3
votes
0answers
120 views

$\pi$, disjunctive numbers, and finite sequences of given length

It is an open problem whether the number $\pi$ is disjunctive in base $10$, i.e., whether every finite sequence appears (at least once) in the base $10$ expansion of $\pi$. Of course, every sequence ...
2
votes
2answers
122 views

Approximating $\pi$ in Binary

I am interested in creating a Java program that generates digits of $\pi$ (in Binary though). To be clear, the number I'm looking for begins: $11.00100100 \dots$ I am unsure of the most efficient way ...
1
vote
2answers
207 views

Computational efficiency of Machin-like formulae

From what I have read, it appears that the most efficient methods of calculating $ \pi $ are Machin-like formulae. And it is known that certain formulas are more efficient than others. Are there any ...
5
votes
3answers
427 views

Calculate $\pi$ in an arbitrary base, to arbitrary precision

I need to calculate $\pi$ -- in base: 4, 12, 32, and 128 -- to an arbitrary number of digits. (It's for an artist friend). I remember Taylor series and I've found miscellaneous "BBP" formulas, but so ...