Pi: A Source Book Book

1	The Rhind mathematical papyrus-problem 50 (ca. 1650 B.C.)	1
2	Engels : Quadrature of the circle in ancient Egypt (1977)	3
3	Archimedes : Measurement of a circle (ca. 250 B.C.)	7
4	Phillips : Archimedes the numerical analyst (1981)	15
5	Lam and Ang : Circle measurements in ancient China (1986)	20
6	The Banu Musa : the measurement of plane and solid figures (ca. 850)	36
7	Madhava : The power series for Arctan and Pi (ca. 1400)	45
8	Hope-Jones : Ludolph (or Ludolff or Lucius) van Ceulen (1938)	51
9	Viete : Variorum de Rebus mathematicis reponsorum liber VII (1593)	53
10	Wallis : Computation of [pi] by successive interpolations (1655)	68
11	Wallis : Arithmetica infinitorum (1655)	78
12	Huygens : De Circuli magnitudine inventa (1654)	81
13	Gregory : correspondence with John Collins (1671)	87
14	Roy : The discovery of the series formula for [pi] by Leibniz, Gregory, and Nilakantha (1990)	92
15	Jones : The first use of [pi] for the circle ratio (1706)	108
16	Newton : Of the method of fluxions and infinite series (1737)	110
17	Euler : chapter 10 of Introduction to analysis of the infinite (on the use of the discovered fractions to sum infinite series) (1748)	112
18	Lambert : Memoire Sur Quelques Proprietes Remarquables Des Quantites Transcendentes Circulaires et Logarithmiques (1761)	129
19	Lambert : Irrationality of [pi] (1969)	141
20	Shanks : Contributions to mathematics comprising chiefly of the rectification of the circle to 607 places of decimals (1853)	147
21	Hermite : Sur La Fonction Exponentielle (1873)	162
22	Lindemann : Ueber die Zahl [pi] (1882)	194
23	Weiserstrass : Zu Lindemann's Abhandlung "Uber die Ludolphsche Zahl" (1885)	207
24	Hilbert : Ueber die Transzendenz der Zahlen e und [pi] (1893)	226
25	Goodwin : Quadrature of the circle (1894)	230
26	Edington : House bill no. 246, Indiana State Legislature, 1897 (1935)	231
27	Singmaster : The legal values of Pi (1985)	236
28	Ramanujan : Squaring the circle (1913)	240
29	Ramanujan : Modular equations and approximations to [pi] (1914)	241
30	Watson. The Aarquis and the land agent : a tale of the eighteenth century (1933)
31	Ballantine. The best (?) formula for computing [pi] to a thousand places (1939)	271
32	Birch. An algorithm for construction of arctangent relations (1946)	274
33	Niven. A simple proof that [pi] is irrational (1947)	276
34	Reitwiesner. An ENLAC determination of [pi] and e to 2000 decimal places (1950)	277
35	Schepler. The chronology of Pi (1950)	282
36	Mahler. On the approximation of [pi] (1953)	306
37	Wrench, Jr. the evolution of extended decimal approximations to [pi] (1960)	319
38	Shanks and Wrench, Jr. calculation of [pi] to 100,000 decimals (1962)	326
39	Sweeny. On the computation of Euler's constant (1963)	350
40	Baker. Approximations to the logarithms of certain rational numbers (1964)	359
41	Adams. Asymptotic diophantine approximations to e (1966)	368
42	Mahler. Applications of some formulae by hermite to the approximations of exponentials of logarithms (1967)	372
43	Eves. In mathematical circles; a selection of mathematical stories and anecdotes (excerpt) (1969)	400
44	Eves. Mathematical circles revisited; a second collection of mathematical stories and anecdotes (excerpt) (1971)	402
45	Todd. The lemniscate constants (1975)	412
46	Salamin. Computation of [pi] using arithmetic-geometric mean (1976)	418
47	Brent. Fast multiple-precision evaluation of elementary functions (1976)	424
48	Beukers. A note on the irrationality of [Zeta](2) and [Zeta](3) (1979)	434
49	Van der Poorten. A proof that Euler missed ... Apery's proof of the irrationality of [Zeta](3) (1979)	439
50	Brent and McMillan. Some new algorithms for high-precision computation of Euler's constant (1980)	448
51	Apostol. A proof that Euler missed : evaluating [zeta](2) the easy way (1983)	456
52	O'Shaughnessy. Putting God back in math (1983)	458
53	Stern. A remarkable approximation to [pi] (1985)	460
54	Newman and Shanks. On a sequence arising in series for [pi] (1984)	462
55	Cox. The arithmetic-geometric mean of gauss (1984)	481
56	Borwein and Borwein. The arithmetic-geometric mean and fast computation of elementary functions (1984)	537
57	Newman. A simplified version of the fast algorithms of Brent and Salamin (1984)	553
58	Wagon. Is Pi normal? (1985)	557
59	Keith. Circle digits : a self-referential story (1986)	560
60	Bailey. The computation of [pi] to 29,360,000 decimal digits using Borwein's quartically convergent algorithm (1988)	562
61	Kanada. Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of [pi] calculation (1988)	576
62	Borwein and Borwein. Ramanujan and Pi (1988)	588
63	Chudnovsky and Chudnovsky. Approximations and complex multiplication according to Ramanujan (1988)	596
64	Borwein, Borwein and Bailey. Ramanujan, modular equations, and approximations to Pi or how to compute one billion digits of Pi (1989)	623
65	Borwein, Borwein and Dilcher. Pi, Euler numbers, and asymptotic expansions (1989)	642
66	Beukers, Bezivin, and Robba. An alternative proof of the Lindemann-Weierstrass theorem (1990)	649
67	Webster. The tale of Pi (1991)	654
68	Eco. An except from Foucault's pendulum (1993)	658
69	Keith. Pi mnemonics and the art of constrained writing (1996)	659
70	Bailey, Borwein, and Plouffe. On the rapid computation of various polylogarithmic constraints (1997)	663
App. I	On the early history of Pi	677
App. II	A computational chronology of Pi	683
App. III	Selected formulae for Pi	686
App. IV	Translations of Viete and Huygens	690
	A pamphlet on Pi	721