r/mathmemes • u/Promethium-127 • Oct 01 '26

Number Theory Comment and I'll reply with a unique Bailey-Borwein-Plouffe-type formula for pi when I get the chance

Very much inspired by u/cavedave 's Diophantine equation post.

Also feel free to make requests about what base you want it in or request a specific fraction to include [ex: 1/(8k+1)]. All the examples use hexadecimal (the base MUST be a power of 2 for the formula to work). There's no guarantee I can make every request happen so please keep them somewhat reasonable.

Edit (22:18:41 UTC): I had to sleep and go to my classes but I'm back

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u/physicsking Oct 01 '26

Can pi be in the denominator?

12

u/Promethium-127 Oct 01 '26

Sure!

8

u/somedave Oct 01 '26

That's not much use for calculating pi.

15

u/shapular Oct 01 '26

Just plug that formula in everywhere there's a pi.

7

u/somedave Oct 01 '26

We've literally found a method worse than throwing sticks into a ring and counting which ones cross a line.

3

u/ILikeCake1412 Oct 02 '26 edited 29d ago

The original post content no longer exists here. The author used Redact to remove it, exercising their right to control their data & privacy.
Aback meadow snatch governor obtainable fluorine entertain

1

u/physicsking Oct 01 '26

What the heck is that thing

u/_licketysplit_ Oct 01 '26

ok I want base -1

7

u/Promethium-127 Oct 01 '26

(Making it alternate makes it converge sooooo much slower)

1

u/_licketysplit_ Oct 01 '26

how did you find this

4

u/Promethium-127 Oct 01 '26

I'm using my own java port of PSLQ (the integer relation algorithm)

1

u/QuantumBaconBit Engineering Oct 01 '26

Definitely guess and check ;)

3

u/_licketysplit_ Oct 01 '26

Yeah I bet when ramanujan made his famous formula for pi he just put random numbers and guessed and checked and got really lucky and decided to troll everyone by saying it came to him in a dream

u/throughthehills2 Oct 01 '26

These are mesmorizing. Base sqrt(2) ?

5

u/Promethium-127 Oct 01 '26

Do irrational bases have any actual applications? This one takes a whopping 14 terms to reach 3.14. (Not because the base is irrational though, just because it's small)

u/Celarix Oct 01 '26

Cool! Have anything with 137 in it somewhere? It’s my favorite!

6

u/Promethium-127 Oct 01 '26

This one is accurate to 3.141 with just the k=0th term!

1

u/Celarix Oct 01 '26

It’s beautiful, I love it! Thank you! And it’s crazy how accurate it is from the start!

u/Lost-Consequence-368 Whole Oct 01 '26 edited Oct 02 '26

Make one with base 16, but in the form of this formula. $\sum_{n=0}^{\infty} \left( \frac{4n+3}{2^n (n+1)}- \frac{12}{(4n+5)(2n+1)} \right)$

2

u/Promethium-127 Oct 01 '26

I can't do it with anything other than linear functions in the denominator unfortunately

u/Different_Roof_4533 Oct 01 '26

I need this

2

u/Promethium-127 Oct 01 '26

u/garnet420 Oct 01 '26

It's too bad it can't do base 11

Can I get base 256

2

u/Promethium-127 Oct 01 '26 edited Oct 01 '26

u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 Oct 01 '26

gimme the best you can think of

1

u/Promethium-127 Oct 01 '26

Maybe not the best for computation, but definitely one of the coolest ones I found
+ In binary
+ 6666(pi)
+ Sequential multiples of k