Recommendation for book on $\pi$?

Question

I'm looking for a book that goes over the history of $\pi$, the mathematics of $\pi$ (like a discussion about the possible proof that all ten digits 0-9 occur with equal probability, viz., $\pi$'s normality), and all the historical and recent methods for computing the digits of $\pi$.

Answer 1

Try these excellent books:

• The Number $\pi$ by Eymard and Lafon.

• Pi: A Source Book by Berggren, Borwein, and Borwein.

Answer 2

In French (as I know not translated to English) The fascinant nombre pi is wonderful. Research-level about pi-approximating algorithms, Pi and the AGM. And the proof of normality of $\pi$ is... still unknown.

Answer 3

For a more historical account, "A History of PI" by Petr Backmann is nice. It doesn't contain any advanced proofs though (it is more of a survey), and it doesn't have the modern results.

The most modern result for computing $\pi$ that I am aware of is the spigot algorithm, it allows you to compute the $n^{\text{th}}$ digit of $\pi$ in $O(\log(n))$ time (or maybe it was polylogarithmic). It is very recent though, so for whatever book you choose, double check to make sure this result is present because is has been very important.