Tau.js
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egraether
Support TAU getting added to the JavaScript standard
This issue is dedicated to gather support among developers, that TAU gets added to the JavaScript standard as Math.TAU, so there is no longer the need of a library.
Show your support through leaving a comment.
Thank you!
I'm finding myself always having to set Math.TAU as a constant, or to include a constant definition library to achieve something similar.
I for one would much rather work out the area of a circle with
var area = 0.5 * (Math.TAU * r) * r
because that shows incredibly clearly that you are working out the triangular area under a graph of the circumference.
To achieve something similar with Math.PI results in either confusing duplication
var area = 0.5 * (2 * Math.PI * r) * r
or an opaque formula that says little of its origin
var area = Math.PI * r * r
Haha, I found this while searching for an ES Dicuss thread about adding Math.TAU to the standard. Then I saw who the repo owner is! Hat tip to @egraether for this suggestion.
I found this while searching for an ES Dicuss thread about adding Math.TAU to the standard
did you find any? I saw a discussion about adding it to Dart, but nothing in es-discuss.
ps: +1 for the idea of couse
I didn't, sadly. But there are very few constants in Math, so I'm not sure Math.TAU makes sense. Unless the JS community vouches for helping promote tau that is :)
In the quickly expanding WebGL using Javascript community 2 * Math.PI is everywhere, and I'd much rather see Math.TAU. Tau is such an integral part of so many equations when dealing with circles, radians, and whatnot. I'm sort of wondering how it hasn't been added into the original standard, it's so easy to implement.
This was proposed to ES Discuss a few days ago: http://esdiscuss.org/topic/math-tau
So, I've finally gotten around to tinkering with node.js, and one of the first things I tried (upon thinking that sin waves might be useful for something, and seeing a reference to Math.PI) was node -pe 'Math.TAU', which, sadly, resulted in undefined. Yes, let's please add Math.TAU to Javascript!
Meanwhile, I'm not familiar enough with JS yet... is it possible for one to add as Math.TAU before it's actually in the standard? In ruby, for example, I could simply do module Math; TAU = 2*PI; end, and then I can reference Math::TAU just as I would Math::PI. Is there something comparable in JavaScript?
Oh, hey, looks like Math.TAU = 2*Math.PI works nicely. Is there a reason your Tau.js isn't just doing that?
The standard technique is to check it it's not already defined, before adding it.
if (!Math.TAU) {
Math.TAU = 2 * Math.PI;
}
@lindes TAU.js is more of a joke trying to show that the usage of TAU might be easier in many cases over using PI.
You are quite right and simply defining it in your code via const TAU = Math.PI * 2 does the trick and really is all you rneed. (possible having to use var depending on you environment)
Still glad you found this thread though.
The usage of TAU is also makes the formulas more consistent throughout.
Using diameter for the circumference and then shifting to using the radius for area and volume is a strong indicator that the radius should be used as well in the circumference.
C = πd = π·2r = 2πr
Due to the radius being consistent now with other formulas like area and volume, we can see if 2π is easily available from those ones too.
A = πr² = ½·2πr² Why is half used? Because that's taking the integral of the circumference, and is consistent with many other integral formulas.
V = 4/3·πr³ = 2/3·2πr³ Why two thirds? Because when comparing a cylinder and a sphere, the sphere is two thirds the volume of the cylinder. And, we can derive this from the equation of a circle, see http://www.mathalino.com/reviewer/derivation-formulas/derivation-formula-volume-sphere-integration
The improvement when using TAU
With τ = 2π we have:
C = τ·r The circumference is directly proportional to the circle's radius.
Integrate τ·r over the radius and we get A = ½·τ·r²
Integrate the equation of a circle (x²+y²=r²) over the radius, to get V = ⅔·τ·r³
The math becomes more beautiful, and the clean clear path is easier to follow from one stage to another, when we start with the correct constants and derive the rest by simple integration.
There is nothing joke-like about these improvements. They can greatly enhance the understanding of the formulas, and the lessons learned can be applied in the same way across many other math disciplines.
@pmw57 thanks for the beautiful write up and the much more in depth explanation. I wanted to add that the 'joke' part of my previous message is not about the usage of TAU over PI in math, which I strongly support for reasons you have nicely explained, but rather making it a JavaScript framework. I simply meant that there is no need bringing in a 3rd party library that just defines one constant.
:two_men_holding_hands:
Not sure but I don't think it's very likely to happen 😞
The argument of defining it with Math.PI * 2 is probably to easy. While I'm a strong proponent of TAU I just doubt it.
But frankly what's the argument against having Math.TAU in the standard and letting the benighted who like to see lots of unnecessary doubling in their code use if (!Math.PI) Math.PI = Math.TAU / 2 ?
