Happy Tau Day!

In this short video, we show one way to visualize the constant tau, which is twice pi, as the area between the curves 1/(1+x^2) and its negation over the entire real line.
Happy Tau Day if you celebrate!
To buy me a coffee, head over to www.buymeacoffee.com/VisualPr...
Thanks!
#mathshorts #mathvideo #math #short #math #manim #radian #circle #radius #tauday #taurus
#calculus
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[@CardThrower-rb6eg]

bro doubled the function and created tau from pi ☠️

[@AbidaSultana-e7k]

It exists, he didn’t create it (if you mean MVP himself)

[@aoifedeborha2420]

The person who decided to write “The Tau Song” is a genius 😂

[@mauschen_gaming]

I've listened to it before when i was younger

[@mauschen_gaming]

This symbol τ which means 2π is very rarely used in mathematics but at least its something to know

[@Daniel31216]

I usually let τ = π/2, because it makes more sense for it to equal that than 2π.

[@ITS_MEEE333M]

​@@Daniel31216 yeah it would kinda look like the letter "m"

[@sophiacristina]

@@Daniel31216 I think not if you consider as a reciprocal.
1/1
1/2..

[@sophiacristina]

In programming it is more used, instead of doubling PI, it is just better to write a TAU constant.

[@mertatakan7591]

​@@Daniel31216You can't, value of tau isn't up to you.

[@tunistick8044]

for anyone not understanding:
ʃ[1/1+x²]dx=arctan(x)

[@erinmac4750]

This is beautiful! Love that someone made "The Tau Song," perfect!
I had not seen this before. Thank you!
2🥧 better than 🥧! 💜

[@LucasBucur]

e² is better than e, if you take exp(2) you get e², amazing!

[@braydentaylor4639]

Yeah, it's better to have two pies than just one

[@ponluxime]

i like how you used "Tau the Song with 6.28318 million notes" as the BGM. As a Blacker, it really was unexpected.
Great visualization, by the way.

[@PC_Simo]

Thank you, and Happy Tau Day to you, too!
😊👍🏻

[@thewok3576]

The integral of 1/(1+x^2) is the inverse tangent function. Therefore, with a little bit of work we can calculate the answer from this integral without using a computer.

[@jasonlin5884]

The result of the integral is 2*pi
Because the arctangent function.

[@morenofranco712]

Yeah, and 2π IS the definition of tau.

[@wahoobear6588]

Tau shape is like spark star 😮

[@xyhilwastaken]

What is this beat? The Acceleration of the notes sound very meaningful!

[@kingeddiam2543]

How do you evaluate integrals from -infinity to infinity?

[@roihemed5632]

same as a regular integral, except you take the limit instead of substituting values.

[@kingeddiam2543]

@@roihemed5632 so for this, how does it evaluate to tau?

[@roihemed5632]

​@@kingeddiam2543the indefinite integral is equal to 2arctan. arctan when approaching infinity is pi/2 and when approaching negative infinity is -pi/2. 2(pi/2 - -pi/2) = 2pi =tau.

[@kingeddiam2543]

@@roihemed5632 thank you so much!

[@MrAlvaro412]

What is tau plz?!

[@Hans_KammlerSS]

Great!

[@jareddparkernacion2629]

I see what you mean
Pi day: 3/14
Tau day: 6/28

[@CatritaAycock]

Saw this at 3:14

[@Pantera1001]

you can use pi instead of tau as well as plus instead of minus minus

[@danielszekeres8003]

No, you can't do either

[@Sumdak]

Nice way to call 0

[@Pronuxish]

0 be like: Am I joke to you?

[@rleroygordon]

With tau, you divide by 2.

[@sophiacristina]

Tau > Pi...

[@Idknlandwh123]

what is the name of music?

[@Themixamika]

The tau song

[@MiraiNono]

Tau isn't just 2pi ?

[@authenticallysuperficial9874]

That's evil

[@JR13751]

τ

[@minor_locrian7]

τmatawhakatangihangakoauauotamateaturipukakapikimaungahoronukupokaiwhenaukitanatahu

[@Gamr-bc6kp]

12

[@noahgilbertson7530]

is this satire 🤣

[@cccexestarted]

Are you a Tau-ist? 😍

[@MathVisualProofs]

I don’t take an opinion on this one :)

[@fsponj]

​@@MathVisualProofssame
(My birthday is on Pi day though)

[@raphner2759]

I'm sorry but that's cheating

[@braydentaylor4639]

I forgot yesterday was Tau Day. That shows how much I don't care about that number.

[@tristan_isnot_here]

I don't tau

[@cantosoares]

Se realmente soubesse matemática, não escreveria - -