Tau replaces Pi - Numberphile

Should Pi be replaced by Tau? Professor Phil Moriarty thinks so.
More links & stuff in full description below ↓↓↓
See our collection of Pi videos at: • Pi on Numberphile
See ViHart's Tau video at: • Pi Is (still) Wrong.
Tau manifesto: tauday.com/
Professor Phil Moriarty is a physicist at the University of Nottingham. His "scrawls" from this video can be seen on Flickr at: www.flickr.com/photos/numberph...
NUMBERPHILE
Website: www.numberphile.com/
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberphile_Sub
Videos by Brady Haran
Patreon: / numberphile
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanblog.com/
Sign up for (occasional) emails: eepurl.com/YdjL9
Numberphile T-Shirts: teespring.com/stores/numberphile
Other merchandise: store.dftba.com/collections/n...

[@rlrsk8r1]

So does that make my Raspberry Pi 2 a Raspberry Tau?

[@openshores4288]

+rlrsk8r1 genius ahaha

[@verward]

lel

[@JannikPitt]

+rlrsk8r1 made my day :D

[@xWood4000]

Great joke!

[@zupanmarko9722]

what shuld i do?? I have a Raspberry Pi 3... is that Raspberry Tau and a half?

[@TehFrasssaa]

I can imagine how this goes: Most of the world adopts Tau, the US refuses and stays with Pi and the UK starts to switch to Tau but stops half way through leaving somethings using Tau and others still using Pi.

[@Hennal_]

basically Kappa

[@BubbaJ18]

You me the UK goes π radiants then stops

[@kyay10]

@@BubbaJ18 I think u mean tau/2

[@BubbaJ18]

@@kyay10 no... Because π for the win

[@boots7859]

TehFrasssaa, lol, we'll switch to Tau when you lot get to the moon. Pi worked fine for us 50 years ago...

[@jschnurrr]

The length of the video is pi + tau :-)

[@bunderbah]

instead of saying pi + tau I would rather say 3pi

[@whitherwhence]

Either 3 pi or tau and a half. Decide which one you use.

[@thefran901]

We should have a new greek letter to represent 3pi then.

[@jimharmon9917]

Not really - It's 9.7 minutes. (j/k I know what you mean)

[@whitetomato]

use epsilon! it looks like 3 in a mirror. whenever you forget that epsilon=3 pi, get a mirror and look. You'll have your answer!

[@Lugh314]

I love how absolutely mad this man is. Also, I can only imagine the jokes he gets with a name like "Professor Moriarty"

[@danielemessina1979]

I find confusing that Pi has two legs and Tau just one, but Tau is supposed to be twice Pi...

[@Brooke-rw8rc]

Think of the top of pi/tau as a sin wave, representing circumference and the "legs" are radii under the fraction. Pi = C / (r+r) Tau = C / r The symbol for pi is two radii under the circumference, and the symbol for tau is one radius under the circumference.

[@Andy-th9kj]

Think of it as the negative space. pi has room for 1 line in the middle, tau has room for 2 around it. Lol

[@Q4056]

actually, tau was originally proposed as a way to express pi/2, and tau looks like half of a pi symbol, but that never caught on. As to why proponents of a symbol for 2pi chose tau, -I imagine it's simply because of the visual similarity and nothing more.- I just thought of something: Tau is roughly equivalent to the English letter 't', which is the first letter of the word 'turn', and tau radians corresponds with one turn around a circle.

[@Brooke-rw8rc]

Exactly, one tau = one turn.

[@Brooke-rw8rc]

Also the similarity, and also to use a symbol that already existed, so you wouldn't have to fight typographers as well.

[@MoneyLounge1]

Why are they talking about me?!

[@1r587]

+Igor Pavlov Because Tau is 2× Pi and you said "too Pi" and too sounds like two.

[@Peter_1986]

+Tau Rios Because they want you to show up at their office and talk about maths.

[@kaina5467]

Your name sounds too pi for me

[@harshsinghal4342]

Most people don't know you exist in this world and they want you to be recognized.

[@syedrehanfida]

Because you're better than Pi! :)

[@BillySugger1965]

The other thing which came to mind while watching this again was that when saying a whole circle is pi radians, pi is defined in terms of diameter and radians in terms of radius. It's relating apples and oranges. A circle being tau radians relates apples with apples, as both tau and radians are defined in relation to radius. Tau then becomes a simple conversion constant between distance and angle, and is a much more powerful concept.

[@fockoff]

circle with diameter 1 has circumference 3.14159... =π apples to apples. when you mesure it, it's easier to get the diameter of a circle/ globe.. yet when you draw it, you use the radius then you have circumference = 2.π.radius here again you have apples with apples. then you go in angle / frequency/ period measurements and calculations that go more or less elegant depending on if you're using π or τ.. and that can reduce easier as well.... everybody say τ=2π.. it would be different if we were all saying π=τ/2

[@dialecticalmonist3405]

@@fockoff But when you construct a circle, you use a radius rotating around a point. The point comes first, then the line, then the circle. A natural progression of dimension. The diameter requires you to first draw a line, then find it's center, then rotate it around that center. Which is not a natural progression of dimension.

[@arpsichord7474]

@@dialecticalmonist3405 doesn't matter, pi is easier to find. Which is one reason why tau will fail.

[@llamahguy7229]

We should have diameterans not radians

[@nutronstar45]

@@arpsichord7474 easier to find ≠ easier to use

[@josephbowlsby7289]

I prefer Pau Pau = 1.5Pi

[@anisvlogsdz9504]

You serious ?

[@MrCrashDavi]

Tau=0,75Pau=2Pi=4Beta Beta is from another youtube comment I found.

[@aryansingh2199]

no, pau = pi+tau over 2, or pau is the mean (average) of pi and tau. You can't exclude tau from the equation finding the value of the compromise between pi and tau.

[@jeffinton9972]

No ω = πtau÷2⁷+π³

[@mirageinthedesert5448]

CrashDavi actually tau = 1 1/3 pau

[@AaronHollander314]

The confusion (and eventual resistance) begins when you define Tau in terms of Pi.

[@MeltedMask]

Tau = circumference/radius Pi = circumference/diameter. No problem here

[@nutronstar45]

pi := tau/2

[@diabl2master]

I know what you mean yeah every time he did that I cringed a bit yeah

[@francescofavro8890]

how can i trust someone named "moriarty"?

[@SianaGearz]

+Francesco Favro Well, i looked it up, and the name roughly translates as "navigator". If you're not gonna trust a navigator, whom or what should you trust? Besides, it's just a common Irish name. Perhaps you shouldn't trust any Irish person either just in case they have a Moriarty in their family tree.

[@francescofavro8890]

damn irish criminal masterminds!

[@MartinSStoller]

+Francesco Favro In this case, at east, implicitly... :) But, not the one in Holmes' world... No no, don't trust that one!

[@quarkyquasar893]

+Siana Gearz Go see sherlock holmes the game of shadows

[@keithdawes2685]

+Francesco Favro: Elementary , my dear Francesco...

[@Falney]

Tau is better than Pi because with Tau you actually get two Pi's for your money... Delicious.

[@1StateofFlux]

+Falney very underrated comment

[@parrybotter6239]

+Falney Radians is the only measure of angles if you want calculus to be beautiful and simple. If x is measured in radians, and y = sin(x) then dy/dx = cos(x). This is only true if x is measured in radians. If x is measured in other units then you get a conversion factor. If x is in degrees then dy/dx = (π/180).cos(x). If x is measured in "turns", i.e. 1 turn = 360 degrees = 2π radians then dy/dx = 2π.cos(x). Taylor Series and second order ODEs become VERY messy without radians.

[@xenon9562]

+Falney Pie is *nasty*.

[@Falney]

+Xenon You are a heathen and a fraud... Get out... And feel free to let the door hit you on the way out :P

[@xenon9562]

Nah. How about the door can hit you instead? Falney

[@denny141196]

But a perfectly good pun would be ruined, and we wouldn't be able to eat pie on pi day.

[@mohammedmiyaji6799]

oh but you missed the point here.. you get to eat TWO PIES on TAU day. :) everyone wins :D

[@randomguy263]

But pi day is actually on 14/03 so it really isn't pi day.

[@crec0269]

How exactly is this not a pi day? Just curious

[@Saturn.argo.]

Imagine having Pi and Tau day. On 03/14 you get one pi and in 06/28 you get two!

[@slice6298]

@@randomguy263 There are some countries Which I'm not gonna name That write this datę as 03/14

[@OmicronChan]

First things first, put tau on the standard scientific calculator. Then it will get used.

[@chadliampearcy]

What came first the chicken or the egg.

[@Catishcat]

Nope, tau/2 will be used more frequently.

[@1r587]

Put both Pi and Tau on it.

[@dangi12012]

Call Tau -> O and π -> D That makes O/2 = D O = 6.2831.... That would make it easy to teach this in school ;)

[@connor4317]

HD_Picard why do you have my profile picture???

[@aeon00000000]

I want this guy as my teacher! "That's one turn!" *turns around*

[@travboat]

The key word there was "clarity." It would make SO much more sense for students learning the unit circle.

[@rohanjoshi3630]

This is a really good introduction to the concept of tau. I like the emphasis on the fact that the importance of tau is that it is a much more natural way to teach angles and trigonometry.

[@thescowlingschnauzer]

"You can call the angle whatever you like, but conventionally we denote it by THEATRE!" Tell me I'm not the only one who happened on that magical mishearing.

[@laurentjacob1729]

How about instead of radians for radius, we had dongers for diameter. Then a circle would have pi dongers as circumference. or pi/4, pi/2, 3pi/2, pi dongers at every 90 degrees !

[@randomguy263]

Because they would get demonetized by KZbin.

[@LittleBishop001]

Diamans ?

[@ragad3]

diametans

[@martinnolin2315]

Then the maths doesn't go together. Calculus and trigonometry builds on radians. Angles are defined as arc lengths of the unit circle. And the diameter of the unit circle is two.

[@martinnolin2315]

PS: Our own number system is based on the unit circle. 0 is the center point and 1 and -1 are the edges.

[@Monsolido]

But right after you learn that Circumference = 2 PI R, you also learn that Area = PI R² so that would make Area = Tau R² / 2. Seems more confusing to me.

[@thefran901]

You can still be using pi, it's just use tau when you have 2pi.

[@llyorig]

I think in fact it's not a problem. Try to separate equation like (Area) = (Tau) (R²/2). So why R²/2 ? You probably know the utility of dérivative in physics (derivative concern the variation of something in time). Firstly, when you derivate x²/2 it gives you x and if you dérivate x² (without the /2) you get 2 x (so a 2 appear). Well, I think x²/2 is more natural in a derivative problem, and the waves are derivative problems. But maybe it's not a way to explain to a student who ask your question why use tau instead of pi, cause pi/tau appear earlier than derivative ^^ But I don't know much more tings about Pi and derivative, so maybe I'm wrong.. or not ^^

[@victorselve8349]

just a random thought what about pi/2 so that you work with a right angel and you would have the important points of the sin cos... also complex numbers would be easier to handel if you use right angels.

[@nameplaceholder]

Well, think about it like this: if you approximate it with triangles with infinitesimally small base and add them all up, the area will be Area = 0.5 * h * b by using the formula for triangles, whereas h = R and b = Tau * R in our case. Area = 0.5 * Tau R² makes sense that way, don't you think?

[@RockGodFuck]

But 1/2xy^2 is one of the most occuring quadratic expression. Distance fallen: y = 1/2 gt^2, Potention energy in a spring: U = 1/2 kr^2, Kinetic energy K = 1/2 mv^2. As you see this term is everywhere.

[@BenjaminWirtz]

It probably wouldn't catch on in America simply because we are not good at transitioning, we still refuse to transition to Metric even though it makes so much more sense.

[@jeremy3046]

Not saying metric is WORSE, but our system does have the advantage of being easy to divide. A yard can be divided into 2, 3, 4, 6, 8, 12, or 18 inches while a meter can be divided into 2, 4, 5, 10, 20, 25, or 50 centimeters. Same number of ways to divide, but 36 is much smaller than 100, making it roughly thrice as dense. Same goes for 12 and 10. Like pi v tau, it is not a trivial decision.

[@BenjaminWirtz]

Jeremy Hoffman I know about that in terms of arguments that a base 12 system is better than base 10 for that reason, but how is a mile easily divisible into feet?

[@TheRealFlenuan]

*Exactly!* This is another reason why we need a global counterculture revolution.

[@siquenoquenoquesi]

Jeremy Hoffman 8 doesn't divide 36, dude. Anyway, I get your point.

[@Sty1a]

***** congratulation you've now made the stupidest comment of march 2015...

[@Cloiss_]

How do you DO this!?!?!?! 9:42 is tau + pi...

[@rich1051414]

+EpikCloiss37 Tau + Tau / 2 = (1 + 1/2)Tau = 1.5 * Tau Did I really need to teach you this? Just treat pi's as half tau's, and it should also make sense in the context, when you actually need a pi and not a 2pi.

[@Froggeh92]

+Richard Smith You missed the point entirely. Classic

[@Cloiss_]

I've been ignoring these notifications forever, but I think I'm going to clear something up. The fact that the video addresses both tau AND pi is why I chose tau + pi and not 3pi or 3tau/2.

[@renedekker9806]

The video is actually 9:41 long for me...

[@Cloiss_]

@Adi Septiana Rhetorical. The question was rhetorical. (and referring to the video length, I suppose)

[@scroggsie1]

this brings me back to learning pi for the first time at school i remember feeling the disconnect between using diameter to define pi but then as soon as you use pi to define other aspects of geometry (area of a circle etc.) you forget about diameter and use radius and it always struck me as weird and a bit redundant and this sorta explains why.

[@kendo512]

Love the energy coming from this guy. It's awesome to hear someone talk about something about which they really care

[@timtran9563]

“Waiter, I want a pie”. The waiter brings over a pie. “Waiter, this is only half a pie.” Waiter says “Nuh Uh, look, I can prove it with math.”

[@kseliascryser5259]

I dare you to order a tau in Germany. Waiter is totally gonna show you the ropes.

[@fluffydragon1525]

Depends on the radius of the pie, though. Half a pie is only pi radians

[@bronzedivision]

It'll be harder, and virtually useless, until there is a Tau button added to calculators.

[@drednaught608]

The bane of my existence is the lack of a tau button on my calculator.

[@Peter_1986]

Most graphing calculators allow you to program a value into a letter; I always have the letter T defined as 2*pi on my calculator. For some extra fun, you can of course also go ahead and plug in various useful values in all the other letters as well, like the gravitational constant into G and so on.

[@perwagenius3721]

Laurelindo yes! it makes classes so much easier

[@tAcOzRtAsTy]

i like how he keeps trying to teach his cameraman

[@iagocesararaujocorreia181]

I'm more of a tau person, but I think Euler's identity with pi gets much more amazing. Think about it, you're investigating logarithms and circular functions, when you realize their relation by the simple and beautiful formula, but not only that, you find out by accident the logarithms of negative numbers! People usually don't pay attention to that.

[@theexcruciator8664]

If teaching is the issue, then it shouldn't be an issue. Young children will only learn the basics, such as calculating the area and circumference of a circle. While it is indeed easier to calculate the circumference using Tau, it is easier to calculate the area using Pi. So clearly, there is no advantage to either of them in this situation. If someone decides to study Maths or Physics in University, they will be old and smart enough to not be bothered by the fact that 2 Pi is everywhere. It is definitely not a problem for physicists and mathematicians because they can already calculate more difficult things than this so calculating 2 Pi won't bother them at all. It's not a problem for children either because Tau and Pi both have a disadvantage so if they were replaced, it would make no difference. Equations with Tau: Tau r Tau/2 r^2 Equations with Pi: 2 Pi r Pi r^2 In fact, I think Pi has the advantage for children. 2 Pi is much easier to remember than Tau/2, especially because it is already in a more complicated expression. So this is about replacing 2 Pi r with Tau r and replacing Pi r^2 with Tau/2 r^2. Just look at how complicated that last one looks. There is literally no point in replacing them.

[@Wynkrs]

I agree, but I think pi is slightly better due to that it is defined by a ratio, and I don't like the idea of a mathematical constant being defined as a ratio times 2, not to mention the fact that we already use it anyways

[@finlaymcewan]

+Evan Follman Tau is defined as C/r

[@Wynkrs]

Finlay McEwan r is d/2

[@finlaymcewan]

Evan Follman I'm just pointing out that Tau is defined by a ratio also

[@Wynkrs]

+Finlay McEwan yea I guess

[@burlapsack7759]

I think most electrical engineers would want a word with you.

[@lynxfl]

Wait why? Even with Fourier transforms the factor is 2pi. The only thing I can think of where pi comes up without 2 is the F transformation of Sin and cosine (with the delta impulses)

[@insomnia20422]

why not just use tau when tau makes more sense and pi when pi makes more sense that'd way too logical i guess

[@Imbeachedwhale]

@@lynxfl Tau is already used as the time constant.

[@lynxfl]

@@Imbeachedwhale Wouldn't mind a change there, an already difficult signals class was made worse with the terms t, T, and τ being used in the same equations

[@davinchristino]

@@insomnia20422 That's be unnecessarily confusing

[@PrimusProductions]

tau/2 radians=180 degrees e^(i tau/2)=-1, you end up backwards, negative. tau radians =360 degrees e^(i tau)=1, a full revolution, you end up at the same place

[@psteffas]

I think what this boils down to is that Tau is a more fundamental value. If Pi is always multiplied by 2 to make it useful than really Tau is the more basic. My take is that in ancient times it was easy to measure a diameter and hard to measure a radius. So Pi the is ratio we use today.

[@BillySugger1965]

True, but to draw an accurate circle you draw it with a radius, not a diameter.

[@janeweber8654]

Billy Sugger Could you elaborate? The way that I see it (I might be looking at it from a flawed/bias perspective), is that whether you use the radius or the diameter, you still get a perfect circle. Or do you mean in a classroom where you use a compass?

[@BillySugger1965]

Practically, you draw a circle with compasses or something which keeps the pen a fixed distance from the centre point. Mathematically, you define a circle as the locus of fixed radius from the centre. The "2" in 2pi is a correction for the inconsistent use of radius and diameter. We define radians in terms of radius, but pi in terms of diameter. So the "2" is required to fix this error. So what better than to use the value "2pi" as the circle constant and call it tau?

[@janeweber8654]

Billy Sugger That's when creating a circle, but when you're measuring an existing one you can't measure the radius unless there's already a point in the center. So in some cases, Pi is better. Also how would you determine the area? Tau/2 * r ^ 2? So why don't we just use both?

[@BillySugger1965]

You can of course use both. You're free to do so. But take the area equation we all know: A = pi.r². That is nice and simple, but it has a missing 1/2 which is inherent in the nature of the solution - integration. It should be of the same form as the area of a triangle, which a circle becomes if unwrapped along a radius so each successive circumference in opened out to a straight line. In this form, A = 1/2.tau.r², not only is the answer the same but the meaning within the equation is more accessible. But if you want a simpler formula, use A = pi.r². As for measuring a circle, the ease of measuring a diameter is an artifact of the practicalities of measurement. So measure 2r and divide by 2 to get r. For the rare occasions you measure a physical circle that's no handicap, and the math with tau becomes much more natural (though less familiar to those already using the pi version).

[@themissingn]

I want to see a 10 hour video of Phil Moriarty spinning around.

[@sociallyawkward99]

Ugh... simple harmonic motion... don't remind me.

[@SirCutRy]

***** We have that in freshman year of high school in Finland. IF you take optional physics courses. But in grad school? You're brain has hardened by then :D

[@Xenro66]

SirCutRy We also have this in the UK, but in college (which is still high school I think), but we do it in the second year.

[@tugafighter]

SirCutRy We only learn it in college in my country, but on the other hand we learn how to distinguish 'your' from 'you're' in the fifth grade. Priorities, priorities...

[@SirCutRy]

Pedro Leitão I know the difference. Sometimes it just slips.

[@DarkLordGiggles]

+sociallyawkward99 It's even worse in quantum mechanics.

[@HellO-ly1bp]

one minor issue i can think of with tau is that as an engineering student, tau is very common notation for time constants, time delays and dimensionless time and stuff like that. whereas pi is pretty much unanimously the circle constant. using the symbol tau might confuse me as an engineer. i wonder if there is another symbol available that could possible be used that wouldn't have this problem?

[@MontagoDK]

I've been a programming for 20 years and EVERY FREAKING TIME i need to do angular maths it's a struggle to remember how degrees convert to radians and vice versa... Using Tao seems so much simpler ! He's right, the direct correlation to one revolution makes it so much simpler to understand instead of the 2PI calculation. it's a bit anoying that 3.141592 is hardcoded in the brain after years and years of math when 6.283185 would be so much more helpful ...

[@LameGeneration91]

EXACTLY !!!

[@andykerr3753]

Agree. If you're a mathematician and you see maths as more a philosophical language of reality and are comfortable with it you might be ok. Tao just seems so much more intuitively correct in it's description to applied, and experimental scientists. Let alone, as was touched apon, how much easier it is for students to scratch beneath the veneer to the substance of the mathematical concepts of reality described.

[@liesdamnlies3372]

It's the last part, when it comes to teaching, that makes me a proponent of tau. Simply because I've had to go back and refresh my trig, and for me at least, ignoring how the book defined radians and instead using tau is really what made it "click".

[@skydude221]

Just do this const tau = math.pi*2 or #ifndef tau #define tau math.pi*2 #endif

[@deeptochatterjee532]

Martin Kirk Tau*

[@lordmetroid]

No gradual adoptions! Just look at the US sticking to their feets and pounds. You have to make a proclamation that from this day forward we will use this so "deal with it!"

[@Brooke-rw8rc]

But you don't have to change the current usage. Just change it in school and wait a generation.

[@YaamFel]

Lord Metroid Like how in '67 sweden simply switched to driving on the right side of the road. A lot of accidents happrned that day

[@IlersichProductions]

en.wikipedia.org/wiki/Dagen_H No, actually. The switch saw a temporary decrease in accidents.

[@erikpetto3672]

It doesn't matter how many accidents happened that day. Compare it to how many accidents would have happened if we switched gradually.

[@VollkinSea]

RedstonerProductions quite the contrary. Everyone was so careful that accidents would be so hard to accidentally cause

[@tobiasgertz7800]

Clocks run "clockwise" because thats the general motion of a sundial. The first clocks mimicked that motion.

[@coastersplus]

Would someone please explain to me why the greek letter tau looks more like half of pi?

[@drednaught608]

Because it's divided by 1/2 :P

[@Algebrodadio]

Drednaught mmmmm....noooooo.... Tau is 2 times pi.

[@drednaught608]

Aaron Wolbach​ You misunderstand, pi / 0.5 = tau. Dividing by a half is exactly like multiplying by 2 and pi * 2 is tau.

[@sabberi]

And if you multiply pi by two, carry the tau, go around, divide again by pi, divide by two (the very same two as previously), to the power of the given radius, times pi, divided by tau, you can never go back home again.

[@sabberi]

There are so many plies when it comes to pi. It's like a perfectly round onion.

[@vuurniacsquarewave5091]

I always had two different versions of pi in my head, one for circles, and one when describing periodic functions (mostly trigonometric functions)

[@yoda-ghost]

but you get this other beautiful equation: e^i(tau) - 1 = 0

[@neoneapolitan2122]

Albert Einstein was born on March 14th, 1879. March 14th (3/14) is also known as Pi Day!

[@jarumboy1]

+Neo Neapolitan he was born on 14/3 not 3/14 because he was born in germany

[@aneeshsrinivas9088]

elon musk was born on tau day

[@c2thamax246]

I like this guy’s energy. Rapid and concise. Willing to spin around several times to illustrate his point.

[@johngraesser4911]

When changing from a finite system that graphs to a circle to a time based system that graphs to a sine wave, the 2 pi notation aids in determinating positive from negative values of the wave.

[@3DCGdesign]

This is a clear explanation, thanks! (I wish when I learned this stuff way back when that we would have used Tau.)

[@TheRealFlenuan]

3:46 You "have no idea" as to why? I'm surprised to hear that coming from a mathematician. Think about it: if you were to measure angles clockwise, you'd start in the positive x-value, negative y-value quadrant (Quadrant IV)-rather than the positive x-value, positive y-value quadrant (quadrant I)! It's the same reason for which the quadrants are measured counterclockwise.

[@boldstar69]

***** I love you.

[@kylepulse1116]

***** I left another comment on whatever video was talking about Zora's paradox, I think it helps with this comment. While the whole positive negative quadrant comment may very well be why we measure counter clockwise, it does not actually mean anything. Going around a circle clockwise is 360 degrees just the same as going around counter clockwise. Numbers do not exist in nature. Numbers and words are purely descriptive about existence and do not define it. That's why you cannot travel negative distance. Mathematically positive is forward and negative is backward but if you walk backwards for 10 miles you successfully looked like a fool for a positive 10 miles. If you walk forward for 5 and backwards for 5 you walked 10 miles and not 0. If you disagree I challenge you to find a mountain and walk up the mountain forwards and down the mountain backwards and then tell your legs you walked a total of zero mountains and see what they say. They won't say anything unless you're in serious need of mental evaluation but the point is your body confirms that terms in math cannot be applied to real life if you forget that math and words are describing and not defining existence.

[@alphamineron]

The Real Flenuan You do realize that quadrants could be the other way around. The fact that they are what they are is what we don't have any idea about. It's just convention

[@TheRealFlenuan]

+AlphaMineron But that's not what he was saying. Given the fact that the convention about how the quadrants are laid out is the way it is, the way angles are measured makes sense.

[@Everest314]

Well, I completely disagree. Why? In my math classes, the first time we came across Pi was circumferrence = Pi * diameter. At that point we also defined r as one half of d, which caused a lot of confusion for many kids. (Why are we measuring from the middle?) By the time we got the part of trigonometry where you start using Sin and Cos (and ...) or rotations in physics, everyone was used to the number Pi. Admittedly, one revolution being 2 Pi caused some confusion again, but that was trivial in comparison with the other problems people had with trigonometry. So, in conclusion I believe that using Tau instead of Pi wouldn't have caused less confusion, but rather caused the confusion earlier on - which I think is worse. It makes sense to me now, but I don't think that it would have helped the kids that struggled at mathematics anyway - and those who didn't struggle never had a problem with Pi in the first place... PS: I love your accent!

[@Crazy_Diamond_75]

I completely agree. The reason pi is easier is because you learn it as C/d or C/2r, and for practical application, *diameters are easier to use*.

[@neildey6783]

I disagree; radii are much more intuitive. We measure the distances between celestial objects as the radius (more technically, 1/2 the major/minor axis). Heck, the tangent of an angle is defined as the slope of the radius of the unit circle. We teach kids that Circumference=pi*diameter. I think we might want to start transitioning to Circumference=tau*radius

[@Crazy_Diamond_75]

Neil Dey All the screws and pipes I work with are defined by diameter, because it's much easier to measure diameter given an arbitrary circle. For celestial purposes, maybe tau is more convenient. But for earthly applications, I would argue for pi.

[@ZanJoKyR]

Everest314 I can't possibly agree that diameters are less confusing or more intuitive. After all, what is the definition of a circle? A circle is the set of all points that are a specific distance (radius) from a specific point (center). If you are actually teaching the definition of a circle, there is NO question about why one would measure a circle by the radius. The issue that is causing confusion, then, is even introducing the idea of a diameter, which is a much more confusing and less intuitive topic than the radius. And, AMGwtfBBQsauce I would agree that it is easier to *estimate* a diameter, but disagree that it is easier to *measure* one. In order to measure a diameter correctly, you still need to know where the center is. Otherwise, you are just measuring a chord. So, sure, if you don't need perfect accuracy, use diameters. But, if you are trying to do any kind of logical, mathematical reasoning or arguing (i.e. the whole point of mathematical education), the radius is superior.

[@Everest314]

zanJoKyR I am only speaking from my own experience in school. Nowadays, I know that a circle is more logically defined via its radius and I see no real difference between 2 Pi and Tau - there are formulas that are "simpler" with either one (are we honestly arguing about an additional 2 or 1/2?). However, we knew what a circle looks like long before we could describe it mathematically and from that perspective i still think that the diameter is easier to grasp than the radius because at that point you have never thought of the centre of a circle (at least most people haven't). I have also experienced the same when I did math tutoring. The "all points with the same distance from the center" never got through, even if they had used it numerous times with their compasses. Okay, those were not the brightest kids... And has others have pointed out, by far the most praticable way to measure the size of a circular object is by using a calliper which gives you the diameter. I just don't think that the advantages of Tau are enough to justify overturning the convention. (Not that i don't see the advantages...)

[@calaphone1]

How about all the calculators that already have PI programmed in. If we switch to Tau we have to either remake every calculator. For example. Ti-83, Ti-84, Ti-89 etc. Or every time we see tau we have to times it by two to get the PI units.

[@theFLacker123]

Funny thing, and I agree with the need for tau, is that I understand pi so much better now!

[@OnEvenKeel]

1 turn = 1 x pi x diadians!

[@Peter_1986]

Can someone tell me why Phil writes the denominator in the Fourier Transform equation under a square root sign? I have never seen that sign there before, and I don't know how it would contribute to the overall equation in any way.

[@raulgalets]

Dude this guy is full chaotic. The circle, the tone, the reckless use of and sense of space. This guys is the butterfly and the hurricane all at once.

[@jadiv]

Can we trust him? He is named Moriarty

[@MemphisPrime]

λ=41π/17 is the best way. And no I'm not trying to misrepresent the Euler-Mascheroni constant.

[@pooiyx]

Where can we find the "game"/comparison he mentioned? (the list of equations that are simpler with tau and those which aren't simpler with tau)

[@bengoodwin2141]

Is there anywhere specific that you would need tau/2 or just pi?

[@3uothd23gd87dua]

my first thought is e^(i*pi) is so elegant we can't possibly replace pi... but e^(i*tau) is even more elegant :D

[@LunizIsGlacey]

1 is sooo much better than -1

[@TheEternalVortex42]

To be fair, e^(i tau/2) actually gives you more insight as to why it's equal to -1

[@Crlarl]

What if you have Torque in an equation with Tau?

[@AttackPenguin666]

Well this is an interesting point but actually Pi is shitter because planes are called Pi1 Pi2 etc usually

[@w00tklumpWn]

+dimmddr1 Thats indeed a thing but it's probably not messing up people. The tau manifeste states some other equations where there are multiple symbols with the completly different meaning. So it wouldn't be the first conflict in symbols at all. And it states, that we should think about using another symbol for torque, some profs would currently establish "N" for torque in some papers, they don't even use tau. Neither as symbol nor as 2*PI. There is a short 15min version of "tau manifesto" on youtube, it's worth it even as piist.

[@GordanCable]

+dimmddr1 Tau is also used for the symbol for the time constant used in electronics. Someone mentioned using "N" for torque, but that is problematic as well because N is also a symbol for the unit of force measurement (newtons) and is also the letter used to denote a vector that is normal to a surface or line. There are a lot of overloaded symbols in math, engineering, and science so there is precedence for it, but I would argue that it makes more sense to find lesser used symbols when making brand new constants. Also does it really need to be discussed the problems with changing an already established symbol in common use? Keep in mind that we already have a symbol for what tau represents, and we are trying to find a way to avoid the addition of a coefficient. This is just a glorified ink-saving measure after all.

[@GordanCable]

dimmddr1 Well, given that Tau is 2 times Pi, maybe it should be a four legged pi, but then we start to cut into the ink savings we got from omitting the 2. Maybe a pi with an extra hump? Its fun to think about.

[@AttackPenguin666]

GordanCable A two-legged pi, but with a double line across the top. Like a roughly equals sign with two lines coming down from the top one

[@insomnia20422]

Im studying to become a maths teacher. Can anyone recommend me if I should try to introduce circles, oscillations... with tau first and only after that with pi? I see a problem of mixing these 2 up for new students especially if you show it with tau but in the official exam its all with pi. Maybe make them understand it with tau but then introduce pi and actually train it with pi? Idk, Im always open for better teaching, this thing really confused me too as a student and gave me trouble getting it right some times so idk what to do...

[@thelearningartist3162]

I ask out of curiosity. Could someone explain what's with the use of brown paper? Is it a deliberate choice to use brown paper instead of a white board? What's the reasoning behind such a choice?

[@vasyan123]

Sorry, but I don't trust Professor Moriarty

[@hetakusoda2977]

Why do we use pi? Simple. Because it's called pi. A number called tau just makes math that much less fun.

[@cxpKSip]

Um... yeah.

[@thefran901]

Just in english, it doesn't mean anything in other languages.

[@otterwesen]

easy as pi: three point one four

[@ferko28]

Funny point: pi is wrongly pronounced in english, it should be pronounced "peah", which sounds a lot like "pee".

[@jhatzi99]

El Ferko and tau is pronounced as "tough". What's more funny now...

[@zedlepplin9450]

0:21 love the humor brady

[@claudioestevez1028]

As far as I know, the story of pi says that Euler used pi to describe the perimeter of a circle. It just happens that the page they looked at looking for the definition of pi had a semicircle not a full circle. But in the same book, in a different page, he has pi = 6.28... So if they would have seen that page first, today we might be using the better way. I don't know if this story is true, but I don't think Euler would have defined pi the way we use it today.

[@JustWatchingVideo56]

Tau is already used everywhere else such as time constants... What if I accidentally cancel something out?

[@QuikProdigy]

JustWatchingVideo56 pi is also used in many places in math, pi can represent different functions such as capital pi of x = x / ln(x), this is a function that gives a rough approximation of how many prime numbers there are that are less than x. All Greek letters are used in several places: theta is used to represent angles, also it’s a constant where (theta)^3^n rounded down will give you a prime number.

[@konstantinkouptsov7513]

I do not think there is a problem. At 7:25 : "omega = 2 pi * f". Now, if you use tau for a time constant, you would commonly have "omega * tau", so, if tau also used for "2 * pi", it would turn into "f * tau^2". Now you can cancel one of the "tau"s without breaking anything. Easy!

[@MuonRay]

Tau is helpful over pi as we are skipping a useless step in the translation from angIes to radians in the unit circle. If we are saying 180 degrees equals pi radians and 360 degrees equals 2pi radians, then the labels are matched so that 1pi = 180 = 1/2 revolution, 2pi = 360 = 1 revolution. So with tau we are skipping the useless step at the start and just agreeing that 1/2 a revolution should be 1/2 of tau. However the argument is circular (no pun intended!) because we need to define what tau is, as 2pi, because it is more natural to get the constant of pi, from first principles, as to get the measure of the ratio of the circumference of the circle to the diameter. To get tau we would have to add a step to define what tau is by finding this ratio and, for no immediately apparent reason, multiplying the circumference by 2. If you were getting pi in the first place you would not know at first why you would multiply it by 2 until after you realize 2pi crops up everywhere. The same would be true if you were acquiring pi from first principles by the Monte Carlo method, except you would multiply the ratio of hits inside the circle to the total number of throws outside by 2 instead of 4 which is misleading to where the formula used for the method comes, namely from the ratio of the area of the circle (pi*r^2) to the area of the square (4 *r^2). So although the first step to multiply pi by 2 appears meaningless it is saving having to do the equally meaningless step in converting degrees to radians by comparing the value, in units of pi, to the rotations around a unit circle. So yes, tau is better for labeling the unit circle, but only after you have pi in the first place, and as I described it is always easier to get pi first. However, and this is why I think pi is far better and will never be replace, in formulas containing pi the pi itself often cancels out in and, particularly in Fourier Series, we are only looking at the fractions the pi is latched with anyway, to label the nodes or antinodes in a wave for example. Take a look at a sine wave and you will see the nodes and antinodes can, in a usual x - y coordinate system, be changed from degrees to radians by multiplying by pi/180 and cancelling as much as possible. the values for nodes would be pi/6, pi/3, pi/2, 2pi/3, 5pi/6. The antinodes would be 7pi/6, pi/3, pi/2, pi/3, pi/6. Notice that the denominators are symmetrical, making the series seem much more related to a circular waveform. But with tau you get really asymmetrical denominators and makes very odd labels with no apparent symmetry The values you would get for nodes would be tau/12, tau/6, tau/4, tau/3, 5tau/12. The antinodes are then 7tau/12, 2tau/3, 3tau/4, 5tau/6, 11tau/12. This for me is why pi makes much more sense to use, both in acquiring the constant in the first place, and to use in sinusoidal formula, in the long run.

[@andreasvinter-hviid4684]

Muon Ray It is not more natural to get pi than tau from first principles. You simple define tau as the ratio of the circumferrence and the radius. Done. You don't have to multiply anything by 2.Using the radius is more natural than the diametre anyways. The radius is the defining characteristic of a circle. There is a reason the unit circle has r=1 and not d=1.

[@Thesterness]

Andreas Vinter-Hviid I don't know about antinodes (that's beyond my current level of math/physics). But as for "naturalness", I agree with Andreas. What is the simplest way to define a circle? I'm not a mathematician but I would argue this: pick a point, let's call it *p*. Now pick a distance, and call it *d*. A circle is the set of all points that are *d* distance from *p*. Simple. It's a bit trickier to define a circle using diameter. I suppose you could define it by saying that it's the set of all endpoints of a line segment of a given length rotated about its midpoint, but I still think it's simpler to just say point+distance=circle.

[@Dill800games]

Or define it as, instead of circumference over diameter, circumference over radius

[@xCorvus7x]

What are those nodes and antinodes you are talking about? Aren't the nodes of a standing sine wave at n*pi*x, where x is the distance in space or in time? And the antinodes at (n+1/2)*pi*x?

[@jonathanmacdonald9609]

For me it boils down to the fact that I would rather work with 2Pi a bunch than Tau/2 a bunch. Division is far more awkward to put in somewhere than multiplication. 1/2Pi? who cares! 1/Tao/2? Annoying. I also think that the argument about intuitiveness of Tau for radians doesn't matter because radians are annoying enough that they're not taught to kids until they've already gotten past so many unavoidably confusing things that 2Pi won't even faze them anymore. (You might argue that they should be taught radians instead of degrees as kids, but what's going to confuse them there is not whether you use Tau or Pi, but the fact that a whole circle isn't a whole number of radians. If you're worried about confusing them, you teach them degrees when they're young and by the time they're ready for radians they won't care about 2Pi) Also, yeah, it's Pi/D and Tau/r *not* Tao/2D Muon, because it's division.

[@leoangere5310]

It's been a while since I've watched, but does the series Fringe have the alternate universe using Tau?

[@3irikur]

They (Numberphile channel) should change their logo to Tau instead of Pi

[@tomjackal5708]

Not really. There's no reason we have to eradicate the use of pi to introduce tau, we could use tau in equations where tau is better, and pi in equations where pi is better.

[@3irikur]

Tom Jackal It was a joke

[@tomjackal5708]

"They should change their logo to Tau instead of Pi" Sounds nothing like a joke.

[@ToastyOs]

Tom Jackal pfffffff

[@MephLeo]

3irikur I don't think so, but if they would, it would be logic to change over Tau/2 =p

[@seansmagee]

What about area and volume equations like πr^2 and (4/3)πr^3? Those equations are much more complicated with τ than with π. We also have Euler's identity e^(πi)+1=0 which gets muddied up with τ. I'd much rather deal with a factor of 2 in some of my equations than a factor of (1/2).

[@Andreas0427]

I know this is an old comment but I would just like to point that the equations aren't actually "much more complicated" with τ. I agree with τ/2*r^2 being slightly more complicated than πr^2 but to me (2/3)τr^3 actually seems less complicated than (4/3)πr^3 and Euler's identity can easily be rewritten as e^(τi)-1=0 or e^(τi)=1.

[@brendanmatthews866]

​@@Andreas0427 The form 1/2*τ*r^2 should also be familiar to anyone with experience in calculus and polar coordinates, as, after replacing the τ with θ, it yields us 1/2*θ*r^2 which is precisely the definite integral of f(θ,r) = θ*r _dr_ with the limits of 0 to r, and so the 2D area 'under the curve' of a circular sector of angle θ. Then, after establishing the base unit angle θ is to be measured in as the angle of a sector with arclength r and defining τ to be the circumference/radius (or: how many arclengths of length 'r' added together equal the circumference), we can state the full angle 'θ' of a circle = 'τ' amount of radians and merely replace θ with τ, ending up with Area = 1/2*τ*r^2, which also makes a clearer connection to Area = 1/2*(C/r)*r^2 = 1/2*C*r. When π is used, it effectively hides that 1/2 coefficient within itself, partially obscuring the full, elegant integral form underlying the extraction of an Area from a line/curve. The distinction is subtle, but relevant imo.

[@seanld444]

So I could just go and make a new thing called "Nup" and then have it equal to 4•Pi, and then I could make millions?

[@keithdawes2685]

+sean wilkerson : Sorry, I have already come up with the Nup...

[@Sakanakao]

The Tau vs Pi video at the end is missing a link (still has a "coming soon" subscriptions link).

[@hoid8069]

If we were to start using Tau, what letter would we use for torque?

[@carultch]

Some books use a capital Gamma, because it looks like a wrench.

[@superjoshua7777]

TL;DR - Tau is the Dvorak of the math world.

[@Bartooc]

Dvořák

[@zaimwaqar2788]

Then what is the colemak of the maths world?

[@Galctic49]

While I agree in general, it's far too much of a hassle to change this, so we never will. It would probably more convenient to have a metric based method of counting time rather than 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, but that will likewise never be changed because it's not worth the hassle either.

[@sallytrengrove9015]

Just a quick question, can I use tau in my high school math class or will I get marked down?

[@Peter_1986]

You should be able to use it if you make sure to clearly define it from the beginning, so that they know what value it is supposed to have (they cannot know for sure that it is supposed to be the Tau constant, and if they aren't sure about that then they would mark you for not being clear enough).

[@philaypeephilippotter6532]

@@Peter_1986 That's absolutely right and I would also suggest that it's better not to use it _in tests/exams_ anything you haven't been taught in class. The examiners will probably mark you down even if you do explain clearly what you mean as they're only interested in knowing that you can use what is in the syllabus.

[@ziba2660]

that make me wondering with pi you rotate with the radius but with tau pi is double to equal tau and why do we only rotate with the radius how about rotation with the diameter you only need a half cycle to complete a rotation

[@morganhatch1513]

A=(T/2)d^2? A=pi*r^2 sounds easier

[@ca-ke9493]

actually the half comes from the integral, being an area. Minute Physics has a simple proof on the area of the circle which amounts to it being a triangle with height=radius and base=Its circumference, which is 1/2 (Tau) r^2.

[@w00tklumpWn]

+Morgan Hatch you are absolutely right. It's what we know now. Plain stolen from the manifesto: Archimedes has NOT discovered, that the circular area is calculated by pi*r². He found, that a circle has the same area as a right triangle with height "r" and a base "C", where C is the circumference of the circle, "r" being the radius. Area of a triangle is 1/2*height*base. In our case, it's 1/2*r*C. The 1/2 here again points out, that there is some sort of integral. You can now choose to replace "C" by pi*d, or by tau * r and solve it. You either end up having pi*r² or 1/2*tau*r². When in need, i would always use pi*r² for the circular area, since it's the smallest form. But where ever there is a freaking 2*pi or i have deduce the origin of a function i would use tau. If i needed to show, that the circular area is actually calculated using an integral, it tau all the way.

[@qclod]

+Morgan Hatch (τ/2)r^2 matches other quadratic forms such as kinetic energy and distance fallen in a gravitational field

[@BGroothedde]

Why not simply teach both?

[@alexandrumoise1511]

I think it will help with understanding and memorising ciclic functions as well, when you have different behaviors for even or uneven multiples of pi. I think it would be easier seeing them as multiples of tau and multiples of tau/2 no?

[@javiermadera8569]

does tau have and end or is infinite?

[@dpo357]

I'm an engineer, and I think this whole discussion of pi vs tau is silly, I don't get why mathematicians take sides so radically instead of just using both at convenience. That being said, when the time comes I'll be teaching my kids trigonometry with tau and substitute it with 2*pi if necessary, it's far better for learning because it's way more intuitive, there will be dickhead close-minded teachers that won't like it, I'm sure, but all arguments are invalid if the procedures and results are correct.

[@MrFennicus]

The problem is that pi is defined by the diameter and radiant is defined by radius. Why don't we use something like "diametriant" instead of radiant, so the length of the angle was diameter instead of radius.

[@zarchy55]

MrFennicus Because the diameter is a "fake" parameter. Circles are defined by their radius, not their diameter. Tell somebody how to draw a circle - you have to start from the radius. If you tell somebody to draw a circle from the diameter, you first have to cut the diameter in half to get the radius. Which is what you should have started with in the first place.

[@MrFennicus]

Yeah that makes sense.

[@Yougottacryforthis]

+zarchy55 u draw a circle with 2 points

[@zarchy55]

Yes, two points separated by a distance equal to the RADIUS.Tal Benjo

[@Yougottacryforthis]

zarchy55 no. Just need any 2 points and u can draw a circle without drawing the radius

[@mrtrvphf]

This is one of the first things I was taught in my Trig class this year. I wonder how it will transition over the year.

[@ediakaran]

Thank you very much for the video! I'm a high school physics teacher and I'll seriously consider it as an option.

[@gaimz1855]

I wish I understood this before 2pi :(

[@iraasta]

The PI is a lie :O

[@samsawesomeminecraft]

The reason we originally used pi instead of tau is because it is much more natural to measure the *diameter* of a circle or cylinder with something like calipers than it is natural to measure the *radius* of the same.

[@MysteryHendrik]

And what about spheres and steradians? A sphere has 4π sr = 2τ sr. So, if we look at a sphere, it is more natural to use another constant which is twice τ (about 12.566). Is there anything that makes my argument invalid? I hope so because I like the idea of τ.

[@SuperJV4x]

I use Tau to dwy me afder a chowr

[@cobalt._.27]

What the truck?

[@draganjonceski2639]

@@cobalt._.27 he uses a towel to dry himself after a shower

[@jorgecastro91]

This guy makes it seem like using 2pi is something that is holding a lot of people back or something that people really struggle with when they are first introduced to it. I haven't come across anybody that has been even remotely confused by this concept. It's really not that confusing at all.

[@Kalumbatsch]

Maybe it's confusing for physicists..

[@Dexerinos]

I watched this today for like 3rd time ... I like to come back to these vids :) But one question wasn't really been addressed in Numbrerphile yet, at least I don't saw it. Why do we count angles in a counter-clockwise fashion, as Prof. M. mentioned ? :) Somebody has to know !

[@allyourcode]

2*pi radians is not the problem. The problem is radians. The most natural unit of angle is "turn". For example, the angle made by two adjacent sides of a rectangle is one quarter turn (0.25 turn), as opposed to pi / 2 radians (which I totally agree is utter brain damage!). The elegance of turn as a unit of angle results from the fact that it does not unnecessarily drag radius or diameter into the issue; turns involves exactly the one thing we care about: angle. Besides being unnatural, another problem with radians is that a complete turn is an irrational (in fact, transcendental) number of radians. This, of course, is a direct consequence of the unnaturalness of radians as a unit of angle. The turn has no such problem. Similarly, under the radian convention, the period of sin is irrational (again, 2*pi); whereas, if we were to adopt the turn, then the period would most elegantly be 1. What could be more satisfying?? Also for people who prefer to work with degrees, if the number of degrees you are dealing with is rational (e.g. the angle made by adjacent sides of a rectangle or regular triangle), then the equivalent number of turns is also rational (and vise versa). Whereas, switching back and forth between degrees and radians inevitably involves irrational calculations, which means that nobody is going to bother with hand calculations. One could probably go on at length about the evils of radians, but I think ya'll can see where this is going: radians are very silly, and turns just make sense.

[@billswingle2672]

So it's a teaching tool. Done. So what?

[@subjectt.change6599]

I think that this debate could benefit from some pragmaticism. If we've already defined all of our conceptions of circles, angles, and curves in terms of Pi, then doesn't redefining all of these concepts in terms of Tau introduce unnecessary confusion to a topic that is already sufficiently clear to permit practical accuracy and precision in our inquiries and activities?

[@GlennHamblin]

So 1/2 Tau * R squared for area?

[@Bananabeacon]

Well why define tau as 2pi and not just the circumference of a circle devided by the radius of said circle?

[@eduardoschiavon5652]

Tau is love, Tau is life..

[@5ilver42]

What I found surprising in this video was learning that I was never taught was a radian was until now -- the angle of an arc along the circumference with a length equal to the radius. I think I would have done better in math 10 years ago if they taught that better in my school.

[@Sarculare]

I had thought the counterclockwise counting of angles were due to graphing using the angular coordinates system. X being a line from left to right, y (the angle) to align closer to the standard down/up direction, at least initially.

[@philipcai9499]

A = pi * r^2 That is something that's taught that will not get simpler.

[@AlchemistOfNirnroot]

A = t/2*r^2 looks horrible

[@RagingPanic]

C=2 x Pi x r That's something that will

[@dororiok]

RagingPanic Or you can write it as C = pi*2r

[@aaligoa23a]

AlchemistOfNirnroot It doesn't, in fact A = 1/2* T * r^2 is a cuadratic form, very used in many other equations, verely Ec = 1/2 m v^2, The energy of an elastic string, Ep = 1/2 * k * x^2. All three expresions become the perimeter, the linear momentum and the force exterted by the spring, when taken the derivative, taking out the 1/2 factor. That is why not the area, but the whole mathematics behind it get simpler, slightly complicating the formula for the area.

[@RagingPanic]

dororiok What I'm saying is that C=Tr is more elegant than C=pi*2*r

[@TheWindWaker333]

Or maybe students should be expected to handle a factor of two with little difficulty? The people who want to introduce tau to replace 2pi are hipsters wanting change for the sake of change and nothing else. Forget the fact that pi is rarely used as a symbol in other contexts since everyone knows what pi means to most people. Let's use tau which already has multiple meanings (proper time, decay time constant, volume in some cases where V is used for voltage or potential, torque!).

[@Dubster9990]

+TheWindWaker333 Pi is used in several areas as well. Chemists have Pi-bonds and the osmotic pressure is denoted as pi. Basically at any point you wish to distinguish something otherwise denoted with a p as a special type of property you'd use pi, just like you would use tau instead of t. Frankly there are not enough letters to denote every single property of something uniquely. The reason why pi even is called pi is from the greek word for periphery. Likewise tau could imply "turn" or something similar.