The ubiquitous \(\pi\) . II. (English) Zbl 0654.10002

Castellanos, Dario

Math. Mag. 61, No. 3, 148-163 (1988).

This brings the account given in Part I (see the preceding review Zbl 0654.10001) up to date by dealing with quadratically convergent formulae involving elliptic integrals and the arithmetic-geometric mean (the proof, on page 149, of the existence of the A.-G.M. needs some re- ordering). Some mnemonics for \(\pi\) are given and some of the ways in which \(\pi\) enters into number theory and probability are noted. The paper ends with anecdotes about \(\pi\), and an extensive bibliography.

Reviewer: H.J.Godwin

MSC:

11-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
01A99	History of mathematics and mathematicians
33E05	Elliptic functions and integrals
65B99	Acceleration of convergence in numerical analysis

Keywords:

approximations to \(\pi \); quadratic convergence; elliptic integrals; arithmetic-geometric mean; mnemonics; anecdotes; bibliography

Citations:

Zbl 0654.10001