New Recipe for Pi - Numberphile

NUMBERPHILE

Videos by Brady Haran

Special thanks to eagle-eyed fact-checkers from The Numberphile Society, including Nate, Mark, Francesco, Debbie, David, Trymain, Tad, Michael and Walter

[Peregringlk]

7:32
- Tony: the 105th trillionth digit of PI is 6.
- Brady: good to know

[dhoyt]

Lifelong Pi mathematician here. It does have to do with circles. Chudnovsky specifically has to do with circles, in the complex plane, using hyperbolic geometry, using 163i as its basis. Ramunujan's is the same, but for 1i. You can make single series reps of pi with ramanujan sato series with all the Heegner numbers 1, 2, 3, 7, 11, 19, 43, 67, 163. You can make infinite ramunjan sato series if you allow multiple sums. There is ALWAYS a circle, lol.

[fonkbadonk]

I never want this channel to end. Brady and I are roughly similarly aged, and if I'm refreshing my YT subs page at 80 and there aren't any new videos, I'm just gonna lay down for good.

[muskyoxes]

The cool thing about the Indian series 1 - 1/3 + 1/5 ... is that it had an error term that vastly increased its usefulness. After ten terms, the sum is way off (3.04) but the error term ((n^2+1)/(4n^3+5n)) zooms it right to 3.14159270

[daviddeweger]

I’m unreasonably happy that the length of this video is 14:28

[Sandeepan]

I went to school with brother Arnab, was two batch junior.

He was already a local legend in that area when it comes to maths back in 2009

[rosiefay]

6:41 640320^{3k}. Shades of exp{π√163}~~640320^3+744.

[billferner]

In earlier days of PC programming (80s 90s), the BASIC did not have pi included. To get it with the program prcision, we used the atan(1)*4

[GENS]

Every time I think of a question the camera man asks it, it's so helpful

[jesusthroughmary]

Last time I was this early the Parker Square was just an erroneous attempt at a magic square

The Madhava series is a Taylor series for arctan(1). I wonder whether this new representation is also a Taylor series of some kind

[Xelianow]

I imagine the optimal lambda values require pi in the first place by beeing a transcendental number themself, which would require knowing pi in the first place to calculate (or better: approximate) that optimal lambda...

Edit: Nevermind, they definitly *are* transcendental numbers, since they are simply rational multiples of pi.

[QuantumHistorian]

I'm incredibly shocked that science (/maths) journalism would overhype and completely misrepresent a technical result. Well, ok, not that shocked. Not shocked at all really.

[jesusthroughmary]

Brady was correct that there must be an irrational value of lambda which yields pi exactly with 0 approximation error, but we will never be able to find it

[kalla]

i love your editing style and how your videos stayed consistent throughout the years. great work!

[billcook]

IIRC, if you had two circles, each the size of the universe, one based on pi and one based on an approximate value of pi, you only need about 60 digits of approximate-pi for the two circles to be exactly the same. Any theoretical difference would be smaller than the Planck length, the smallest possible distance in the fabric of space.

[xyzct]

Brady, the gawking rabble demands an explanation of where Ramanujan's and Chudnovsky's series come from.

[cyrilio]

If pie is the meal then the series is the recipe.

Lovely way of describing a math formula.

[acelm]

"So the story goes back to another Indian…"
Me: "Yeah, Ramanujan!"
"around the late 14th century called Madhava."
Me: "Oh."

[ajsmith]

Tony's enthusiasm and his ability to communicate a complicated subject to duffers like me, make him a must watch.