The quest for PI

Abstract

his article gives a brief history of the analysis and computation of the mathematical t constant = 3.14159. including number of formulas that have been used to com-

Mathematical Vanity Plates

“…At that time Kanada held the world record, having recently computed p to 134,214,700 decimal places. He had helped with the first calculation that exceeded 2 million places, in 1981, but that record didn't last long; Gosper had topped 17 million places in 1985, using some ideas of Salamin, and Bailey had surpassed 29 million in 1986, before Kanada got back in the lead [3]. More than two further decades of continued progress have led to the astonishing present record of nearly 2.7 trillion decimal places, announced on 31 December 2009 [5].…”

“…by which the nth hexadecimal digit of p can be efficiently computed without evaluating the previous n -1 [3].…”

Brouwer-Heyting Sequences Converge

“…1 At the time that Brouwer developed his theory (1908) and even at the time that [6] was written, it seemed wellnigh impossible that the first occurrence of any 10-digit sequence in ~-could ever be determined.…”

“…Included are some details of times, machinery used, digit distribution, etc. The key algorithms used are as in the recent survey in this journal [1], with the addition of significant numerical/arithmetical enhancements and subtle flow management.…”

Computational Discovery in Pure Mathematics

“…This formula is interesting as it can be used to calculate the nth hexadecimal digit of π without calculating the first n − 1 digits, as discussed in (Bailey et al, 1997). Until this discovery, it was assumed that finding the nth digit of π was not significantly less expensive than finding the first n − 1 digits.…”