add tau to racket/math

[willghatch]

I want to add tau to racket/math.

For an in-depth look at why tau is better than pi, see the tau manifesto. The biggest obvious and practical benefit for Racket users is probably doing rotations and such. A quarter turn of an image is τ/4 rather than π/2, so you don't have to keep track of the extra factor of 2, or whether to multiply it or divide it.

The biggest potential problem is that people could already be using the name tau in modules using racket/math. Perhaps it would be better to use the unicode symbol τ, but that could also be used.

This PR isn't really ready. I haven't added documentation and I'm not really sure that this is the best way to calculate tau. But I want to float the idea and see what people think, especially of the naming issue.

[bennn]

If pkg-build doesn't report a name conflict, then my 2c is to go ahead and add tau to racket/math.

A safe alternative would be to make a new module, like racket/math/constants racket/math/constant or racket/math/extra. I don't dislike this alternative.

[LeifAndersen]

I agree with Ben. I honestly don't care one way or the other about adding tau to racket, but if tau, then why not phi, e (besides in just mzlib, or exp), avagadro's constant, G, c, or one of the many many other super useful constants. At that point, it probably makes sense to put them in a 'constants' module. :)

[rfindler]

If we're going to go crazy with these things, then somewhere in math is probably better. For tau, racket/math seems acceptable (pending the check suggested above).

Locally (researchwise), however, tau has a different meaning, that maybe we might worry about. :)

[soegaard]

2018-07-21 23:15 GMT+02:00 William G Hatch <[email protected]>:

I want to add tau to racket/math. For an in-depth look at why tau is better than pi, see the tau manifesto <https://tauday.com/tau-manifesto>. The biggest obvious and practical benefit for Racket users is probably doing rotations and such. A quarter turn of an image is τ/4 rather than π/2, so you don't have to keep track of the extra factor of 2, or whether to multiply it or divide it.

I am not fond of the idea - mostly based on my impression that tau is not standard mathematical notation. Besides tau is used to denote other mathematical concepts: http://mathworld.wolfram.com/Tau.html A litmus test: Would you use tau in a paper without explaining its meaning? /Jens Axel

[lexi-lambda]

As a purely anecdotal data point, I was personally already familiar with the use of tau to mean “twice pi”, and I would personally find such a definition useful. Including that definition in the standard library of a programming language is rare, but it is also not completely unheard of: Python has included math.tau since version 3.6, and Processing includes a TAU constant.

[samth]

tau seems very likely to be used in some module that also imports racket, since all of racket/math is already exported by racket.

[willghatch]

I'm not terribly worried about modules that use #lang racket, since a user's definition or import of tau would shadow the module language import. But I can easily imagine many modules that (require racket/math) also define tau at the top-level, which would cause an error.

Honestly, I think it would be best to have a constants module that includes numbers like tau, pi, etc. The main reason I would want it in racket/math is that pi is already there. Essentially, I'm on a quixotic quest to put tau on equal standing with pi. Every time in my life that I've used pi, tau would have been easier to use as well as more revealing of the underlying mathematical concepts I was working with. I think it's a pedagogical slam dunk. But perhaps tau in a constants module and pi and tau having cross-references between each other in the documentation it would be just as good.

[LeifAndersen]

Honestly, I suspect Pi being in racket/math rather than math is just a historical accident. If math existed earlier (and it wasn't a TR focused lib), it would probably have been in there. But ¯_(ツ)_/¯, I'm just as happy with racket/math/constants as I would be with math/constants.

[LiberalArtist]

In terms of "the best way to calculate tau", this observation is from the discussion of adding math.tau to Python:

I'd test that tau is exactly equal to 2*pi. All Python platforms (past, present, and plausible future ones) have binary C doubles, so the only difference between pi and 2*pi should be in the exponent (multiplication by 2 is exact). Else we screwed up one or both mantissas (typed the constant wrong, and/or the C compiler is rounding incorrectly) - which would be bad.

[mnieper]

Being a professional mathematician, I can confirm that tau is not a well-established mathematical constant and that their is no major move in mathematics to replace (* 2 pi) with tau. To be honest, adding such a constant to the Racket standard library looks like nonsense to me.

[AlexKnauth]

As a non-mathematician, but someone who occasionally programs games in Racket for fun, I often define tau, or sometimes turn, as (* 2 pi) and then use turn to do rotation and trigonometry calculations for the game. It's much easier to see that something is being rotated a 1/4 turn when it says (* 1/4 turn), and using tau (* 1/4 tau) is just as easy.

[soegaard]

Note that it is common practise to use tau to denote time in physics: https://en.wikipedia.org/wiki/Time_constant Den tor. 18. okt. 2018 kl. 15.30 skrev Alex Knauth <[email protected]

…

: As a non-mathematician, but someone who occasionally programs games in Racket for fun, I often define tau, or sometimes turn, as (* 2 pi) and then use turn to do rotation and trigonometry calculations for the game. It's much easier to see that something is being rotated a 1/4 turn when it says (* 1/4 turn), and using tau (* 1/4 tau) is just as easy. — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#2180 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AAcLxYBippiL0kglyBP1PQlBC1ZO3zXZks5umIJ2gaJpZM4VZw_i> .

-- -- Jens Axel Søgaard

[LiberalArtist]

I didn't explicitly say this earlier, but I was also previously familiar with tau and have written (define tau (* 2 pi)) in various programs. I have particularly heard about tau in pedagogical contexts, which resonates with Racket's roots.

I also see a practical benefit to including tau in #lang racket, rather than some library that must be imported specially. If the main benefit of having tau in the standard library is convenience (given that defining tao is trivial), having to write (require math/tau) (to take an extreme I don't think anyone is proposing) would provide little convenience over having to write (define tau (* 2 pi)). Including it in a module of other mathematical constants would be better, but I often want tau when I don't need other mathematical constants: especially, as @willghatch and @AlexKnauth have mentioned, for expressing rotations.

On the other hand, I do know tau has other meanings in other contexts. (What Greek letter doesn't?) I would mostly second @bennn's suggestion to try adding it and see what the impact actually is: if adding tau to racket/math doesn't break any existing packages, then it seems safe to me.

[LiberalArtist]

As another point in the design space, the Elm standard library includes a function turns equivalent to (λ (x) (* tau x)).

[gfbee]

As a compromise, how about just naming it 2pi and/or 2π?

[willghatch]

@LiberalArtist I think the turns function is a great idea. It is perhaps more convenient as a function than a value -- (turns 1/4) seems slightly easier than (* tau 1/4), I guess, and you rarely want to use tau/pi without multiplying it by some value. It seems like it might be better for name collisions as well, though I really have no idea.

[LeifAndersen]

I mean, I frequently find myself wanting to multiply it by i...
https://en.wikipedia.org/wiki/Euler%27s_formula

[AlexKnauth]

Even when you're multiplying by i for Euler's formula, you'd probably be multiplying i·τ·x in most cases, so (* +i (turns x)) still fits, just one extra pair of parens relative to (* +i tau x).

[LeifAndersen]

The point is that turns makes sense in a drawing library (like racket/draw. Much less so in a generic math library.)

[LeifAndersen]

(By turns I mean the name turns.)