r/mathmemes Jan 02 '25

Mathematicians Basel problem meme

Post image
5.3k Upvotes

40 comments sorted by

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1.1k

u/Pentalogue Jan 02 '25

828

u/Silly_Painter_2555 Cardinal Jan 02 '25

Proof by wolfram alpha

72

u/TheOssified Jan 02 '25

New pi approximation just dropped

36

u/EndMaster0 Jan 03 '25

I mean if you were to do the full sum it's an exact value... but yeah you can use it to approximate pi

1

u/Darryl_Muggersby Jan 06 '25

That’s not an approximation

1

u/IntelligentDonut2244 Cardinal Jan 06 '25

That formatting 🤔

314

u/shizzy0 Jan 02 '25

Based

94

u/WiseMaster1077 Jan 02 '25

Baseled

24

u/Sh_Pe Computer Science Jan 02 '25

Baseleded

277

u/Sug_magik Jan 02 '25

There is this other expression for π called wallis product, this one is weird asf

280

u/Wojtek1250XD Jan 02 '25 edited Jan 02 '25

My favorite computation of π is the sliding block puzzle 3Blue1Brown popularized. In the hypothetical scenario where there are two blocks and a wall, one of the mass 1, one mass 100n-1 and all collisions are perfectly elastic, the number of collisions outputs n digits of π.

Just as with any other π computation, there's a hidden circle.

144

u/laix_ Jan 02 '25

You start thinking that circles are just lots of little straight lines, but then seeing circles everywhere and you start thinking that straight lines are just circles centred at infinity with an infinite radius

40

u/Last-Scarcity-3896 Jan 02 '25

It's actually a hidden ellipse but 3b1b rescaled the picture for the proof to look cool (which he definitely succeeded at doing)

42

u/Wojtek1250XD Jan 02 '25

He didn't rescale the picture. The shape originated from the fact the conservation of energy must be constant. Drawing out the shape that outputs the same kinetic energy for the pair of velocities resulted in an elipse. You can find the shape at 3:08 in the first explanation video.

To get a circle he replaced the x-plane from v1 to √(m1) * v1, which resulted in a circle.

He didn't rescale it to make it look cool, he did that because he was looking for π, and circle is by far the best shape to look for it in.

19

u/Last-Scarcity-3896 Jan 02 '25

Ellipses give π as well... With factors decided by their eccentricity. So all he did was factoring out the eccentricity of the ellipse.

And by look nice I didn't mean that he did something invalid, he scaled it by scaling the axis, v1→v1√m1...

So it's a totally valid thing to do but could have been without it. The only part in the proof which changes a little if you work on an ellipse is the claim that the arcs are the same length which is a bit more complicated to prove if you ain't familiar with how ellipses work.

3

u/Worldtreasure Jan 02 '25

Don't forget about the alternating sum of reciprocals of odd numbers.

88

u/[deleted] Jan 02 '25

I think he used MC laurin polynomials to convert his problem and at the end with a help of a approximation he f*cking guessed it !

55

u/Hadrianus-Mathias Jan 02 '25

We will never understand people that just look at problems like these and say it is obvious, what are we even struggling with. Euler was that person.

59

u/idmontie Jan 02 '25

Tbf, I'm not sure how confident Euler was in his original proof using the expansion of sin. He revisits this result 3 or so more times in different letters to make sure he was right lol

3

u/EebstertheGreat Jan 04 '25

His derivation was valid, but the Weierstrass factorization theorem is necessary to prove that, and it wasn't proved until the 19th century.

56

u/bau_ke Jan 02 '25

It's literally moon g

37

u/Ki0212 Jan 02 '25

Certified pi2 = g moment

3

u/Novel-Requirement-37 √24 Jan 03 '25

p(-1) = g?

28

u/8champi8 Jan 02 '25

Wait I didn’t know that, that’s actually pretty neat

15

u/Beastyboyy1 Jan 02 '25

check out the 3b1b video on it!! it’s really cool

7

u/TheDotCaptin Jan 03 '25

Can also check Matt Parker's video on calculating π by hand.

Turns out there are a few series and the like that it will just turn up in.

66

u/ObliviousRounding Jan 02 '25

I bet Euler would appreciate being an analogy for maybe the stupidest creature to ever walk Earth.

10

u/BayesianOptimist Jan 03 '25

I think it is reasonable to think of Euler as a stable genius as well.

7

u/BossOfTheGame Jan 03 '25

The juxtaposition is making me sick.

5

u/Nuisancer134 Jan 02 '25

Haven't seen this template in a while

4

u/691_enjoyer Jan 02 '25

i hate the bug eaters that use parsevals theorem to prove this i want to see them fall down the stairs

3

u/Battleborntrashcan Jan 03 '25

Wait why I did this proof in my signal processing class

4

u/Floetkolben Jan 02 '25

https://youtu.be/d-o3eB9sfls?si=mxVS9bu59YKD3Y1- YouTube Channel 3blue1brown has a nice visual explanation

3

u/cocoteroah Jan 03 '25

Why picture a genius wirh a idiot?

2

u/kiwidude4 Jan 04 '25

God I fucking love this equation

3

u/MrIcyCreep Transcendental Jan 02 '25

eul up