created 3 global variables (A B C) and stored the values (4 5 6) into them. Then each of the following programs is executed:
Code:
o1 «    1 2 3     →    A B C    « A B C * + » » o2 «    1 2 3    →    A B C    'A+B*C' » o3 «    1 2 3    →    A B C    « A B C * + »    « A B C * + » →NUM » o4 «    1 2 3    →    A B C    'A+B*C'    'A+B*C' →NUM »

o1 result: 7. Note that the local variable context supersedes the global variables which are already defined.

o2 result: 7. Same result as o1, same reasons.

o3 result: 7 34. Note that the exact same source code has two very different results. The local variables went out of context after the first sub-program was executed, so the same variable names in the following statement (which looks the same, but actually isn't) now refer to the previously defined global variables instead of the locals.

o4 result: 7 34. Same result as o3, same reasons.

The use of locals in RPL programs definitely has a learning curve, but the advantages in program clarity and the reduction of "stackrobatics" they afford is very real. You've got a good start on this, keep it up!
01-10-2022, 11:45 AM
Post: #13
 oierpa Junior Member Posts: 12 Joined: Dec 2021
RE: 50g multiple output
Hi all.
First of all I would wish you happy new year to everybody.
I apologize for my long absence, I had some trip for work just before Christmas, then holiday and then Covid ...

The explanations of Nlj and DavidM were more useful than the manuals.
Of course I remember that variable name are case sensitive, I just written the wrong variable name "a" instead of "A", but in my calculator it was right.

I'm sure the RPL language is very solid, otherwise it wouldn't be as widespread. I just have to get into the operating logic and it is obviously my problem.

But in program o3 and o4 of DavidM I've some errors during execution (in o4 I've "-> NUM error" and in o3 "* ERROR: undefined name").

I just typed same program.
01-10-2022, 12:16 PM
Post: #14
 DavidM Senior Member Posts: 906 Joined: Dec 2013
RE: 50g multiple output
(01-10-2022 11:45 AM)oierpa Wrote:  But in program o3 and o4 of DavidM I've some errors during execution (in o4 I've "-> NUM error" and in o3 "* ERROR: undefined name").

I just typed same program.

Just a guess: did you first create the global variables A, B, and C before executing the programs? See the note at the beginning of the code listings: In this situation, I have created 3 global variables (A B C) and stored the values (4 5 6) into them. Then each of the following programs is executed...

Part of what I was trying to convey here is what happens when you already have global variables defined when running code with locals using the same names.
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text:
# Tension vs Tensile Strength

A Brief Explanation of the Issue

A common problem type for vector calculus students or introductory physics/engineering students is tension problems. For instance, if a mass of $$10$$ kg is suspended from two taut cables of length $$3$$ m and $$5$$ m at angles of $$52^\circ$$ and $$40^\circ$$, respectively, then the corresponding tensions in the cables are $$75.12$$ N and $$60.37$$ N.

To make this concrete to students (in terms of application), one might talk about the strength of the cable material, e.g., would this arrangement break either of the cables. Looking up material strengths, these are most often measured in kPa. So from my understanding, the 'failure' in this situation is a measure of resistance to pressure in terms of tensile strength.

The Question

How would one determine if catastrophic failure of the cables would occur? Naturally, this criterion is expressed as a pressure, but what is the area I would be using? Would this be the area of a slice of the cable attaching the cable to the object and to where the cable is 'grounded'? Would it be the area of the cross section where the cable is thinnest? Is it an average size of a cross section of the cable? While I assume the tension is constant in the cable as a whole, the pressure from the object is not constant throughout the cable, correct? Or given that the cables are at an angle, would some analysis of the forces from a cable's tendency to rotate until it is vertical due to the weight weight be more relevant, i.e., some type of twisting force? If anyone could clarify the situation in this case, or more generally, this would be wonderful.

[Note: I am a mathematician, with only an undergraduate background in physics, if this helps with the type of explanation that would be most understandable to me or my students.]

Considerations

I teach college students, typically freshmen/sophomore engineering students who have taken their calculus sequence up to multivariable/vector calculus but have had only an introductory physics course—if any at all.

• A little more background may help. Are you teaching high school students? What is the overall purpose of the class (physics, engineering concepts, other)? Is this your student's first exposure to physics? Aug 14, 2020 at 19:51
• @DavidWhite Thank you, that would probably be useful to specify. I will add it as an edit. Aug 14, 2020 at 20:12
• A great reference, easily understandable to you and your students, is Beer and Johnson's Mechanics of Materials (or, really, any other best-selling mechanics of materials textbook—the curriculum has solidified at this point). The upshot is, divide the tension by the smallest cross-sectional area of the cable and compare the quotient to the strength parameter of interest. @BobD's answer gives a more complete framework. Aug 15, 2020 at 4:06

Looking up material strengths, these are most often measured in kPa. So from my understanding the 'failure' in this situation is a measure of resistance to pressure in terms of tensile strength.

The term usually used is yield strength, which is the maximum tensile stress before a specified amount of plastic deformation is produced, usually taken as 0.2 percent of the unstressed length. Tensile stress is the more applicable term than "pressure", though the units are the same.

How would one determine if catastrophic failure of the cables would occur?......(etc.)

There are really too many questions here to answer point by point. What's more, cables are a special application of materials, as opposed to general applications such as columns and beams, and there are probably specific standards on how to test the tensile strength of cables. It does appear that the cable diameter is used to qualify the tensile strength, as in the following example link. https://componentsupplycompany.com/Stainless-steel-wire-tensile-strength.php

Just to put things in perspective, the figure below is a generic stress strain curve which gives you terminology related to the various levels of strength of materials, if you will.

Proportional limit: Basically this is the maximum stress where the stress-strain curve is linear and follows Hooke's law. When the applied stress is removed the specimen returns to its original length (no permanent deformation).

Yield strength: This is what I referred to in the beginning. It is the maximum tensile stress before a specified amount of plastic (permanent) deformation occurs.

Ultimate strength: This is the point where the specimen can no longer withstand any further increase in applied stress, the curve turns downward and failure (fracture) is imminent.

Fracture: Here the specimen fails.

If you are going to teach this stuff, you should probably apply it to general principles and applications of mechanics of materials, rather than the specific application of cables. There may be a separate science associated with cables, but I don't know.

Hope this helps.

• Thank you. This certainly gives me a bit more I can discuss with them and give them just a bit more beyond the basic tension calculations for their Calculus sequence. Aug 15, 2020 at 22:07
• @mathematics2x2life You're very welcome. Good luck with your teaching. Before I retired I taught engineers to pass their professional engineering tests. Since joining the exchange, I've increased my knowledge of many subjects considerably. You should continue using the Exchange as a valuable resource. I like to say "when you teach you learn (by listening to others), then what you learn you teach." Aug 15, 2020 at 22:11

One approach

Teach the tension and tensile strength concepts over several lesson plans.

1. Lecture on tensile strength of different materials, and how that tensile strength is measured in the lab

2. Schedule a hands-on lab where students get to actually measure the tensile strength of a few different materials. This would probably require thin wires of different materials, a micrometer, some weights, etc., with the usual amount of instruction on how to use the equipment

3. Lecture on static equilibrium, with example problems illustrating how a given weight can put varying amounts of tension on suspension wires, depending on the angles involved

4. Schedule a hands-on lab involving the various angles encountered in step 3 (above), with spring scales, load cells, or some other force measuring device, that will allow students to actually measure the effect

The combination of lecture first, immediately followed by hands-on experience, should give students a good idea of what is happening.

Now, to directly answer the questions. Catastrophic failure occurs when the force on a cable exceeds its tensile strength. This failure will occur at the minimum cross-sectional area of a cable, if the cable's cross-sectional area varies (and it will vary, even if on a microscopic level). Also note that for the usual situation, the weight of the cable is not significant, so you can assume constant tension in the cable. A review of intro physics literature on this subject should answer your questions in quite a bit more detail.

• I am just trying to give them a bit more utility and context beyond their basic Calculus tension problems. But this certainly addressed some of the questions I had. (+1) Aug 15, 2020 at 22:08
• @mathematics2x2life, I taught high school physics for 13 years, and my post is the way that I would teach your class. Good luck. Aug 16, 2020 at 16:58

If they are engineering students, it is interesting also to present the type of cable that are normally used for lifting loads: wire rope.

Except for small loads, it is difficult to have a steel cable that is at the same type strong and flexible. The solution is a bunch of wires hold together.

In principle, the tensile strengh of the rope is the sum of the strenght of all of the individual wires, but it is better to follow the manufacturer specification, that takes in account the friction and the fact that some of them can be damaged during its lifetime.

They can fail suddenly if the load is above the specification, but also if they are badly damaged and people don't inspect to discard them when necessary.

• Thank you! I will use this for the example! Aug 15, 2020 at 22:08

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# Homework Help: Remaining in the same spot on a spinning disk

1. Dec 1, 2017

### Fibo112

This might be better

File size:
52.7 KB
Views:
121
2. Dec 1, 2017

### haruspex

Yes, I can now read the lettering, but I cannot find an OCR app that can. If you can be bothered to type it all in, I can try various translation packages.

3. Dec 1, 2017

### Staff: Mentor

Sorry. I still don't get what you're saying. If I suddenly increment the velocity of the body so that it is permanently zero in the laboratory frame of reverence, it will stay at a constant radius, and it will be rotating in the opposite direction or the original rotation as reckoned from the frame of the rotating turntable. So its acceleration will be radially inward as reckoned from the rotating turntable.

4. Dec 1, 2017

### Fibo112

I missread the question myself and missed some crucial details, apologies. Here is the question.

Inclined rotating disc:
We consider a frictionless, rotatably mounted disc which is inclined at a constant angle β relative to the earth's surface, see Figure 4. The disc has a radius of R = 2 m, a thickness of 5 cm and a mass density of ρ = 1 g / cm3.

On the plate is a child with a mass of m = 30 kg. The finite extent of the child, as well as friction due to air resistance and storage of the disc can be neglected. We choose a spatially fixed coordinate system so that the disk surface rotates in the xy plane and the origin of the coordinates coincides with the center of the disk. The system is under the influence of gravitational force Fg. Note: Numerical values are to be calculated only in part a) and b).

d) We assume that the disc is initially at rest and that his father puts the child at the point {R / 2, 0, 0} as shown in the figure on the right. The child now tries to stay at this point in the laboratory system by starting to move in positive y-direction with constant acceleration a relative to the disk. How big should this acceleration be, so that the child remains in the same place in the laboratory system? Which angular acceleration of the disk ˙ω corresponds to this? How do you interpret the dependence on the angle of inclination β? What happens in the limit case β = 0?

So in this case the weight of the child will cause a torque which will beginn to accelerate the disc. The childs acceleration would have to be (d/dt w)*R/2, is that correct? On a side note would it be correct to say that if the kid was dropped on the disk after the disk was already rotating the kids acceleration would also have to have an x component for him to remain in place?

5. Dec 1, 2017

### haruspex

Ok, I get it at last! My mistake was to interpret "acceleration relative to the rotating disc" as acceleration relative to a neighbouring point on the disc. That is not the same as acceleration in a frame of reference rotating with the disc.
If A is a fixed point next to a disc centred at O and B is a point on the edge of the disc currently passing A, the actual acceleration of B is towards O. So the acceleration of stationary A relative to B must be away from O. Yet an observer at B sees A as accelerating towards O.

6. Dec 1, 2017

### haruspex

Yes, but don't forget that the child's attempt to stay in place will also affect the torque.
In order to stay in place in that context the child would need to have her feet moving to match the disc speed on landing. Thereafter, it is the same problem as before - the right tangential acceleration will keep the child in place.

7. Dec 1, 2017

### Fibo112

(R/2*30*(sin(b)+a)/Moment of Inertia)*R/2 = a. Is this equation for determining a correct?

8. Dec 1, 2017

### Fibo112

I am having trouble picturing what is even meant by this childs acceleration. I guess what is meant is what is the childs acceleration in the rotating frame of reference which is the disk? From the point of view of the disks frame of reference the child is rotating with an increasing velocity isn't it? If something is rotating with an increasing velocity doesn't it have a tangential and a radial component of acceleration? Am I making any sense?

9. Dec 1, 2017

### haruspex

No.
Let's take this in steps. What forces act on the child? What equation does that give?
What forces act on the disc?

10. Dec 1, 2017

### Fibo112

The way I thought was that the childs weight creates a torque of R/2*30kg * sin(b). I also thought that the Force for the childs acceleration has to come from friction so this will create a torque of R/2*30kg*a. So then I thought since T=d/dt(MOI*w)=MOI*d/dt w I would get d/dt w = T/MOI. Lastly I thought that acceleration is equal to R/2 d/dt w...

11. Dec 1, 2017

### haruspex

That is dimensionally wrong. You forgot something.
But please, let us do it the safe way, with free body diagrams, ΣF=ma etc.

12. Dec 1, 2017

### Fibo112

yes I forgot g

13. Dec 1, 2017

### haruspex

Right... and please see my edit above.

14. Dec 1, 2017

### Fibo112

Ok. So since the child remains motionless in an Inertial system we have a=0. The forces on the child are the Gravitational force, the normal force of the disc and the friction force of the disc. The component of the Gravitational force which is perpendicular to the disk will cancel out with the discs normal force. The remaining forces on the child are 30kg*g*sin(b) for the remaining gravitational force and a frictional force of equal magnitude and opposite direction to compensate the gravitational force. By newtons third law the child enacts an equal and opposite force on the disk. The normal component causes no torque. The frictional component causes a torque of T= R/2 30kg*g*sin(b). This causes an angular acceleration of T/Moment of Intertia. The acceleration of the disk at the point of the child is R/2*T/Moment of inertia.?

15. Dec 1, 2017

### haruspex

Yes.
Note that this differs from what your equation in post #27 would have given, even after restoring the g factor.

Out of interest, note that your analysis interprets this:
as meaning relative to the tangential acceleration of the disc, not an acceleration of magnitude a relative to the reference frame of the disc. I think you have the right reading.

16. Dec 1, 2017

### Fibo112

I am still bothered by this questions notion of acceleration, it just doesn't make any sense to me to be talking about acceleration without a clear frame of reference as to where this acceleration is taking place...

17. Dec 1, 2017

### haruspex

The question states that the child is to stay in the same place in the laboratory frame. That is enough to determine the force the child must exert on the disc, and the disc's consequent acceleration.
The slightly awkward part is that it asks for "the child's acceleration relative to the disk." I now consider that ambiguous. I think what they want is relative to the tangential acceleration of the disc. But if it means relative to the reference frame of the rotating disc then you would have to add the apparent radial acceleration, $-\omega^2\frac R2\hat r$.

18. Dec 1, 2017

### Fibo112

Ok. Thanks a lot for your help.


text:
+0

# Physics question

0
184
9
+78

A windmill is a device for extracting kinetic energy from the moving air. The moving air is used to turn large blades. In modern windmills, the turning blades are used to rotate magnets near loops of wire, which creates electric currents. In this way, kinetic energy in the wind is turned into electric energy and fed into the power grid.

Suppose that when the wind blows at 5.0 m/s the kinetic energy per unit time that blows past a windmill is 0.50 MJ/s This is also known as 0.5 MW The W stands for watts. One watt is one joule per second, so the kinetic energy of the air passing by the windmill per unit time is half a megawatt or half a megajoule per second. Energy per unit time is called power, so the watt is the SI unit for power.

Windmills cannot capture all the kinetic energy from the air passing by them. This is because if they did, the air would come to a stop, and would pile up behind the windmill, preventing any more air from getting through.

The maximum possible efficiency of a windmill is called the Betz limit. At the Betz limit, a windmill can extract 16/27 of the kinetic energy of air passing through it. Even this is just the theoretical maximum efficiency; real windmills are not quite this effective.

Suppose that the wind speed increases to 10.0 m/s If the windmill we considered before can operate at 80% of the Betz limit, how many megawatts of power does it produce?

Jul 18, 2021

#1
+2

From reading, here are the useful facts to solve this question:

1-A windmill is a device for extracting kinetic energy from the moving air.

2- kinetic energy in the wind is turned into electric energy. Denote kinetic energy: $$E_k$$ and electrical energy: $$E_e$$

3-Suppose that when the wind blows at 5.0 m/s the kinetic energy per unit time that blows past a windmill is 0.50 MJ/s

Let the initial speed: $$v_{initial}=5.0 m/s$$, and given the initial kinetic energy, $$E_k=0.50*10^6 J$$
Hint: (Although the text is talking about power and energy, they are the same here due to "1 second" (Since P=E/t -->P=E if t=1))

By the Kinetic Energy equation:

$$E_k=\frac{1}{2}mv^2$$, we can find the mass, m of the air. $$m=\frac{2E_k}{v^2}=\frac{2*0.50*10^6}{(5.0)^2}=40 000 kg$$     (1)

4-Windmills cannot capture all the kinetic energy from the air passing.

From this, we deduce that windmills are not 100% efficient (Thus, we will use the equation of Efficiency), and the text explained this further:

5-The maximum possible efficiency of a windmill is called the Betz limit. Given, the theoretical Betz limit: 16/27 of the kinetic energy of air passing through it.

Now to the question:
Suppose that the wind speed increases to 10.0 m/s  (Denote, $$v_{final}=10.0m/s$$)

If the windmill we considered before can operate at 80% of the Betz limit, how many megawatts of power does it produce?

It is crucial to note from this, that it is the same windmill, thus the following is an accurate assumption in solving: mass of air passing through the windmill blades is constant, as found in (1) -->40000kg.

Applying the efficiency equation: $$Efficiency=\frac{E_e}{E_k}$$

Given, the efficiency is 80% of the betz limit -->$$0.80*\frac{16}{27}=0.47407407$$ is the efficiency.

$$E_k=\frac{1}{2}(40000)(10^2)$$ $$=2.0*10^6 J$$

Thus, $$E_e=0.47407407*2.0*10^6=948148.14 J$$

Recall, this is the energy per second hence the power.

So the question wans the final answer to be in megawatts:

$$948148.14J/s=948148.14W=0.94814814MW$$

Which can be approximated to be: $$0.95MW$$

Jul 20, 2021
#2
+78
+1

Ah, that makes much, much more sense now. My answer was a bit different, sitting at $$\fbox{1.9 MW}$$

PBJcatalinasandwich  Jul 21, 2021
edited by PBJcatalinasandwich  Jul 21, 2021
#3
+2

If you are still confused from anything, you can always ask!

Guest Jul 21, 2021
#4
+78
+1

Thank you!

PBJcatalinasandwich  Jul 21, 2021
#5
+2234
0

Neither of you two dumb-dumbs have the correct answer.

The change in power is proportional to the ratio of the cubed velocities.

$\Delta P = \dfrac {V_2^3}{V_1^3}$

$\Delta P = \dfrac {10^3}{5^3} = 8$

Then

$0.5MW *8 = 4 MW$

This is solvable using kinetic energy equations. But you have two errors in your second equation.

Your second equation has an erroneous value for the mass. Also, you multiplied by the coefficient of efficiency instead of dividing. In this case, you should have done neither.

Dividing gives the actual kinetic energy of the air that’s required to produce this power output.  However, if you do this on the second equation you have to do it on the first equation. The results will be the same if the proportions are the same. Despite its mention in the question, the coefficient is not needed to solve this question. In fact, most of the BS written in the context isn’t needed for the question.

$E_k=\dfrac{1}{2}(40000)(10^2) = 2.0MJ$ – Your result without multiplying by the coefficient of efficiency.

Consider carefully: if you have twice the velocity there will also be twice the mass in the same unit of time.

So...

$E_k=\dfrac{1}{2}(80000)(10^2) = 4.0MJ$

------------

Defining how kenetic energy relates to power:

$KE = \dfrac{1}{2} M * v^2$ the velocity may be expressed as $\left(\dfrac{\dfrac{m}{s}}{s}\right)$

And power as:

$P = \dfrac{KE}{\Delta t} | \;\; t \;\; \text { is in seconds.}$

Then

$P = \dfrac{1}{2}*\left(\dfrac{{\dfrac{\dfrac{m}{s}}{s}}}{s}\right)$

Then

$P = 0.5 M * v^3$

------------

Hint: (Although the text is talking about power and energy, they are the same here due to "1 second" (Since P=E/t -->P=E if t=1))

Power and energy are related and one can be derived from the other, but they are never the same. Just as kilometers per hour is never the same as kilometers. It does not matter that the time unit is one (1); they have different units: for power it’s watts and Joules per second. For energy it’s Joules and watt-seconds.

------------

The general equation for power produced by a wind turbine is

$P = 1/2 \pi * r^2 * v^3 * \rho * \eta \;\;| \;\; \tiny \text {where r is the radius of the turbine blade, v is velocity of the wind,$\rho$is the air density, and$\eta$is the efficiency factor.}$

With this equation you can reconstruct the basic parameters of the wind turbine.

This equation was not included, but a lot of BS filler was.

------------

Both the question and the guest answer look like they could have been written with a quill...

That is, written in a narrative style consistent with the lecture circuit of the nineteenth century.

The great masters of physics and science, such as Michael Faraday and Joseph Henry gave public lectures on various subjects. But for every true master there were dozens of morons, idiots and charlatans, who either did know the subject or couldn’t teach it with any kind of coherent logic.

Here’s an example in written form.

https://web2.0calc.com/questions/what-is-the-linear-value-of-one-knot-at-the-equator#r2

The presented question post is factual, but the most of the facts are worthless as they relate to the question.  Anyone who might have the basic skills needed to answer the question would already know them anyway.

Moving from the mid nineteenth century to the mid twentieth century we might find a radio or teleplay encourage children to pursue a career in a science-related field.

Here’s a hypothetical of such a teleplay:

Tommy: What do you want to do when you grow up, Billy?

Billy: I want to build windmills that catch and stop all the wind. I drew a diagram of one with my quill. I based it on my helicopter hat.

Tommy: If you stop all the wind, what will make the windmills go around?

Billy: I already figured that out. We’ll have bunches of electrical power; so all we need to do is plug in big fans and blow them on the windmills.

Tommy: That is so smart. I never thought of that.

Billy: Well it helps to have some physics education.

Tommy: What’s that?

Billy: I don’t know, but someone told me that.

-------------------

Would anyone care to write a sequel? ...Either in the same era or fifty years later.

GA

Jul 23, 2021
edited by GingerAle  Jul 23, 2021
#6
+1

Oh, that must be the correct answer! Thanks for explaining this idea about mass doubling due to time being considered! (Never thought of it before)!
Sorry guys for my completely wrong answer(guest) above. If u can delete it somehow go ahead as I can't.

Guest Jul 23, 2021
#7
+1

Though a question..:
you referred to "v" as velocity, shouldn't it be speed?

(Because K.E. is scalar not vector, and scalar quantities must be of either: Vector x Vector or scalar x scalar).

Guest Jul 23, 2021
#8
+2234
0

There is no need to delete your answer. I usually leave my mistakes, unless they are a major distraction to the continuity of the post. They are uinique monuments to exceedingly rare events.

Your solution is well thought out and explained; you just have mistakes in the application. The more complex the subject, the easier it is to make mistakes. Physics becomes very complex, very fast.  We learn from our mistakes; others learn from them too. It’s part of educating ourselves.

------

After rereading the question, I realize I made a mistake too, so I’m adding my name to the list of dumb-dumbs.

------

The initial energy of (0.5MW) is what passes through the wind turbine system—the input power, not the output power.  Doubling the wind speed increases the input power to (4MW). The input power is then multiplied by the coefficient of efficiency (4.0MW * 0.47407) giving the output power of 1.9MW.  (This is consistent with the OP’s answer, which I dismissed because there wasn’t any associated work product.)

GA

GingerAle  Jul 23, 2021
#9
+2234
0

you referred to "v" as velocity, shouldn't it be speed?

(Because K.E. is scalar not vector, and scalar quantities must be of either: Vector x Vector or scalar x scalar).

That’s an interesting question.

Most equations use velocity to define kinetic energy. Though I have seen speed used. Kinetic energy is produced when mass is in motion without regard to its direction; however, in most closed systems there is at least an implied direction.

In the case of the wind turbine, the implied direction is at zero (0) degrees relative to the face of blades. If the mass of the wind was vectored at 90 degrees to the face of the blade then none of the kinetic energy would translate to the mass of the blades.

GA

GingerAle  Jul 23, 2021


text:
# Mathematics new site theme is live

We rolled out the new site theme for Mathematics. It is live now.

## What new theme?

If you're like, "What the heck are you talking about?", then you should read the Meta Stack Exchange post entitled Rollout of new network site themes (and maybe the posts it links to for the full background).

You are one of the first sites to get a new, unified theme. I previously posted the designs for theme in meta. The feedback given to that post was considered prior to rolling out the theme. Please help us look for issues/bugs and post the details (including images where needed) as an answer below.

If you have concerns or issues regarding the left nav then this Meta Stack Exchange post is the right place for feedback. If you have issues with any functionality that is unrelated to the new theme, then please post a new question.

As you see, the team working on this theme design is seriously studying the criticism here, and responding to it. Editing this to allow anyone so inclined to change their vote.

• I'm afraid it's as bad as it was on Meta and SO. The consistent downvotes and complaints every time this was rolled out (or even mentioned) have been ignored. It's sad to see that user feedback is no longer relevant for the SE staff. – 6005 Aug 9 at 16:51
• As a follower of Questions: Newest, the font has been decreased (I find it harder to read, and I'm sure I'm not the only one.) One reason I used "Questions: Newest" was precisely because the questions and titles were more prominent. – amWhy Aug 9 at 16:55
• I think that there is so much negative response because we only got to see screenshots. In the future, it would be a good idea to let people sign up for beta testing, where they can actually interact with the new design and make remarks. – Asaf Karagila Aug 9 at 18:02
• Clearly people aren't happy about this (ahem) imperfect change, but I would humbly recommend that this post doesn't get downvoted below -8. This is because such downvoted questions are hidden from the main meta.math page, so users looking for information about why everything is different (and not working properly) all the sudden will have a harder time finding it. The change might not be good, but this post actually serves a useful function. – castor occupatus Aug 9 at 18:14
• Why are the up/down vote arrow shadings so close in contrast on the main site?! I can barely tell if I've upvoted a question or not, there. They are much clearer for me on the meta site. This is just strange. – rschwieb Aug 9 at 18:34
• There should be an arrow next to the sidebar that when clicked would make it disappear. I'm thinking of the Adobe Acrobat/PDF designs. – TheSimpliFire Aug 9 at 19:07
• Just as @rschwieb said, the votes in the main site are very close in color. There are people with colorblindness that can't see the difference at all and there is no reason for this to happen, it should be either like the meta site or use 2 very different colors for natural and voted. And the same with the links – Holo Aug 9 at 20:08
• @holo Can't do much with a comment. Feel free to post an answer. – Joe Friend Aug 9 at 20:26
• I hate to pile on with my downvote, but ... see my answer. Looks like whoever is designing these ignores the problems of users like me. – Jyrki Lahtonen Aug 9 at 20:31
• @castoroccupatus A good point, but seeing that this is now the third most negatively received math meta post of all time (in half a day I might add) I think that ship has sailed.... – T. Bongers Aug 10 at 5:01
• I assume the rationale behind the new theme is "we wanted to change things, so we did". It's hard to see any benefit, and easy to see many issues. – Martin Argerami Aug 10 at 5:35
• Quickly going through the list of most downvoted posts on Meta, this is third in overall downvotes and has the second lowest net score. This post might actually achieve the lowest net score this Meta site has seen. Somewhat annoying this change was made during election week, during an election on the meta site when I am forced to use the meta site. Things like this are what beta testing is for. – Brevan Ellefsen Aug 10 at 12:21
• @BrevanEllefsen Now the most downvoted. Which isn't really a surprise. – TheSimpliFire Aug 11 at 12:23
• I could tell it was live, because it shocked me. – Calum Gilhooley Aug 11 at 17:20
• @TheSimpliFire this is absolutely horrible. I've spent the last two hours reading through all the posts from other SE sites hit by this same UX change - only to find that almost no recommendations from the users were taken into consideration on any site, even though the suggestions were given TWO MONTHS AGO. It's to the point where a chunk of the top users on TeX.SE are even considering boycotting and perhaps creating their own site, and I don't blame them - I've lost a great deal of faith in the SE team this week.... – Brevan Ellefsen Aug 12 at 2:06

My biggest complaint is about all the wasted space. I think the text size of the headers is the biggest culprit.

When I go to the main page of math.se, there's just an egregious amount of wasted space.

A user on meta suggested one improvement here. Whether you agree with that suggestion or not, there's got to be a way to use the space more efficiently. (I also really dislike the left navigation panel with its column of wasted space below, but I'm going to disable it so I won't complain about it more than this. My dream would to instead have the buttons from the left nav placed horizontally to the right of MATHEMATICS.)

EDIT: As Aaron Shekey mentions in his comment below, some of this space will soon be used by new features, as discussed here.

When I click on one of my watched tags, I get the following page.

The page is dominated by this huge box that is almost entirely useless to me. I just clicked on one of my watched tags, so I'd like to see the new questions with that tag. Instead I get this box whose features are things that I won't use on a regular basis, and hence don't deserve this prime real estate at the top of the page. I know that I just clicked on the tag, so I don't need the enormous "Questions tagged [abstract-algebra]" reminder of that at the top. Scaling this down and moving the Ask A Question button to the line above would probably already help a lot and might allow me to see another question. I also don't need a description of the tag here: this is a tag I've clicked on hundreds if not thousands of times. (Maybe the description could be drop-down or hover-over?) I also don't think the unwatch and ignore buttons need to be so large and so prominently displayed here. If I really wanted to edit my watched and ignored tags, I'd be more likely to use the panels on the righthand side.

These boxes for tags were already a little annoying when they were changed (somewhat recently, I think?), but the new header text size and new placement of the Ask Question button have really exacerbated the issue. Here's what I'd rather see.

And just for comparison, here's what a similar tag page on another SE site still using the old layout looks like.

• I came to write the same complaints about space and the annoying clutter on the tags page. Thank you~ – DanielV Aug 9 at 19:11
• Excellent post: shows vividly all the white- space currently! And how un-intuitive the current design can me. – amWhy Aug 9 at 19:32
• The white space on the left is particularly bad. It forces me to make the browser window wider to make the questions acceptably wide. – Carl Mummert Aug 9 at 20:17
• @Carl You can get rid of the white space on the left by checking "Hide Left Navigation" in your profile preferences. However, as far as I can tell, this also completely gets rid of the links to "Home", "Questions", "Tags", etc. – Theoretical Economist Aug 9 at 23:30
• Would someone inform the design team that my monitor is in landscape mode, not portrait? – Antonio Vargas Aug 9 at 23:34
• @Carl Actually, if you hide the left nav, you can recover those links by clicking on the left-most icon on the top black bar. – Theoretical Economist Aug 9 at 23:53
• +1 for hand-drawn red circles – Robert Frost Aug 10 at 6:28
• My dream would be that we can drag and drop questions onto the left nav to pin them there, add our favourite links for chat rooms, meta, etc., all the things we use the most. – Robert Frost Aug 10 at 6:54
• +1 for hitting the nail on the head. – gandalf61 Aug 10 at 7:42
• It’s even narrower on the iPad. – Thomas Andrews Aug 10 at 22:59
• @ThomasAndrews I'm not surprised. If you look under the heading Principle #1: Flexibility in the blogpost accompanying the new layout, there are illustrations of what the new layout will look like on various devices. On a phone, it looks like the left nav panel will take up about 40% of the screen... – Quasicoherent Aug 10 at 23:12
• I'd also add that the "Ask Question" appears inside the same box as question titles, which is borderline confusing and somewhat annoying. – Asaf Karagila Aug 11 at 12:12
• I hate the sidebar with a passion. Wasted space, making questions and such get crammed into a smaller area. And my eyes are accustomed to that not being there on all of the other sites, so when I jump to Math it's extremely jarring. Half the time I just go "ugh!" and go back where I came from. – zibadawa timmy Aug 14 at 4:27
• Change obviously hurts familiarity, and people usually like the things they already know. So, any change needs to have significant benfits to outweigh the damage. I don't see any. – bubba Aug 15 at 3:36
• With meta.stackexchange.com/questions/312781/… shipping, the space will be used in a way that makes a lot more sense. – Aaron Shekey Aug 15 at 20:35

Yet another problem with this is that (at least in a comment) a link is barely distinguishable from usual text.

How is anybody supposed to tell at a glance that 7 old answers is a link? THE LACK OF CONTRAST IS A SERIOUS PROBLEM.

In other words, the problem is not unlike what I complained about last time.

Did anybody actually test this in advance? I mean, somebody other than a 20-something with a graphical design degree and a 72-inch monitor. I will reach 55 in October. My eyesight is quite ok, I have an 18-inch laptop. Thankfully, in meta a link is using a distinguishable color (see three lines up). We need the same in main.

Update: links in answers and tag-wikis (in main) are similarly affected. Possibly the color scheme is the same, so fixing it in one place will fix it everywhere.

• The screenshot is from here. – Jyrki Lahtonen Aug 9 at 20:26
• Also depicted in this screenshot: the barely-noticeable contrast between the up and down vote arrows. – rschwieb Aug 9 at 20:35
• Interestingly on meta they are also underlined now(?). Or was this always the case. – quid Aug 10 at 0:46
• Hey, @JyrkiLahtonen I'm that designer. Nice to meet you. I'm 28, no design degree (actually no degree at all) and two 27-inch monitors next to each other (I guess that's 54?). And I also couldn't notice that link! So now that we know each other's bio, I'm happy to announce that fix for links color in question body and comments is coming. Also, happy birthday in advance! 🎂 – Paweł Aug 10 at 11:00
• Thanks @Pawel! Sorry to criticize your work this much. Well, this happens when you make GOMs face a change :-) – Jyrki Lahtonen Aug 10 at 11:03
• @Paweł: since you are reading this thread, you could also think of fixing everything else. And tell us what was the point in all these rushed and unwarranted changes. – Martin Argerami Aug 10 at 12:39
• @JyrkiLahtonen It's all good. On serious note, we're launching new layout/design for bunch of sites at the same time. They are not perfect and they are not polished – we're aware of that. In this particular case we've decided to move fast, break things & iterate. Maybe it doesn't look like one, but it's actually tremendous project – in terms of code, design, infrastructure, information architecture and so on. We're making baby steps and bugs are expected. Math is one of first sites where we launched new design. It's not final, it's work in progress. And feedback from all of you is priceless. – Paweł Aug 10 at 12:49
• Our feedback should not comprise common sense, though, otherwise, expect a sh**-ton of it. – Cleric Aug 10 at 14:36
• A fix for this should go live in our next build. – Aaron Shekey Aug 10 at 16:48
• Thanks @Aaron. Looking forward to it. – Jyrki Lahtonen Aug 10 at 16:58
• Seems to be fixed now. Didn't check it everywhere yet. – Jyrki Lahtonen Aug 10 at 21:47
• > "it's actually tremendous project". Then why are you doing it?? There's an obvious down-side: people don't like new and unfamiliar things. There need to be some significant benefits to outweight this and the time/effort spent on the project. What are those benefits? – bubba Aug 15 at 3:40
• @bubba Our legacy themes often get in the way of our ability to ship bug free features to Stack Overflow and beyond. We need to reign these in and refactor so we can ship new features more easily and regularly. – Aaron Shekey Aug 15 at 20:33

A couple of little problems:

1. When you ask a question, there is an info box on the right which gives advice on how to ask a question. The text "Provide details" is a link. It is hard to tell that it is a link (due to the low contrast and lack of bolding).

Indeed, as pointed out in the comments below, this is a a more global issue—there are two links in the following screenshot other than the "edit" button.

1. Displayed math now has scrollbars.

• You beat me to a post about the scrollbars by less than a minute! – Robert Howard Aug 9 at 18:01
• The link issue is broader than that one example--the link color is generally very hard to tell apart from ordinary text. So for instance, words in the middle of questions and answers that have links are very hard to notice. – Eric Wofsey Aug 9 at 19:15
• Looking at some of my answers, I've found that some of my equations do not have scrollbars; paradoxically, the ones that don't have scrollbars are commutative diagrams, which are bigger than simple equations. – Arnaud D. Aug 10 at 12:03
• In fact, even normal equations don't all have scrollbars. I've even found several answers where some equations have scrollbars and others don't, for no apparent reasons. – Arnaud D. Aug 10 at 12:13
• A fix for the link contrast should have merged and will go live with the next build. – Aaron Shekey Aug 10 at 16:47
• @AaronShekey Wunderbar. When does that happen? – Xander Henderson Aug 10 at 18:02
• @XanderHenderson it's already done – Joe Friend Aug 11 at 5:29

Let me comment with CSS style overrides I use, slightly updated for the new theme. Those style overrides also apply to first-time visitors to which the new site theme must appear like a torrent of voluminous screams under which the good stuff is buried, by now almost without trace.

Let me note that I am an old-school desktop user who does not like eternal sessions. I frequently close my browser and have it forget all session data then. As a result, I get to see the first-time visitors layout frequently, with all that "Here is how it works" stuff, GDPR consent banners, announcement banners and other useless stuff. Honestly, had the site looked like this back in the days, I would never have created an account here.

/* Remove Stackexchange's useless Logo + Link from SE's top bar */
.top-bar .-logo {
display: none !important;
}

/* Remove Stackexchange's redundant "Here is how it works" info box */
.s-hero, .old-hero {
display: none !important;
}

/* Remove Stackexchange's nuisance banners. */
#js-gdpr-consent-banner, #announcement-banner {
display: none !important;
}

/* Remove Stackexchange's left sidebar. */
.js-pinned-left-sidebar {
display: none !important;
}
/* Reclaim its space for actual content */
.container > #content {
width: calc(100% - 16px) !important;
}

Edited: Changed the sidebar selector so that its pendant in the topbar menu remains available.

Edited: Changed the content selector to something less generic.

Here is how MSE looks to new visitors:

That's repulsive. Here is how I like it, with the style overrides:

Same for SO. To new visitors without style overrides:

Horrible. Just horrible. Here is how I prefer it, with the style overrides:

Notice how much more usable space can be gained by hiding the blurb?

Remember that Google became so popular not only because its search algorithm produced useful results, but also because its search form was free of clutter?

• Oh, yeah, Totally. This is exacerbated when you use a phone, with a smaller monitor. Practically 60% of the screen is these annoying banners. Puts me back in 2002, when you'd go into and the first thing to do was to fight pop-ups that covered 60% of your screen. – Asaf Karagila Aug 11 at 16:31
• +1 for this simple css fix. – Paramanand Singh Aug 11 at 17:24
• Of course the CSS override doesn't help first-time users. Indeed, had I been greeted with the current version when I first discovered Stack Overflow (the first network site I found and used), I'm one hundred percent certain that I would not have stayed, but I would have run away and probably never come back. – celtschk Aug 15 at 10:17
• @celtschk: The CSS overrides work as soon as the browser knows about them, and that preparation can be made more durable than SE session cookies (which I clear often). But yes, actual first-time visitors typically do not have this installed and are probably deterred very efficiently by now. I have long stopped recommending SE because of that terrible presentation. – ccorn Aug 15 at 20:46

Here is a screenshot of the behavior I mentioned in the comment.

Note how the title of one question is completely misaligned. This happens precisely on questions with tags I have as favorite. I am using Chrome for Linux.

• And props to all who can spot that the question is a favorite based on the color on a flat screen monitor which is not perfectly centered. – Tobias Kildetoft Aug 9 at 17:25
• One can always customize that color with, say, a Tampermonkey script. With JQuery it would look like $("div.tagged-interesting")$. But yes, the color difference is painfully small. – barto Aug 11 at 11:15
• What linux distro is that? – user159517 yesterday
• @user159517 Ubuntu with Cinnamon desktop. – Tobias Kildetoft yesterday

## 1. Repeated/overlapping equations in duplicates previews (for example through review queues):

(Go to review queues, review question that has flagged duplicate, click to Close, select duplicate of...). I don't remember seeing this before the new theme (I might be wrong though, but anyway would be nice to have this fixed). This happens in Chrome 68.0.3440.106, also in IE 11.0.9600.19100. It's also worth mentioning it happens in every single case if the duplicate has mathjax in it, not just occasionally.

This is not one time occurrence, happens almost always when there is and equation.

## 2. Plenty of [Math Processing Error]s before and after selecting duplicate

This might be related to previous one, but symptoms are quite different, so having this separately. In previous case, there are unusually many [Math Processing Error] occurrences, before selecting and after. However before selecting it seems that it needs to have more questions in review, but still it seems quite reproducible, not a single occurrence.

Example in list of review questions:

Example after selecting question:

## 3. Link underline going through math expressions:

Played with CSS a little, and seems that adding display: inline-block; does the trick, but content is then a bit taller and also forces whole link to be on one line in some cases...

• Is the first problem related to this older problem? Also reported here? – Jyrki Lahtonen Aug 15 at 5:22
• @JyrkiLahtonen It at least looks the same, but through the review queues it seems easily reproducible now (at least for me, I see it in every single case), while the linked ones seem to be rare. Also the refresh does not help in this one. But who knows, maybe it is manifestation of the same issue and it just got exploited better now... – Sil Aug 15 at 6:18
• Does by the way anyone else apart from me see it too, or is it just me? (see also added animation for reproducibility...) – Sil Aug 15 at 6:38
• I see the overlap problem too. Refreshing the page does seem to fix the body (but not the question title) about half the time. Clicking on the question title loads the full question into a box on the page and that fixes it pretty reliably. If it wasn't common in the past, this seems like a regression. Perhaps related, I did see one preview with [Math Processing Error] in it. – Jon Ericson Aug 16 at 0:14
• @JonEricson Nice observation, I am seeing the processing error as well in many cases both in questions review and after selecting one, added it to the list too. – Sil Aug 18 at 6:52

As mentioned in the comment, the left nav is still availble under the hamburger menu in the top left.

I did go to left nav link and turned off left nav panel as instructed (with some difficulty). But now I can't navigate at all - my work flow is to go back to the question list after looking at a question. The back button isn't always the best way to do that.

I will go to left nav link and post this there too, But I need to vent in several places.

• If you turn off the left nav, there is button you can click on the far left of the top bar to access it. – Eric Wofsey Aug 9 at 17:05
• It'd have been helpful if this information were on the settings page that lets you hide the left nav. Otherwise, it seems like there was no way to find those links on the page. At least, it did to me, for a while. – Theoretical Economist Aug 9 at 23:56
• I see that this is true. However, after the left nav panel is turned off, there is still wasted space to the right of the right panel. (I use screen res 1366x768px.) The main panel could be made to use all the width not occupied by the right panel. – Rosie F Aug 14 at 11:17

The new design is TERRIBLE. Please, delete it or put an option to rollback. PLEASE!!!

Delete as soon as possible the left navigation column.

• Go to your profile settings, site settings, preferences, check the "Hide left navigation" box. This is not a helpful suggestion of what can be improved. – Asaf Karagila Aug 10 at 10:35
• Of course it is helpful, it is what many here seem to think. And after "hiding the left navigation box", the "questions" link (that many of us use all the time) is hidden behind a menu. – Martin Argerami Aug 10 at 12:42
• @Martin: This is no more useful than asking that your friend is revived after their body has been through the wood chipper, and you are asked what could be improved. Yes, it would be better if that didn't happen, but reality is different. – Asaf Karagila Aug 10 at 14:07
• @AsafKaragila Great way to put it. Thanks for the laugh. – 6005 Aug 10 at 17:47
• @6005: I've had Fargo on my mind for some reason, I guess... :P – Asaf Karagila Aug 10 at 17:59

I don't see this here yet, but : in the Safari browser on a Mac, math that is larger than a normal text line seems to be cut off. See the integral signs in the top line here: and more seriously the \lfloor nx \rfloor at the bottom here:

Previously, the ambiguity was relieved by the bug allowing me to scroll the display math :) Now I have to right click and inspect the TeX commands.

My setup- Macbook Pro 2016 15 inch, macOS High Sierra 10.13.6, using the Safari browser. Note, the problem does not present itself in Google Chrome. Also the math is not cut off here in math.meta. Test code- $$\begin{array}{ccc}\mathbb R&\longrightarrow&R\\x&\mapsto&\left[\begin{array}{ccc}\mathbb{Z}&\longrightarrow&\mathbb Z\\n&\mapsto&\lfloor nx\rfloor\end{array}\right].\end{array}$$

• If you have a wide formula, it used to line break. Now it can happen that the end seems truncated. On iPad I see no scroll bars but am able to move the content around, e.g. scroll to the left manually. So far I reformatted manually to avoid running into invisible scroll areas. – mvw Aug 12 at 15:50
• Another example of cut off at the bottom. – mvw Aug 12 at 16:46
• I'm working on fixing this, but currently playing bug whack-a-mole with math rendering. Argh! – Aaron Shekey Aug 13 at 20:36

I normally use the site in Firefox on smartphone with "request desktop site" feature of the browser.

The right side-bar which includes meta links, watched/ignored tags and hot network questions no longer appears on right side but is put after list of questions. Very annoying.

I guess this is primarily because of responsive design and I am not sure if something can be done to fix it.

On the plus side I love writing in the edit box (like this answer) while holding my phone in portrait mode (as the responsive design resizes the edit box properly).

Update: I finally did some experiment on desktop and found that if one reduces the widow width beyond a certain point then the right sidebar goes to the bottom. Reducing further width of window moves the left side also to a menu button on top left (in the black bar). So this is their responsive design in action.

The same behavior can be seen if one starts increasing font size (ctrl+) gradually. This is exactly what happens on a smartphone as you have large fonts on 5.5 inch 1080p display. Similar behavior should be seen by default on tab (iPad) in portrait mode although I have not checked it.

I think the way they move the left sidebar automatically into a menu button, there should be a way to move the content in the right sidebar into some menu button at the top.

• Hear hear! ${}{}$ – Asaf Karagila Aug 10 at 15:43
• @ParamanandSingh - The way I attempt to fix that is to uncheck "Request Desktop Site", go to the bottom of the webpage and choose "full site", now recheck "Request Desktop Site" - now you should see the desktop view of StackExchange using Firefox for Android. Sometimes it sticks and sometimes it reverts into a semi-mobile view, not exactly mobile but certainly not the desktop view. --- If they don't fix it soon I'm going to file a bug report. – Rob Aug 10 at 17:27
• @Rob: thanks man, your suggestion works for me and the world feels a much better place now :) – Paramanand Singh Aug 11 at 4:51
• @Rob: I added few more observations and it appears the behavior is by design. Also your suggested workaround seems to turn off responsive design. – Paramanand Singh Aug 12 at 5:16
• @ParamanandSingh - I have responsive on. As I mentioned, the bug is still present, it's not a complete fix: "Sometimes it sticks and sometimes it reverts into a semi-mobile view, ..." --- Now when you reload, or un-check / re-check 'Desktop Mode' most 'new' sites reload as Desktop, and your 'Profile Page' should just load as Desktop without uncheck/check or reloading - sometimes it sticks and on some sites you lose and are stuck with the semi-mobile view ('cuz it's not exactly the same as if you didn't go to the bottom of the page and choose "Full Site") - part of the bug is CSS Bug. – Rob Aug 12 at 5:25
• This Screenshot shows the desktop view I see, (I rechecked the left Menu for the purposes of making this screenshot, usually I have that disabled). It's not particularly sticky and reverts; forcing one to uncheck/recheck 'Request Desktop Site' to reactivate the desktop view (though the 'Profile webpage' remains correct, without the gymnastics). If responsive means fluid that's never worked for me (nor claimed to be avail. yet), but the webpages says it's on 4 me. – Rob Aug 13 at 3:28
• This problem is persistent despite the fixes suggested here in comments. Every time I come back to MathSE or MetaMathSe, it reverts to this "everything in one column" view, not the desktop version. The mobile version is even worse since it just removes all besides the Q&A boxes. This "responsive" design ruins the ability to use full-feature MathSE on mobile. I doubt I am the only one who will stop bothering to come back. – Nij 2 days ago
• @Nij: yeah the responsive design is the culprit here. I wonder if the developers have tested the full site on a smartphone. There should be some way to show the right sidebar along with the list of question. – Paramanand Singh 2 days ago

When I use a zoom > 100, say 125% , the subscripts and the low parts of the equations are masked by the scroll-bar, for example :

I read somewhere that zoom > 100% is not supported. Of course, this explains why the malfunction occurs. Never mind. Nevertheless this is a shame because the people with poor eyesight have trouble reading the equations especially the small characters.

Can we expect this will be fixed ?

• By zoom you mean page zoom (of browser) or the zoom feature in MathJax menu? I normally use the zoom from MathJax, but there are problems now with the MathJax zoom also in the sense that some portion of the equations is not visible after zoom. – Paramanand Singh Aug 16 at 1:36
• @Paramanand Singh : I mean the zoom of the browser (Internet Explorer). It is basically set to 125%. and I avoid to change it because this requires manipulations of setting and re-setting. I did not even try the MathJax zoom. – JJacquelin Aug 16 at 5:42
• Then I think the issue is serious and related to the new theme in which they enabled scrollbars for mathjax equations. There should be some way to disable these scrollbars, but I am not aware of it. – Paramanand Singh Aug 16 at 6:23

There's always been a very slight discrepancy between the line breaks in the preview and in the posted version; every once in a while, one more letter would fit in in the posted version than did in the preview.

This discrepancy has become much more significant with the new theme. The line breaks are in completely different places now, and planning them using the preview has become impossible. This means that longer bits of math that don't allow line breaks can cause severely truncated lines, because you can't rewrite the text to prevent them from occurring at a line break.

This more severe discrepancy occurs only in the preview when the answer is first posted. When a posted answer is edited, the edit preview seems to correspond well with the posted version. If I remember correctly, in the old theme the milder discrepancy on the order of single letters occurred in both previews.

The discrepancy seems to be due to a significant difference in width that occurs because the posted version and the edit preview have the vote count next to them and the original preview doesn't.

Here are screenshots for this answer where I wrote the text such that a long link was all in one line in the original preview, and it's broken in half in the posted version:

Original preview:

Posted version and edit preview:

The screenshots were made in Firefox 61.0.2 under Mac OS 10.13.6 (17G65); the appearance is the same in Safari 11.1.2 (13605.3.8).

The web page is a bit crowded. I'd like it to be more clean and focus more on the question content.

The sidebar in the first figure is not used frequently, leaving it blank looks more relaxed. The "Hot Network Questions"(the second figure) is unnecessary, I think people on one site are less interested in the content on the other unrelated site, and without it we can pay more attention to the question itself on current page.

I really like the stackexchange sites, and hope it can grow better!

Please, center the "Mathematics" site title again. It has only whitespace to its side anyway, and glued to the left side it IMHO looks ugly.

Alternatively, find something useful to put on the right to it. For example, the "Top Questions" page title and the "Ask Question" button would nicely fit there. That would also reduce the amount of wasted space at the top.

But even in that case, the full line (consisting of site title, page title and ask button) should be centered, not glued to the left side.

The font for posts on main is a serif font, while the one on meta is sans-serif.

I'd prefer the same font on both main and meta (either font is fine with me).

[I hope that's not a dupe, but I did not find it.]

• Btw the profile page of any user on main site uses sans serif. Only when we visit questions the serif font is used. This should also get fixed with one font everywhere (main and meta). – Paramanand Singh 2 days ago

New version of MSE makes writing/editing questions very much difficult, i.e. when zooming the page topics to select (Home, Questions, Tags, ...) in the left hand side intrude the text :

# MathJax Zoom doesn't work properly

I'm pretty sure that this is at least partially related to the new theme. In the MathJax context menu (right-click some MathJax) you can enable a zoom feature (MathJax Settings → Zoom Trigger). It appears that currently the zoom box is limited to the size of the MathJax area for displayed (block) math, and it wasn't before the design change. (Oddly, it seems to work properly for inline math.)

Here is a screenshot of an attempted zoom on math.se:

and here is a zoom of the same Markup from physics.se's "sandbox":

Both math.se and physics.se use MathJax v.2.7.4, so I don't think this is a MathJax problem. Physics.se is still using the old theme, which leads me to believe it is a problem with the implementation of the new theme.

(I am using Google Chrome v.68.0.3440.106 under Windows 10.)

Here is a snippet of the Markup for your own testing.

Given $\left\{ a_{n}\::\:n=1,\:2,\:3,\:\cdots\right\}$ is an infinite sequence in $\mathbb{R}$, and every term is positive. How to prove that the set

$$\left\{ \frac{2+a_{n}}{\sqrt{2+a_{n}^{2}}}\::\:n=1,\:2,\:3,\:\cdots\right\}$$ has a limit point?

Bolzano-Weierstrass theorem says that every bounded infinite subset of $\mathbb{R}$ has a limit point. But how to prove

• Thanks for bringing it up here. I had mentioned about it in comments but did not explore the problem fully. – Paramanand Singh 2 days ago

The current mobile theme is unchanged and as such there is no left nav.

## Show / Hide Left Nav Inaccessible

As shown on the screen shot, it's impossible to show or hide the left-nav on mobile because the hamburger's off the left hand edge of the page. Occurs on both Chrome and Firefox, on HTC One M8.

• I don't think this change was supposed to affect the mobile skins. If you search the Ch-ch-ch-changes post on meta.se for mobile you'll find this: "First up is desktop (the mobile skin isn't going anywhere for now)." – castor occupatus Aug 10 at 10:52
• This is how it looks for all sites on the mobile skin, even the ones that don't have responsive design. It hasn't changed recently as far as I'm aware. – Catija Aug 11 at 4:54

Can we do something about the color of the tags? The blue(?) color makes the whole site appear depressing, like a Picasso from his "blue period".

And it could just be my visual taste, but it seems very clunky what with the warmer greenish(?) hues of the featured sidebar and the highlighted questions.

The Ask Question button’s text blends in with the background (unreadable), if it is a visited link:

Main:

Meta:

• I don't have that issue. I think it's a local issue on your side. – Asaf Karagila Aug 12 at 22:22
• (-1) for being too shouty and non-replicable. – T. Bongers Aug 13 at 2:01


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## G = C6×C4⋊Q8order 192 = 26·3

### Direct product of C6 and C4⋊Q8

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — C6×C4⋊Q8
 Chief series C1 — C2 — C22 — C2×C6 — C2×C12 — C6×Q8 — C3×C4⋊Q8 — C6×C4⋊Q8
 Lower central C1 — C22 — C6×C4⋊Q8
 Upper central C1 — C22×C6 — C6×C4⋊Q8

Generators and relations for C6×C4⋊Q8
G = < a,b,c,d | a6=b4=c4=1, d2=c2, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c-1 >

Subgroups: 370 in 290 conjugacy classes, 210 normal (14 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C6, C6, C2×C4, C2×C4, Q8, C23, C12, C12, C2×C6, C2×C6, C42, C4⋊C4, C22×C4, C22×C4, C2×Q8, C2×Q8, C2×C12, C2×C12, C3×Q8, C22×C6, C2×C42, C2×C4⋊C4, C4⋊Q8, C22×Q8, C4×C12, C3×C4⋊C4, C22×C12, C22×C12, C6×Q8, C6×Q8, C2×C4⋊Q8, C2×C4×C12, C6×C4⋊C4, C3×C4⋊Q8, Q8×C2×C6, C6×C4⋊Q8
Quotients: C1, C2, C3, C22, C6, D4, Q8, C23, C2×C6, C2×D4, C2×Q8, C24, C3×D4, C3×Q8, C22×C6, C4⋊Q8, C22×D4, C22×Q8, C6×D4, C6×Q8, C23×C6, C2×C4⋊Q8, C3×C4⋊Q8, D4×C2×C6, Q8×C2×C6, C6×C4⋊Q8

Smallest permutation representation of C6×C4⋊Q8
Regular action on 192 points
Generators in S192
(1 2 3 4 5 6)(7 8 9 10 11 12)(13 14 15 16 17 18)(19 20 21 22 23 24)(25 26 27 28 29 30)(31 32 33 34 35 36)(37 38 39 40 41 42)(43 44 45 46 47 48)(49 50 51 52 53 54)(55 56 57 58 59 60)(61 62 63 64 65 66)(67 68 69 70 71 72)(73 74 75 76 77 78)(79 80 81 82 83 84)(85 86 87 88 89 90)(91 92 93 94 95 96)(97 98 99 100 101 102)(103 104 105 106 107 108)(109 110 111 112 113 114)(115 116 117 118 119 120)(121 122 123 124 125 126)(127 128 129 130 131 132)(133 134 135 136 137 138)(139 140 141 142 143 144)(145 146 147 148 149 150)(151 152 153 154 155 156)(157 158 159 160 161 162)(163 164 165 166 167 168)(169 170 171 172 173 174)(175 176 177 178 179 180)(181 182 183 184 185 186)(187 188 189 190 191 192)
(1 104 26 92)(2 105 27 93)(3 106 28 94)(4 107 29 95)(5 108 30 96)(6 103 25 91)(7 121 187 133)(8 122 188 134)(9 123 189 135)(10 124 190 136)(11 125 191 137)(12 126 192 138)(13 115 20 127)(14 116 21 128)(15 117 22 129)(16 118 23 130)(17 119 24 131)(18 120 19 132)(31 97 42 109)(32 98 37 110)(33 99 38 111)(34 100 39 112)(35 101 40 113)(36 102 41 114)(43 79 55 67)(44 80 56 68)(45 81 57 69)(46 82 58 70)(47 83 59 71)(48 84 60 72)(49 85 61 73)(50 86 62 74)(51 87 63 75)(52 88 64 76)(53 89 65 77)(54 90 66 78)(139 163 151 175)(140 164 152 176)(141 165 153 177)(142 166 154 178)(143 167 155 179)(144 168 156 180)(145 169 157 181)(146 170 158 182)(147 171 159 183)(148 172 160 184)(149 173 161 185)(150 174 162 186)
(1 71 32 89)(2 72 33 90)(3 67 34 85)(4 68 35 86)(5 69 36 87)(6 70 31 88)(7 160 20 142)(8 161 21 143)(9 162 22 144)(10 157 23 139)(11 158 24 140)(12 159 19 141)(13 154 187 148)(14 155 188 149)(15 156 189 150)(16 151 190 145)(17 152 191 146)(18 153 192 147)(25 82 42 76)(26 83 37 77)(27 84 38 78)(28 79 39 73)(29 80 40 74)(30 81 41 75)(43 100 61 106)(44 101 62 107)(45 102 63 108)(46 97 64 103)(47 98 65 104)(48 99 66 105)(49 94 55 112)(50 95 56 113)(51 96 57 114)(52 91 58 109)(53 92 59 110)(54 93 60 111)(115 178 133 172)(116 179 134 173)(117 180 135 174)(118 175 136 169)(119 176 137 170)(120 177 138 171)(121 184 127 166)(122 185 128 167)(123 186 129 168)(124 181 130 163)(125 182 131 164)(126 183 132 165)
(1 119 32 137)(2 120 33 138)(3 115 34 133)(4 116 35 134)(5 117 36 135)(6 118 31 136)(7 94 20 112)(8 95 21 113)(9 96 22 114)(10 91 23 109)(11 92 24 110)(12 93 19 111)(13 100 187 106)(14 101 188 107)(15 102 189 108)(16 97 190 103)(17 98 191 104)(18 99 192 105)(25 130 42 124)(26 131 37 125)(27 132 38 126)(28 127 39 121)(29 128 40 122)(30 129 41 123)(43 148 61 154)(44 149 62 155)(45 150 63 156)(46 145 64 151)(47 146 65 152)(48 147 66 153)(49 142 55 160)(50 143 56 161)(51 144 57 162)(52 139 58 157)(53 140 59 158)(54 141 60 159)(67 172 85 178)(68 173 86 179)(69 174 87 180)(70 169 88 175)(71 170 89 176)(72 171 90 177)(73 166 79 184)(74 167 80 185)(75 168 81 186)(76 163 82 181)(77 164 83 182)(78 165 84 183)

G:=sub<Sym(192)| (1,2,3,4,5,6)(7,8,9,10,11,12)(13,14,15,16,17,18)(19,20,21,22,23,24)(25,26,27,28,29,30)(31,32,33,34,35,36)(37,38,39,40,41,42)(43,44,45,46,47,48)(49,50,51,52,53,54)(55,56,57,58,59,60)(61,62,63,64,65,66)(67,68,69,70,71,72)(73,74,75,76,77,78)(79,80,81,82,83,84)(85,86,87,88,89,90)(91,92,93,94,95,96)(97,98,99,100,101,102)(103,104,105,106,107,108)(109,110,111,112,113,114)(115,116,117,118,119,120)(121,122,123,124,125,126)(127,128,129,130,131,132)(133,134,135,136,137,138)(139,140,141,142,143,144)(145,146,147,148,149,150)(151,152,153,154,155,156)(157,158,159,160,161,162)(163,164,165,166,167,168)(169,170,171,172,173,174)(175,176,177,178,179,180)(181,182,183,184,185,186)(187,188,189,190,191,192), (1,104,26,92)(2,105,27,93)(3,106,28,94)(4,107,29,95)(5,108,30,96)(6,103,25,91)(7,121,187,133)(8,122,188,134)(9,123,189,135)(10,124,190,136)(11,125,191,137)(12,126,192,138)(13,115,20,127)(14,116,21,128)(15,117,22,129)(16,118,23,130)(17,119,24,131)(18,120,19,132)(31,97,42,109)(32,98,37,110)(33,99,38,111)(34,100,39,112)(35,101,40,113)(36,102,41,114)(43,79,55,67)(44,80,56,68)(45,81,57,69)(46,82,58,70)(47,83,59,71)(48,84,60,72)(49,85,61,73)(50,86,62,74)(51,87,63,75)(52,88,64,76)(53,89,65,77)(54,90,66,78)(139,163,151,175)(140,164,152,176)(141,165,153,177)(142,166,154,178)(143,167,155,179)(144,168,156,180)(145,169,157,181)(146,170,158,182)(147,171,159,183)(148,172,160,184)(149,173,161,185)(150,174,162,186), (1,71,32,89)(2,72,33,90)(3,67,34,85)(4,68,35,86)(5,69,36,87)(6,70,31,88)(7,160,20,142)(8,161,21,143)(9,162,22,144)(10,157,23,139)(11,158,24,140)(12,159,19,141)(13,154,187,148)(14,155,188,149)(15,156,189,150)(16,151,190,145)(17,152,191,146)(18,153,192,147)(25,82,42,76)(26,83,37,77)(27,84,38,78)(28,79,39,73)(29,80,40,74)(30,81,41,75)(43,100,61,106)(44,101,62,107)(45,102,63,108)(46,97,64,103)(47,98,65,104)(48,99,66,105)(49,94,55,112)(50,95,56,113)(51,96,57,114)(52,91,58,109)(53,92,59,110)(54,93,60,111)(115,178,133,172)(116,179,134,173)(117,180,135,174)(118,175,136,169)(119,176,137,170)(120,177,138,171)(121,184,127,166)(122,185,128,167)(123,186,129,168)(124,181,130,163)(125,182,131,164)(126,183,132,165), (1,119,32,137)(2,120,33,138)(3,115,34,133)(4,116,35,134)(5,117,36,135)(6,118,31,136)(7,94,20,112)(8,95,21,113)(9,96,22,114)(10,91,23,109)(11,92,24,110)(12,93,19,111)(13,100,187,106)(14,101,188,107)(15,102,189,108)(16,97,190,103)(17,98,191,104)(18,99,192,105)(25,130,42,124)(26,131,37,125)(27,132,38,126)(28,127,39,121)(29,128,40,122)(30,129,41,123)(43,148,61,154)(44,149,62,155)(45,150,63,156)(46,145,64,151)(47,146,65,152)(48,147,66,153)(49,142,55,160)(50,143,56,161)(51,144,57,162)(52,139,58,157)(53,140,59,158)(54,141,60,159)(67,172,85,178)(68,173,86,179)(69,174,87,180)(70,169,88,175)(71,170,89,176)(72,171,90,177)(73,166,79,184)(74,167,80,185)(75,168,81,186)(76,163,82,181)(77,164,83,182)(78,165,84,183)>;

G:=Group( (1,2,3,4,5,6)(7,8,9,10,11,12)(13,14,15,16,17,18)(19,20,21,22,23,24)(25,26,27,28,29,30)(31,32,33,34,35,36)(37,38,39,40,41,42)(43,44,45,46,47,48)(49,50,51,52,53,54)(55,56,57,58,59,60)(61,62,63,64,65,66)(67,68,69,70,71,72)(73,74,75,76,77,78)(79,80,81,82,83,84)(85,86,87,88,89,90)(91,92,93,94,95,96)(97,98,99,100,101,102)(103,104,105,106,107,108)(109,110,111,112,113,114)(115,116,117,118,119,120)(121,122,123,124,125,126)(127,128,129,130,131,132)(133,134,135,136,137,138)(139,140,141,142,143,144)(145,146,147,148,149,150)(151,152,153,154,155,156)(157,158,159,160,161,162)(163,164,165,166,167,168)(169,170,171,172,173,174)(175,176,177,178,179,180)(181,182,183,184,185,186)(187,188,189,190,191,192), (1,104,26,92)(2,105,27,93)(3,106,28,94)(4,107,29,95)(5,108,30,96)(6,103,25,91)(7,121,187,133)(8,122,188,134)(9,123,189,135)(10,124,190,136)(11,125,191,137)(12,126,192,138)(13,115,20,127)(14,116,21,128)(15,117,22,129)(16,118,23,130)(17,119,24,131)(18,120,19,132)(31,97,42,109)(32,98,37,110)(33,99,38,111)(34,100,39,112)(35,101,40,113)(36,102,41,114)(43,79,55,67)(44,80,56,68)(45,81,57,69)(46,82,58,70)(47,83,59,71)(48,84,60,72)(49,85,61,73)(50,86,62,74)(51,87,63,75)(52,88,64,76)(53,89,65,77)(54,90,66,78)(139,163,151,175)(140,164,152,176)(141,165,153,177)(142,166,154,178)(143,167,155,179)(144,168,156,180)(145,169,157,181)(146,170,158,182)(147,171,159,183)(148,172,160,184)(149,173,161,185)(150,174,162,186), (1,71,32,89)(2,72,33,90)(3,67,34,85)(4,68,35,86)(5,69,36,87)(6,70,31,88)(7,160,20,142)(8,161,21,143)(9,162,22,144)(10,157,23,139)(11,158,24,140)(12,159,19,141)(13,154,187,148)(14,155,188,149)(15,156,189,150)(16,151,190,145)(17,152,191,146)(18,153,192,147)(25,82,42,76)(26,83,37,77)(27,84,38,78)(28,79,39,73)(29,80,40,74)(30,81,41,75)(43,100,61,106)(44,101,62,107)(45,102,63,108)(46,97,64,103)(47,98,65,104)(48,99,66,105)(49,94,55,112)(50,95,56,113)(51,96,57,114)(52,91,58,109)(53,92,59,110)(54,93,60,111)(115,178,133,172)(116,179,134,173)(117,180,135,174)(118,175,136,169)(119,176,137,170)(120,177,138,171)(121,184,127,166)(122,185,128,167)(123,186,129,168)(124,181,130,163)(125,182,131,164)(126,183,132,165), (1,119,32,137)(2,120,33,138)(3,115,34,133)(4,116,35,134)(5,117,36,135)(6,118,31,136)(7,94,20,112)(8,95,21,113)(9,96,22,114)(10,91,23,109)(11,92,24,110)(12,93,19,111)(13,100,187,106)(14,101,188,107)(15,102,189,108)(16,97,190,103)(17,98,191,104)(18,99,192,105)(25,130,42,124)(26,131,37,125)(27,132,38,126)(28,127,39,121)(29,128,40,122)(30,129,41,123)(43,148,61,154)(44,149,62,155)(45,150,63,156)(46,145,64,151)(47,146,65,152)(48,147,66,153)(49,142,55,160)(50,143,56,161)(51,144,57,162)(52,139,58,157)(53,140,59,158)(54,141,60,159)(67,172,85,178)(68,173,86,179)(69,174,87,180)(70,169,88,175)(71,170,89,176)(72,171,90,177)(73,166,79,184)(74,167,80,185)(75,168,81,186)(76,163,82,181)(77,164,83,182)(78,165,84,183) );

G=PermutationGroup([[(1,2,3,4,5,6),(7,8,9,10,11,12),(13,14,15,16,17,18),(19,20,21,22,23,24),(25,26,27,28,29,30),(31,32,33,34,35,36),(37,38,39,40,41,42),(43,44,45,46,47,48),(49,50,51,52,53,54),(55,56,57,58,59,60),(61,62,63,64,65,66),(67,68,69,70,71,72),(73,74,75,76,77,78),(79,80,81,82,83,84),(85,86,87,88,89,90),(91,92,93,94,95,96),(97,98,99,100,101,102),(103,104,105,106,107,108),(109,110,111,112,113,114),(115,116,117,118,119,120),(121,122,123,124,125,126),(127,128,129,130,131,132),(133,134,135,136,137,138),(139,140,141,142,143,144),(145,146,147,148,149,150),(151,152,153,154,155,156),(157,158,159,160,161,162),(163,164,165,166,167,168),(169,170,171,172,173,174),(175,176,177,178,179,180),(181,182,183,184,185,186),(187,188,189,190,191,192)], [(1,104,26,92),(2,105,27,93),(3,106,28,94),(4,107,29,95),(5,108,30,96),(6,103,25,91),(7,121,187,133),(8,122,188,134),(9,123,189,135),(10,124,190,136),(11,125,191,137),(12,126,192,138),(13,115,20,127),(14,116,21,128),(15,117,22,129),(16,118,23,130),(17,119,24,131),(18,120,19,132),(31,97,42,109),(32,98,37,110),(33,99,38,111),(34,100,39,112),(35,101,40,113),(36,102,41,114),(43,79,55,67),(44,80,56,68),(45,81,57,69),(46,82,58,70),(47,83,59,71),(48,84,60,72),(49,85,61,73),(50,86,62,74),(51,87,63,75),(52,88,64,76),(53,89,65,77),(54,90,66,78),(139,163,151,175),(140,164,152,176),(141,165,153,177),(142,166,154,178),(143,167,155,179),(144,168,156,180),(145,169,157,181),(146,170,158,182),(147,171,159,183),(148,172,160,184),(149,173,161,185),(150,174,162,186)], [(1,71,32,89),(2,72,33,90),(3,67,34,85),(4,68,35,86),(5,69,36,87),(6,70,31,88),(7,160,20,142),(8,161,21,143),(9,162,22,144),(10,157,23,139),(11,158,24,140),(12,159,19,141),(13,154,187,148),(14,155,188,149),(15,156,189,150),(16,151,190,145),(17,152,191,146),(18,153,192,147),(25,82,42,76),(26,83,37,77),(27,84,38,78),(28,79,39,73),(29,80,40,74),(30,81,41,75),(43,100,61,106),(44,101,62,107),(45,102,63,108),(46,97,64,103),(47,98,65,104),(48,99,66,105),(49,94,55,112),(50,95,56,113),(51,96,57,114),(52,91,58,109),(53,92,59,110),(54,93,60,111),(115,178,133,172),(116,179,134,173),(117,180,135,174),(118,175,136,169),(119,176,137,170),(120,177,138,171),(121,184,127,166),(122,185,128,167),(123,186,129,168),(124,181,130,163),(125,182,131,164),(126,183,132,165)], [(1,119,32,137),(2,120,33,138),(3,115,34,133),(4,116,35,134),(5,117,36,135),(6,118,31,136),(7,94,20,112),(8,95,21,113),(9,96,22,114),(10,91,23,109),(11,92,24,110),(12,93,19,111),(13,100,187,106),(14,101,188,107),(15,102,189,108),(16,97,190,103),(17,98,191,104),(18,99,192,105),(25,130,42,124),(26,131,37,125),(27,132,38,126),(28,127,39,121),(29,128,40,122),(30,129,41,123),(43,148,61,154),(44,149,62,155),(45,150,63,156),(46,145,64,151),(47,146,65,152),(48,147,66,153),(49,142,55,160),(50,143,56,161),(51,144,57,162),(52,139,58,157),(53,140,59,158),(54,141,60,159),(67,172,85,178),(68,173,86,179),(69,174,87,180),(70,169,88,175),(71,170,89,176),(72,171,90,177),(73,166,79,184),(74,167,80,185),(75,168,81,186),(76,163,82,181),(77,164,83,182),(78,165,84,183)]])

84 conjugacy classes

 class 1 2A ··· 2G 3A 3B 4A ··· 4L 4M ··· 4T 6A ··· 6N 12A ··· 12X 12Y ··· 12AN order 1 2 ··· 2 3 3 4 ··· 4 4 ··· 4 6 ··· 6 12 ··· 12 12 ··· 12 size 1 1 ··· 1 1 1 2 ··· 2 4 ··· 4 1 ··· 1 2 ··· 2 4 ··· 4

84 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 2 2 2 2 type + + + + + + - image C1 C2 C2 C2 C2 C3 C6 C6 C6 C6 D4 Q8 C3×D4 C3×Q8 kernel C6×C4⋊Q8 C2×C4×C12 C6×C4⋊C4 C3×C4⋊Q8 Q8×C2×C6 C2×C4⋊Q8 C2×C42 C2×C4⋊C4 C4⋊Q8 C22×Q8 C2×C12 C2×C12 C2×C4 C2×C4 # reps 1 1 4 8 2 2 2 8 16 4 4 8 8 16

Matrix representation of C6×C4⋊Q8 in GL6(𝔽13)

 3 0 0 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 0 12 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 12 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 0 12 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 12 0 0 0 0 0 0 0 6 11 0 0 0 0 12 7
,
 9 3 0 0 0 0 3 4 0 0 0 0 0 0 4 3 0 0 0 0 3 9 0 0 0 0 0 0 1 7 0 0 0 0 9 12

G:=sub<GL(6,GF(13))| [3,0,0,0,0,0,0,3,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,1,0,0,0,0,0,0,0,6,12,0,0,0,0,11,7],[9,3,0,0,0,0,3,4,0,0,0,0,0,0,4,3,0,0,0,0,3,9,0,0,0,0,0,0,1,9,0,0,0,0,7,12] >;

C6×C4⋊Q8 in GAP, Magma, Sage, TeX

C_6\times C_4\rtimes Q_8
% in TeX

G:=Group("C6xC4:Q8");
// GroupNames label

G:=SmallGroup(192,1420);
// by ID

G=gap.SmallGroup(192,1420);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-2,-2,336,701,344,2102,520]);
// Polycyclic

G:=Group<a,b,c,d|a^6=b^4=c^4=1,d^2=c^2,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations

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