Long Live π!

Poll - Total Votes: 15

The only π I like is apple π.

Stick with your books, old nerd!

You may be a math nerd, but you're sexy as hell!

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(This is an old post but I thought it might be a good idea to resurrect it today...)
Happy birthday π !

Today (3/14) is π day.

(1) π is equal to the ratio of the circumference of a circle and its diameter.

(2) π is a transcendental number. Briefly, this means that we do not know its value, and we never will, haha. π, you’ll always be a mystery.

(3) π is (most likely) a normal number: the distribution probability of digits within π is random. If we assign a pair of consecutive digits to a character (such as "65"="A", cf. ASCII code table) we will find the contents of each book that has ever been written (even bad books, those behind the front row on our shelves) somewhere along the digits of π, and also any book that has not been written, and all variations thereof. There will be a version of Hamlet where Ophelia is called Helen.

(4) The value of π is more fundamental than the physical constants. If the universe did not exist, the physical constants would loose their meaning, but π would remain the same, indicating that spirit is more fundamental than matter. We, as humans, can change a lot of things, but we can’t change π. Even God cannot change π, sorry Sir, You may have created the world but You did not create π. It’s always been there. And you don't know the value of π either.

(5) π is considered to be one of the five fundamental numbers: i, e, π, 1, and 0. These numbers appear in the famous equation e^(i*π) + 1 = 0 (Gauss? Euler? Don’t remember.)

Happy birthday π!
You’re one of a kind, and we are big fans!

We love you π !

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ElwoodBlues · M

Happy pi day!!

My favorite pi approximation: 355/113

FYI, 355/113 - pi is approx 2.66764189x(10^-7)

helenS · 36-40, F

@ElwoodBlues Pretty good! Although in fact nobody needs to know π to more than 5 significant digits...

helenS · 36-40, F

@ElwoodBlues Oh, there is, to the best of my knowledge, no series or sequence which converges to π as a limit rapidly. As opposed to it's cousin e.

ElwoodBlues · M

@helenS When I read that yesterday, I was vaguely aware of a CPU benchmark program called y-cruncher that calculates digits of pi. I have since gone down a bit of a rabbit hole into y-cruncher! (It might be a lower case gamma, not a y, but everybody just types y. It's a highly parallel algorithm).

First, a few results. The table linked is time to calculate 10 billion digits. https://www.numberworld.org/y-cruncher/benchmarks/charts/10b.html
44.059 sec . . . AMD Epyc 9R14 . . . . . . . 740 GB RAM
56.102 sec . . . Intel Xeon W7-2495X . . . 64 GB RAM

The AMD EPYC 9R14 has 96 cores, 192 threads, and AVX-512 fused multiply-add instructions. The Intel Xeon w7-2495X has 24 cores, 48 threads, and of course AVX-512. AVX-512 allows each core to issue eight parallel double precision (64 bit) floating-point multiply+add instructions every clock cycle. It takes a dozen or more clock cycles for the instruction to complete, but due to pipe-lining, a new instruction can be issued every clock.

Which raises the question: WHAT THE HELLL possible algorithm could calculate TEN BILLION DIGITS of π in UNDER SIXTY SECONDS???

It's called the Chudnovsky brothers algorithm, published in 1988, based on a Ramanujan series. It involves multiplying polynomials, and uses the Fast Fourier Transform in double precision floating point to accelerate those multiplications. y-cruncher was constructed as a highly parallel implementation of the Chudnovsky alg, making best use of available cores and AVX-512 vector math. FFT for accelerating multiplication was as deep as I got in the rabbit hole!! As a benchmark, y-cruncher is considered a test of both floating point math speed and memory speed.

FYI, these folks computed π (pi) to 314 trillion digits in 110 days.

Unlike some previous π record attempts that relied on massive cloud computing resources or distributed clusters, this run was carried out on a single Dell PowerEdge R7725 server by the StorageReview team.

Their system used dual AMD EPYC processors and 40 high-capacity NVMe solid-state drives, 34 of which ran the specialized number-crunching software y-cruncher continuously for roughly 110 days to complete the calculation.

https://tech.yahoo.com/articles/pi-day-breakthrough-obliterates-world-120052525.html

helenS · 36-40, F

@ElwoodBlues Thank you! The only algorithm I know of which calculates an arbitrary amount of digits of π fast, is CORDIC. I would assume that CORDIC (or any variation thereof) is implemented in all pocket calculators currently available.
CORDIC is fascinating; it can be used to calculate not only trigonometric functions, but also hyperbolic, exponential, and logarithmic functions.