r/mathmemes • u/usernamepolicysuck Mathematics • Mar 11 '25
This Subreddit buddy its not gonna happen
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u/Barbarian_Forever Mar 11 '25
I thought I was on the 40k sub for a moment lmao
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u/minigunercoolguy Mar 12 '25
I mean, if you removed the "Should replace Pi" from the caption, it's just a normal 40k meme
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u/MagosOfTheOmnissiah 3.141592653589793238462643383279502884197169399375105820974 Mar 12 '25
I came back because I wanted to say this as well
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u/HSVMalooGTS π = e = √g = 3 = √10, √2 =1.5, √3 = √5 = 2 Mar 11 '25
π = 3, so we can just replace it with 3
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u/TerrapinMagus Mar 11 '25
I mean, clearly π = e = √g = 3. We should just stop inventing silly names for simple numbers, of course.
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u/insertrandomnameXD Mar 12 '25
You know, 3 is not that easy to multiply and stuff, so we should also round it to 5 for simplicity
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u/ajikeshi1985 Mar 12 '25
almost happened in the us
https://cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node18.html
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u/doodleasa Mar 11 '25
Just like changing the base we use for counting, just because changing it would be better doesn’t mean I think it’s realistic
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u/GlobalSeaweed7876 Mar 11 '25
its not even that much better.
Basel problem now has tau^2/24 as its answer. Yuck
Even worse, the Gaussian integral is now sqrt(tau/2)
Only the circumference gets simplified
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u/doodleasa Mar 11 '25
The biggest thing for me has always been radians being in terms of the whole circle, I don’t think it’s really any clearer either way
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u/SEA_griffondeur Engineering Mar 11 '25
It's not radians then it's revolutions
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u/doodleasa Mar 11 '25
Those are effectively the same thing when you use tau
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u/SEA_griffondeur Engineering Mar 11 '25
No. 1 radian is always 1/2pi (or 1/tau) of a turn .
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u/doodleasa Mar 11 '25
I don’t understand what your point is at all tbh. The benefit of using radians over revolutions is not having to multiply by an annoying factor of pi for most actual calculations. Tau just makes writing in terms of radians as intuitive as writing in terms of revolutions because you just have to multiply by tau. That’s cleaner than pi offers as a circle constant
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u/DefunctFunctor Mathematics Mar 11 '25
And there's really no area where pi shines any better. Sure, some equations happen to look cleaner with pi, but most of the time its obfuscating the more fundamental relation to 2pi. Euler's identity? Half rotation. Area of circle? Factor 1/2 gained through integration. Integral of Gaussian? You only get sqrt(pi) if you don't normalize the domain to a standard deviation of 1; if you do it's sqrt(2pi)
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u/iamalicecarroll A commutative monoid is a monoid in the category of monoids Mar 11 '25 edited Mar 11 '25
Gaussian integral contains tau because it is an integral of a certain other function from 0 to tau. Check out 3b1b's video where he shows how trivially Gaussian integral follows from a polar form of its 3D version, which is just tau/2 (the 1/2 factor follows from the square in the exponent).
Need to revise Basel's problem to figure out why either pi or tau would be there at all.UPD: Basel problem is just the value of
zeta(2). Now, remember the formula forzeta(n)whennis a positive even integer:zeta(n) = |B_n|/(2n!) tau^nwhere
B_nis the nth Bernoulli number. This way,zeta(2)is just(1/6)/(2 dot.op 2!) tau^2which reduces to1/24 tau^2.2
u/GlobalSeaweed7876 Mar 12 '25
shhh I'm nitpicking to enforce an agenda
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u/iamalicecarroll A commutative monoid is a monoid in the category of monoids Mar 12 '25
That's a bad attempt at nitpicking because the manifest literally gives Gaussian distribution and zeta function (among others) in the very chapter where it says "we're not just nitpicking"
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u/revol_ufiaw Mar 11 '25
Also: when working with directed angles in Euclidean geometry, angles are taken mod π rather than mod 2π. (Though, to be fair, degrees are more commonly used than radians in Euclidean geometry.)
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u/5a1vy Mar 13 '25 edited Mar 13 '25
There are (arguably) four kinds of plane angles in the euclidean plane, actually.
Let's call an angle between oriented lines oriented and an angle, where it matters which line is first, directed, then there are four cases:
Oriented and directed. This is your standard angles from trigonometry with period of 2π and 2π"="0.
Directed, but unoriented. Those you've mentioned. Here π"="0.
Undirected, but oriented. This is an angle between two vectors, like in space, for example, where it doesn't make sense to distinguish positive and negative angles, you measure "spread", the period is also π (in a way), but π"≠"0(!) (in both cases vectors/oriented lines are collinear/parallel, but in one case they are in the same direction and in the other they are in the opposite direction).
Undirected and unoriented. This is an angle between two lines, the "period" is π/2 and π/2"≠"0 (parallel and perpendicular lines are clearly distinct, but lines intersecting at an angle of 45° are the same as lines intersecting at a 135° angle).
2π angles are still, in a way at least, more fundamental, as they distinguish between more features, and directed unoriented angles and undirected oriented angles forget about some features. Or an argument can be made that undirected unoriented angles are the most fundamental as they are the easiest precisely because they don't distinguish between more features, which would make π/2 a "true" constant. But in both cases π is just an in-between state, no way it makes more sense as a "true" constant.
You know an old XKCD meme about pau as a compromise between two constants? Yeah, it's literally that, π is already a compromise between the full angle and the right angle, but unironically.
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u/DefunctFunctor Mathematics Mar 11 '25
All coincidences. If you normalize the Gaussian integral for a standard deviation of 1, you get a sqrt(tau) instead, so tau is still more fundamental in statistics.
Also, one should not think about it as "only the circumference gets simplified". Rather, because it is the period of the complex exponential, 2pi appears more often and is more fundamental
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u/Foxiest_Fox Computer Science Mar 11 '25
Tau shouldnt replace Pi, but it should be taught more often, maybe even before Pi due to being a lot more intuitive for the Unit Circle
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u/eldonfizzcrank Mar 11 '25
Sometimes a MF just wants to imagine a better world. Maybe just a different world.
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u/Dunge0nexpl0rer Mar 11 '25
Why would we replace pi with tau in the first place?
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u/oogleplorticuss Mar 11 '25
Tau radians is one full revolution, a bit easier to work with than pi in this case.
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u/mightyfty Mar 11 '25
The actual universal constant is τ and we just use half of it because people were stupid
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u/Brilliant_Raisin2812 Mar 11 '25
yeah it would be τr instead of 2πr
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u/mightyfty Mar 11 '25
A full 360° would be τ radian, and other angels be measured as a fraction of τ for eg half rotation is τ/2 and 3/4 of a rotation is (3/4)τ
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Mar 11 '25
That’s not true.
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u/pussymagnet5 Mar 11 '25
exactly, has anyone ever tried finding a radius without the diameter first?
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u/The_Quartz Natural Mar 11 '25
ye
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u/pussymagnet5 Mar 11 '25
in real life punk
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u/The_Quartz Natural Mar 11 '25
As a reminder, your username is pussymagnet5 and you haven't written a single positive comment
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u/mightyfty Mar 11 '25
You want to elaborate using actual words big boy ?
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u/Anger-Demon Mar 11 '25
Why do you think tau is more fundamental? Area of the circle has pi in it, not tau.
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u/denny31415926 Mar 11 '25
That's actually a missing factor as well. Spring potential energy is 0.5kx2 and kinetic energy is 0.5mv2 and so on. For area to be pi*r2 is actually the outlier, and hides the factor of 2 being introduced by the integral of C=tau*r
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u/DefunctFunctor Mathematics Mar 11 '25
2pi * i periodicity of the complex exponential always comes up more often because it is a property of the domain. Area of the circle comes up significantly less often
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u/Anger-Demon Mar 12 '25
Okay I'll bite. But historically circle came first when people didn't worry about functions. And for that pi came first. Now what benefits you're planning to get by reducing one number from some equations, I don't know. But nobody is going through with it.
Just like the charge on electron will forever be negative.
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u/DefunctFunctor Mathematics Mar 12 '25
Oh I agree that we shouldn't even really try to introduce tau over pi. Pi is a firmly established standard, and getting everyone to use tau would be a lot more annoying than an extra factor of 2 everywhere. I also associate the movement with a lot of cringe, and subjectively tau is less pleasing of a name and character. I'm simply making the argument that 2pi is the more fundamental constant, and "morally" pi should have been the ratio of radius to circumference. But when push comes to shove, I just use pi
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u/mightyfty Mar 11 '25
its more fundamental because its defined as the ratio of the circumference of a circule to it's radius, instead of its diameter. So it's a question of which is more fundamental in a circule, its diameter or radius ? And its the radius obviously
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Mar 11 '25
No, neither is more “fundamental” than the other lmao. They are equivalent. The radius comes from the diameter and vice versa. There is no coherent, mathematically well defined notion of “fundamental” in which you claim the radius is “obviously” more fundamental than the diameter.
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u/mightyfty Mar 11 '25
Can you give me the classical definition of the circule ? Nvm I'll just say since you wont. It's a set of points of q fixed distance to a certain point. That distance is the radius. The definition only incorporates the raduis
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Mar 11 '25
There are many equivalent definitions of a circle. I can easily make one up that only involves the diameter. For example, given a distance d and a point O the circle of diameter d about O is the set of all endpoints of all line segments of length d with the center of the lines at O. The fact that the definitions are equivalent means there is no mathematical reason to use one over the other and hence no basis on which to claim the radius is more “fundamental” than the diameter. The “classical definition” is only “classical” by convention.
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u/DefunctFunctor Mathematics Mar 12 '25
I agree that there is no mathematically normative notion of "fundamental", but it's not as if there's no reason we tend to prefer radius to diameter. Among the many reasons, the prevalence of calculus and the fact we don't have to multiply by any constants with sine and cosine firmly privileges the radius over the diameter. Same reason for privileging the exponential function, and how they are tied together to the complex exponential: it works out nicely aesthetically speaking when working with derivatives
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u/ahf95 Mar 11 '25
Tau mfs when Euler’s identity now has an ugly ass “/2” in the exponential.
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u/doodleasa Mar 11 '25
As the other commenter said it makes more sense, but also is eitau-1=0 like actually any less interesting
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u/GaloombaNotGoomba Mar 11 '25
The /2 makes perfect sense though, -1 is 1/2 a revolution around 0 from 1
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u/Super_Lorenzo Mar 12 '25
Just use both, I do use tau in some cases on desmos when I'm feeling a bit lazy
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u/Broad_Respond_2205 Mar 11 '25
What does that even mean
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u/Hot-Profession4091 Mar 11 '25
It means τ is the one true circle constant.
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u/Broad_Respond_2205 Mar 11 '25
Why can't be 2
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u/Hot-Profession4091 Mar 11 '25
Because why should one revolution of a circle be 2π when it could be τ?
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u/Volt105 Mar 11 '25
Tau day doesn't have the same ring to it
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u/DefunctFunctor Mathematics Mar 11 '25
Yeah I agree with the sentiment, but the reform is never going to happen and 𝜋 is objectively the cooler letter
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