The fact that so many textbooks still name π as "the greatest or most significant or most influential" geometric...

Without a doubt in my mind, [math]Ω[/math] (Chaitin's constant). Don't ask me what it is, because not even the fuckers who created it know what it is.

>a number that we can't even approximate, but we can "prove" it "exists"
Wildberger warned this kind of shit would happen.

Euler would be fucking ashamed if he could see the absolute state of amateur mathematicians today.
[math]e^{i\pi} + 1 = 0[/math]
>beautiful, simply sublime, elegant in every way
vs.
[math]e^{i\frac{\tau}{2}} + 1 = 0[/math]
>hurr durr I'm literally fucking retarded

Way to fucking ruin one of the purest examples of mathematical beauty, you goddamn pseudointellectual shits.

That's the point. The copypasta's author is comparing experts in one field (geometry in this case), whose views and tastes (loving [math]\pi[/math], which is very mainstream) he sees as sophomoric (read: mainstream), to experts in two other fields (physics and complex analysis), whose views and tastes (loving [math]G[/math], [math]c[/math],
and [math]i[/math], which are not as mainstream as more popular constants) [he sees as more advanced and intellectual (read: contrarian).
If it makes more sense, in the original copypasta, the author is talking about rock critics loving the Beatles (who were very popular in their time) and comparing them to jazz critics, who love Duke Ellington and John Coltrane (who were allegedly not very popular in their time), and classical critics, who love Beethoven (who was also allegedly not very popular in his time).

>tau/2
you absolute fucking moron

You can't win an argument with these people because "tau" is literally just 2pi, so any place where pi appears they'll claim it's really .5tau.

[math] e^{i\tau} - 1 = 0 [/math]

I don't see the problem.

Cases in point:

What's the normalization constant for the Fourier transform? tau, not pi.

What's the regularized product of all natural numbers? tau, not pi.

Quick! What's 3/5 of a turn? Hurr durr lemme multiply by 2... 6/5 * pi because fuck logic.

How about [math]e^{i \tau} = 1[/math] you fucking simpleton?

>using fourier transform definiton with normalization constans

absolutely disgusting

Engineer here, can I round tau to 6 because if so I don't really care which one I use.

>still uses [math]2\pi[/math]
>fucking blind to irony

I agree with you on the tau part tho

>how far geometry still is from becoming a serious science

Mathematics is not a science. Opinion disregarded :^)

Yes but it's double the error of rounding pi.

but twice the fun tho

>error of rounding
As an engineer I don't understand these fancy science words.

you're a larper not an engineer if half of every of your report wasn't error analysis

SolidWorks does the error analysis and even makes an automated pretty print out. All sorts of graphs and charts red is bad blue is good. Don't understand what any of it means tho.

>he doesn't realize why Euler's identity is beautiful in the first place
It's not just "hurr durr sine of pi is -1", it's that [math]e^{i\pi} + 1 = 0[/math] incorporates:
>e
>i
>pi
>exponentation
>multiplication
>addition
>1
>0
Meanwhile, your retarded bastardization incorporates:
>e
>i
>2pi (because that's all tau is)
>exponentation
>1

What's the ratio of a circle's circumference to its diameter? pi, not tau.
What is [math]4 * (\frac {1}{1} - \frac {1}{3} + \frac {1}{5} - \frac {1}{7} + \frac {1}{9} - \dots) [/math]? pi, not tau.
Quick! What's the area of the unit circle? Hurr durr lemme multiply by 2... 1/2 * tau because fuck logic.
Here's a fun one: try to evaluate the area of an n-ball in n dimensions with tau instead of pi.

How about:

\[ e^{i \theta} = \sin \theta + i \cos \theta \]

>What's the ratio of a circle's circumference to its diameter? pi, not tau.
You should use the radius.

Here's the thing: the area of a circle is found through integration: τ 0.5 r2 is found through integrationg τ ∫ r dr.

>What's the area of a circle with radius 1?

>HURRRRR it's tau over two DURRRRRR

it's a logical connection to calculus and also an early hint for kids to where all of those [math]\frac{1}{2}x^2[/math] came from

>What's the circumference of a circle with radius 1?

>HURRRRR it's pi times two DURRRRRR

You're fucking braindead. HURR DURR I added 0 to the equation so it's more elegant DURR! If you love 0 so much why don't you marry it? Suits your accomplishments well enough.

[math]e^{i \tau} = 1 + 0[/math]

[math]e^{i \tau} = 1[/math] tells us that [math]\tau[/math] gets you a full turn. [math]\pi[/math] only gets you halfway there. Much like yourself at life.

>What is [math]4(\frac{1}{1}-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\ldots)[/math]? pi, not tau.

Are you fucking retarded? At best you can use that to argue that [math]\frac{\pi}{4}[/math] is a natural constant, not fucking [math]\pi[/math] you brainlet.

but seriously, will [math]\tau[/math] ever get into grade school kids books?

"science" means "systematic study" in a very general way. It doesn't mean "employs scientific method to build models of the natural world"

>At best you can use that to argue that [math]\frac{\pi}{4}[/math] is a natural constant
sure, [math]\frac{\pi}{4}[/math] is second in line, and often used to argue with [math]\tau[/math] supporters, but it kinda proves the point which [math]\tau[/math] is trying to make.

then what means "employs scientific method to build models of the natural world"? since that's the only relevant thing here

>You should use the radius.
You mean [math]\frac{d}{2}[/math]? :^)
No, but seriously. Somebody draws a circle on a sheet of paper and tells you to find the radius. How are you going to find it? Are you going to hope that God guides your hand to the exact centerpoint of the circle, or are you just going to find the end-to-end distance (read: the circumference) and divide by 2?
And, actually, the area of a circle is found from pic related.

>Somebody draws a circle on a sheet of paper and tells you to find the radius. How are you going to find it? Are you going to hope that God guides your hand to the exact centerpoint of the circle?

Somebody draws a circle on a sheet of paper and tells you to find the diameter. How are you going to find it? Are you going to hope that God guides your hand to the exact antipodal point of the circle?

Obviously you use marbles to approximate the area of the circle and then calculate the radius of the circle from the area.

Yes, you're right. You are far more accomplished and intelligent than Leonhard Euler, the most prolific mathematician of all time. Truly only you and the other wise tau-ist scholars know what is beautiful in math.

>[math]e^{i2\pi} = 1[/math] tells us that [math]2\pi[/math] gets you a full turn
lmaoing at failing to understand the most basic of equations
>[math]\frac{\pi}{4}[/math] is a natural constant
Uhhh hurr durr I think you mean [math]\frac{\tau}{8}[/math].
Face it, brainlet. As Shakespeare said, "brevity is ... wit." [math]\pi[/math] is more brief, and therefore more witty, than [math]\frac{\tau}{2}[/math].

>Somebody draws a circle on a sheet of paper
then it's not a circle

God drew the circle to be perfect. God is not, however, going to guide your hand to the center point of the circle.

who cares

>God is not, however, going to guide your hand to the center point of the circle.
God is in the centre of the circle, and the radius represents the path to the God.

[math]\tau[/math] is more brief, and therefore more witty, than [math]2 \pi[/math].

What's the period of the fundamental trigonometric functions: sine and cosine?

Hint: It ain't [math]\pi[/math].

What's the ratio of the circumference of a circle to its diameter?
Hint: It ain't [math]\tau[/math].
The area of a circle is certainly more brief, and therefore more witty, if you write it as [math]\pi r^2[/math] as opposed to [math]\frac{\tau}{2} r^2[/math].

>mfw I notate infinite products with a big [math]\frac{\tau}{2}[/math] instead of [math]\Pi[/math]

If anyone ever needed more proof that Veeky Forums is full of pseuds, look no further than this thread.

How often do you see just π and how often do you see some fractions like 3/4π, 7/8π? Introduction tau would just make you divide all the constants by 2 and otherwise nothing changes

give me one reason to use tau

and don't say "it'll make things easier" since adding a new standard won't do anything except make the engineers heads hurt more than they already do

IUT

of course it is lol this isn't your uni

>adding a new standard won't do anything except make the engineers heads hurt more than they already do
that alone makes it worth it

dumb irrelevant shit
amateur mathematicians, KYS!

>t/2roduct

tauday.com/tau-manifesto

>What's the ratio of the circumference of a circle to its diameter?
>Hint: It ain't ττ.

No one gives a fuck. The fact that sine and cosine have a period of [math]2\pi = \tau[/math] is more important and fundamental. Who the fuck even uses diameter in pure mathematics? Brainlets like you, that's who.

>The area of a circle is certainly more brief, and therefore more witty, if you write it as [math]\pi r^2[/math] as opposed to [math]\frac{\tau}{2}r^2[/math].

There's a reason that factor of [math]\frac{1}{2}[/math] is supposed to be there, though it's probably way beyond your comprehension. Hint: It involves this really simple concept called integration. Hence why you see [math]\frac{1}{2} m v^2, \frac{1}{2} k x^2, \frac{1}{2} I \omega^2[/math].

The area of a circular sector subtended by angle [math]\theta[/math] is [math]\frac{1}{2} \theta r^2[/math]. Thus [math]\frac{1}{2}\tau r^2[/math] is just the special case [math]\theta=\tau[/math]. [math]\frac{1}{2} \tau r^2[/math] makes this clear, unlike shitty [math]\pi r^2[/math].

>How often do you see just π and how often do you see some fractions like 3/4π, 7/8π? Introduction tau would just make you divide all the constants by 2 and otherwise nothing changes

How often do you see just η = π/2 and how often do you see some fractions like 3/2η, 7/4η? Introducing π would just make you divide all the constants by 2 and otherwise nothing changes.

>It's not just "hurr durr sine of pi is -1", it's that eiπ+1=0 incorporates:
>>e
>>i
>>pi
>>exponentation
>>multiplication
>>addition
>Meanwhile, your retarded bastardization incorporates:
>>e
>>i
pi (because that's all tau is)
>>exponentation

Yes, it makes hardly any difference if we give a special name to a period of sin, to half the period, quarter the period, 7/8 the period, so arguing whether we should use Tau or something else instead of pi is just like saying "look, I'm autistic" and brings nothing into maths. And the use of pi is already well established in all the maths books and papers, so it's easier to just stick to using it than sperging about this tau.
Maybe you faggots should start arguing in favor of f=e/2 because reasons and fuck the conventions

>The area of a circle is certainly more brief, and therefore more witty, if you write it as [math]\pi r^2[/math] as opposed to [math]\frac{\tau}{2} r^2[/math].

Do you not see the irony in the fact that you're using [math]r[/math] rather than diameter to describe the area?

>Yes, it makes hardly any difference if we give a special name to a period of sin, to half the period, quarter the period,

Yes it does. It's connected to all sorts of facts in mathematics, such as the branches of the complex logarithm function, the regularized factorial of infinity, Stirling's approximation, etc.

>And the use of pi is already well established in all the maths books and papers, so it's easier to just stick to using it than sperging about this tau.

Slow down there buddy. I'm not arguing we should stop the presses. I'm only arguing that tau is easier to use and more elegant than pi, that's it.

Thank you for your searing hot take, imbecile. Now try the actual formula for the volume of a ball in [math]n[/math]-dimensional Euclidean space with your silly pseud excuse for a constant.
[math]V_n(R) = \frac{\pi^\frac{n}{2}}{\Gamma (\frac{n}{2} + 1)} R^n[/math]
Here's a hint: this is how the area of a circle (2-ball) is ACTUALLY found. You can also use this for the volume of a sphere (3-ball), the hypervolume of a 4th-dimensional hypersphere (4-ball), the length of a line segment (1-ball), or volume of a point (0-ball; it comes out to 1 regardless of what you put in for the radius, which I'm spelling out for you because I wouldn't expect a brainlet like you to know).
You'll notice it's already looking pretty hairy with all those fractions in the mix. But it gets even worse: check out that weird looking bracket thing in the denominator! What's that? Oh, it's Euler's gamma function. There are many ways to write it, since Euler wasn't a braindead pleb like you (hence his usage of [math]\pi[/math] in his identity and not [math]\tau \over 2[/math]), and one such way is referred to as the Pi function. That's right, not the [math]\tau \over 2[/math] function, the Pi function. I'm not even going to bother formatting it in TeX for you, brainlet, just Wikipedia it and then contemplate how you'd cram your pathetic "hurr durr 2pi/2" into that. Once you're done with that array of mental gymnastics, contemplate how you would fit what you just shat out into the equation I so generously provided above and realize there's a reason that mathematicians have been using [math]C \over d[/math] as opposed to [math]C \over r[/math] for literal thousands of years.

>Thank you for your searing hot take, imbecile.

u mad bro

It's not easier, for every tau you write in place of 2 pi there will be tau/2 in place of pi. And the argument hurt it's easier to understand may hold if we're talking about elementary school students, but why should we change the notation we're all familiar with just for the sake of couple of kids understanding trig and geometry better? And teaching kids about tau and using pi in real maths is also dumb

>Euler wasn't a braindead pleb like you (hence his usage of [math]\pi[/math] in his identity and not [math]\frac{\tau}{2}[/math])
>implying math notation hasn't advanced since the 18th century

>one such way is referred to as the Pi function. That's right, not the [math]\frac{\tau}{2}[/math] function, the Pi function.
>confuses the name of a function with a numerical quantity

Holy shit, you're actually fucking retarded. The use of [math]\Pi[/math] in the Pi function has absolutely nothing to do with the [math]\pi[/math] constant. It's the name of a function, not a numerical quantity. How does it feel to be this stupid?

>there's a reason that mathematicians have been using [math]\frac{C}{d}[\math] as opposed to [math]\frac{C}{r}[\math] for literal thousands of years.
>uses [math]r[/math] rather than [math]d[/math] to describe the area

>τd^2/8
Good job retard.

>and then calculate the radius of the circle from the area
>and then calculate the radius
>the radius

>τd^2/8
HAHAHAHAHAHAHAHAHAHAHAHAHA

>The area of a circle is certainly more brief, and therefore more witty, if you write it as [math]\pi r^2[/math] as opposed to [math]\frac{\tau}{2} r^2[/math].

Since you insist on defining the circle constant from diameter rather than radius, you should do the same with area:

[math]A = \frac{\pi d^2}{4}[/math]

What a steaming pile of shit.

>[math]V_n(R) = \frac{\pi^\frac{n}{2}}{\Gamma(\frac{n}{2}+1)} R^n[/math]

Shouldn't you be using [math]D^n[/math] bro?

>the use of pi in the pi function has absolutely nothing to do with pi
Mind saying that again, tardlet?

hello terry

The fact is that modern geometry doesn't concern itself with this stuff, anyone who debates this is an undergrad or highschooler.

Jesus Christ, how can you mention C, G and pi in the same sentence, let alone the same paragraph? Pi is a mathematical constant, independent of our universe. It has fuck all to do with physics, although physicists make good use of it because reality is full of near circular and near spherical objects. C and G, on the other hand, are values physically measured constants. They are not mathematical.

TLDR so you don't hurt your evidently tiny brain: Pi is a math constant, C and G are physics constants. Absolutely no comparison to be made.

Yeah but c and G are equal to 1...

That's the point you numbnut. The original copypasta is comparing rock critics who are "blinded by commercial success," worshipping the Beatles just because they're best-sellers and super mainstream, to jazz and classical critics who praise John Coltrane and Beethoven respectively, both of whom were supposedly not best-sellers and mainstream yet are acknowledged by their respective critics for their talent. Due to this disparity, the author claims, rock criticism will never be taken seriously since they only care about commercial success.
OP just replaced "rock" with "geometry," "the Beatles" with "π," "jazz" with "physics," and so on and so forth.

Needless to say, the copypasta is widely-mocked for being contrarian shit. A perfect metaphor for the Tau Manifesto, then.

You get one for each language. It's not a single number.

>Needless to say, the copypasta is widely-mocked for being contrarian shit.

>This old article by Piero Scaruffi has won several international awards as the most professional analysis of the career of pop group the Beatles ever written. While the interests of the author have long left popular music behind, the vast success of the article makes him believe it should continue to be posted here. Feel free to duplicate on your websites. For a list of his favorite music, the "essentials", click here (and then scroll down in that page for the best of rock music). But please note that this is just one of 8,600 bios of musicians on this website. And thank you for all the recognition.

>[citation needed]
Pic related is on his website. Searching for it literally only gets you /mu/ threads talking about how he literally made up the NMC Award for Music Taste lmao

this, in higher mathamatics, we set e=pi=1, and use those as the naturel units. it is much more naturel to consider something like 1^x

>confuses name of function with the mathematical constant [math]\Pi[/math]

literally retarded

yet here you are IIT...

that's because mathematics as an institution has a raging fetish for defending and reframing things to justify existing assumptions (as seen by axiom autism) instead of considering new approaches

OP posted a very interesting question and you retards are arguing about fucking pi again.

>fails to see the pi literally right there in the equation
Literally braindead

btw complex/imaginary numbers are pure retardation

no u

>trivial redefinition of some constant
>new approach

Sqrt(2) was like ancient Greece

Is it painful to be this dumb?

[math]\pi[/math] is not in the definition of [math]\Pi[/math] it's in a *different equation* below. original user was talking about the *function name* [math]\Pi[/math] as if it were the same as [math]\pi[/math], the mathematical constant.

I really can't explain it any more simply than that. If you still don't get it, you're beyond help.

>he still is literally incapable of seeing the [math]\pi[/math] and chooses to believe I'm talking about the [math]\Pi[/math]
You're not right, you're obtuse.

...