Τ VS π which is better and why?

Pi is a social construct

Of course it is, all mathematics is a social construct.

Pi is better, because it weeds out retards who are too stupid to understand that tau just equals 2*pi

they are almost the same shit

Pi is a unitless ratio.
Tau is the magnitude of the circumference of the unit circle.

Whenever I think of tau, I think of a length of measurement.

Discarding the units masks the true origins of the number and makes you wonder why it's used at all.

Pi is better in every possible way

pau (1.5 x pi)

only correct answer in the whole thread

samefag

It doesn't matter. No matter which you use, you get the same results.

What year is it? 2012?

2 vs 4. Which is better and why?

>pi is a ratio
No. π is first and foremost a number, and just happens to show up in the equation relating the radius of a circle in the Euclidean plane to its circumference. When you change the norm, you also change the value showing up in the equation. You do NOT change the value of π. It's a useful number, and that is all.

Useless argument, shit changes.

Bullshit. We used to write equations as sentences. We have used TONS of incompatible notations. We STILL use symbols in completely incompatible ways -- think of all of the different meanings of "e".

??? DELET THIS, multiplying pi by two does not endow it with units.

This is almost as bad as the Pluto thing. It makes people think that all Mathematicians do is sit around and argue about the names of things and what notation is better. This is the sort of argument you would see on the Big Bang Theory. The truth is that nobody cares. I have never seen tau used seriously and I doubt I ever will.

Circumference = length
2x radius = length

Pi = circumference / 2x radius unitless

Tau = circumference of unit circle = length so it has units

That's how it would be defined. Not just simply 2pi.

Also, the unit circle sucks with tau

Dude, if we're talking about circles, the "natural unit" is radians. There are 2pi radians in a revolution of the circle and tau revolutions. These things don't have units though, they're just constants. The previous poster is right and you're either trolling or really dumb.

HOLY TITS I JIST REALIZED A TAU SYMBOL IS HALF OF A PI SYMBOL MY FUCKING MIND

It really doesn't matter unless you're intentionally acting autistic. Tau is more intuitive when you're looking at trig functions I suppose, but pi is better for finding the area/circumference (actually, circumference doesn't matter, kek) of a circle.

[math]\tau=\frac{\pi}{2}[/math]

What the fuck is τ

is this one of those "science fan" things?

τ but only when togheter with duodecimal system

Off topic, but what's the name of that comic?

smbc

kys my dudes

who cares, the symbol [math]\pi[/math] is better served as a projective mapping
NUMBER THEORISTS NEED NOT APPLY fuck your primes

Two times pi.

Wrong again, sorry to say.

Radians are defined in terms of pi, just like Tau.

Of course they're equivalent, but if you don't know where the units come from, it's hard to justify using it.

If tau replaced pi, we'd have to teach trig before geometry for the formulas to make any sense.

This goes against the historic development of mathematics and doesnt make calculations any easier.

I'd liken this debate to the discussion about replacing the English system with the metric in the US. We could do it, but why bother?

> implying scientists weren't once science fans
Are you guys able to forget old phone numbers too?

angles are fucked.
use half turn instead

Tau makes more sense. We talk about whole revolutions of the circle just way, way more than halves. Think about how often you see 2pi instead of pi in geometric formulas.

Pi works better when you talk about diameters which is why the greeks used it. It is easier to measure the diameter of a circle than the radius - just measure it. To find the radius you first have to find the center of the circle. In our day and age we are more comfortable using radii. We have a coordinate style view of the radius.

Ideally we would use tau, but pi is so ingrained in all things math it'd be hard to switch.

...

That was the most retarded metaphor I've seen all day. It's more like "Which is better for measuring the geometric and topological properties of an apple: a whole apple or a half apple?"

I fail to see how you actually think a constant multiple of two brings units into the picture.

>Radians are defined in terms of pi, just like Tau.
>If tau replaced pi, we'd have to teach trig before geometry for the formulas to make any sense.
>This goes against the historic development of mathematics and doesnt make calculations any easier.
>I'd liken this debate to the discussion about replacing the English system with the metric in the US. We could do it, but why bother?
All of this makes me almost positive that you're trolling because of how nonsensical it is.

Nearly ALL formulas make MORE sense using tau. You apparently haven't seen them. Whether the context is radians -> revolutions, radians -> arc length, or radians -> sector area, the constants involved make all formulas much more intuitive without relying on external knowledge that a constant of two is standard.

Literally no formulas make more sense with tau. They make the same sense.

>external knowledge that 2 is standard
This isn't even true. Only reason 2pi radians in a circle is because the circumference of the unit circle is broken up into chunks. That's the only place the 2 comes from. If you don't know the equation for a circle, you shouldn't worry about any other math concepts.

Even by your own logic, tau wouldn't be superior because it would rely on the external knowledge that there are tau radians in 1 revolution of a circle.

Besides that definition, there is nothing that gives tau significance. That is the only way you could teach it. But that begs the question. Why are there exactly tau radians? Can you prove it without using pi? Can you even make a geometric argument that the constant tau isnt just some arbitrary number without talkING about pi first?

No, you can't, because it's a fucking useless definition.

Might as well call the speed of light c, 2r while we're at it.

>Why are there exactly tau radians? Can you prove it without using pi? Can you even make a geometric argument that the constant tau isnt just some arbitrary number without talkING about pi first?
Rudin defines pi as half the value of a 0 of the sine function in a certain interval.

Did you hear that, you fucktard? HALF the value of some zero. Take the actual value and you get tau

This. But the butthurt makes them avoid your post.

You're a troll or an idiot, not sure which. Calling the speed of light 2r is exactly like calling a revolution 2pi. It's fucking stupid.

If Rudin took the step to replace pi himself, the entirety of Veeky Forums would worship it. Incapable of thinking for themselves, follow the masses. Pi is popular and has history so it's right!!!!!

But then you must explain a Sin function before you have even approached the concept of pi.
You silly goose.

Do you not know what radians are? How many times can the radius of a circle wrap around the circumference? The answer is about 6.28. This is tau. There are tau radians in a revolution (one time 'round the circle with a radius of one radian).

To be clear, I really don't care about this issue.

I came to this thread to see the autism and it didn't disappoint. Thanks.

>pi
>irrational
>ratio

pi/2 is best. It's the fundamental right angle.

And?

On a related note, how do you define sin(x)?
f''+f=0, f'(0)=1, f(0)=0?

youtube.com/watch?v=1qpVdwizdvI

>implying real numbers even exist

[math] \nexists f: \mathbb{Q} \to \mathbb{Q}; f''+f=0, f'(0) = 1, f(0) = 0 [/math] tho

>>>/reddit/

if you only use pi, [math] 2\pi [/math] is easy to write and looks relatively good on a single line

but if you only use tau, and you need pi, you get [math] \displaystyle \frac{\tau}{2} [/math]

i guess you could use them both, but that just seems silly to me

>Whenever I think of tau, I think of a length of measurement.
I think of the particle or of its neutrino, pi isn't used to define anything else so it it easier to know what one is talking about \.

I have thought about this long and hard, and I use [math]\pi[/math] everyday without trouble, but I really think that the circle constant should be 2*pi=1 turn (using [math]tau[/math] is retarded because it's used everywhere; the "three legged pi" is better but not standard).

There are only two arguments I've heard for [math]pi[/math]:
1) It's the traditional constant.
2) It is the angle in Euler's formula that first fully returns to the real axis.

The argument for turn is:
1) It's easier to interpret the angle.

One could say that it would be confusing if the angle and the length of the arc subtended on the unit circle where the same number, but that's why I attach units to everything when working.

Altogether, I am the type of person who says buck convention if the alternative is more attractive. The argument that [math]\pi[/math] is in wide spread use is a bad one in my opinion. Turn being easier to think in is a very good argument in my opinion. And for those people like who say it doesn't matter, I think people who use [math]\pi[/math] on a regular basis would be lying if they said they didn't have to sometimes juggle fractions to get a mental picture of where on the unit circle they are.

You absolutely can't ignore the fact that people know what you are talking about when you say [math]\pi[/math]. Still, it's tempting to work privately in turns.

> he thinks pi was defined for all spaces, not just Euclidean ones

Oh, two other things.

1)The WHOLE reason why the circle constant is phrased in terms of diameter rather than radius is because it's operationally difficult to measure a radius, whereas diameter is very easy to measure. Try to measure the radius and diameter of a pencil if you don't believe me.

This is a practical matter in the realm of engineering, and why [math]\pi[/math] is defined in terms of diameter, in contrast to pretty much every other mathematical fact and formula you know about radially symmetric objects.

This scores points for [math]\pi[/math]. But honestly, how hard is it to divide a radius by 2? And why should a math constant definition be a historical relic of some obscure measurement technicalities?

2) For some reason, the type of people who argue to keep [math]\pi[/math] because it's a standard, seem to get really hurt over the suggestion of turn, like it's an insult to their mathematical heroes or something. It's just a number.

> not knowing about the Buckingham-Pi theorem
this is why I don't like physicists

Give this man a medal.

wait did you mean to call tau, turn? or was that autocorrect?
Because at first I thought you were referring to the rational rotation equivalent of angle, called "turn"

>But honestly, how hard is it to divide a radius by 2? And why should a math constant definition be a historical relic of some obscure measurement technicalities?
This makes the first problem completely non-issue. If we are going to be involving the constant 2 somewhere, we might as well involve it early to make the rest of the process better.

The second is true but disturbingly stupid. We used to write equations as sentences. The first abbreviations were awful in modern terms. Pic related is all I could find quickly in my laziness, and it is relatively nice compared to some of the more lengthy forms I've seen for attempting to abbreviate verbal equations.

/thread

Tau is more fundamental in every way that matters and would make for nicer formulas. If you think otherwise, you're wrong. It doesn't make much difference anyway, of course, so I personally don't care.

Define it by a function series.

Anyway, the whole discussion is for retards who don't know real math.

π. it's the same reason we use base ten, There are more useful bases but everyone uses ten so fuck it.

Are you retarded

This is not an argument for tau. Tau doesn't clean up shit, and if you claim it does, then you have never gone beyond calculating the circumference of a circle.

There are better arguments for tau.

...

No, it's [math] \pi[/math] that just equals [math]\frac{\tau}{2}[/math].

>Tau doesn't clean up shit, and if you claim it does, then you have never gone beyond calculating the circumference of a circle.
It's not magical but it makes the constants involved more intuitive which I find to be "cleaner".

>There are better arguments for tau.
How about contributing then?