Ebook: Pi: A Source Book

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Content:
Front Matter....Pages i-xix
The Rhind Mathematical Papyrus-Problem 50 (~ 1650 B.C.)....Pages 1-2
Quadrature of the Circle in Ancient Egypt....Pages 3-6
Measurement of a Circle....Pages 7-14
Archimedes the Numerical Analyst....Pages 15-19
Circle Measurements in Ancient China....Pages 20-35
The Measurement of Plane and Solid Figures (~850)....Pages 36-44
The Power Series of Arctan and Pi (~1400)....Pages 45-50
Ludolph (or Ludolff or Lucius) van Ceulen....Pages 51-52
Variorum de Rebus Mathematicis Reponsorum Liber VII (1593)....Pages 53-67
Computation of π by Successive Interpolations....Pages 68-77
Arithmetica Infinitorum (1655)....Pages 78-80
De Circuli Magnitudine Inventa....Pages 81-86
Correspondence with John Collins (1671)....Pages 87-91
The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha....Pages 92-107
The First Use of π for the Circle Ratio....Pages 108-109
Of the Method of Fluxions and Infinite Series (1737)....Pages 110-111
On the Use of the Discovered Factors to Sum Infinite Series....Pages 112-128
Mémoire Sur Quelques Propriétés Remarquables des Quantités Transcendentes Circulaires et Logarithmiques....Pages 129-140
Contributions to Mathematics Comprising Chiefly the Rectification of the Circle to 607 Places of Decimals....Pages 141-146
Sur La Fonction Exponentielle....Pages 147-161
Zu Lindemann’s Abhandlung: „Über die Ludolph’sche Zahl“....Pages 162-193
Ueber die Transcendenz der Zahlen e und π....Pages 194-206
Quadrature of the Circle....Pages 207-225
House Bill No. 246, Indiana State Legislature, 1897....Pages 226-229
The Legal Values of Pi....Pages 230-230
Squaring the Circle....Pages 231-235
The Marquis and the Land-Agent; A Tale of the Eighteenth Century....Pages 236-239
The Best (?) Formula for Computing π to a Thousand Places....Pages 240-240
An Algorithm for the Construction of Arctangent Relations....Pages 241-257
A Simple Proof that π is Irrational....Pages 258-270
An ENIAC Determination of π and e to more than 2000 Decimal Places....Pages 271-273
The Chronology of Pi....Pages 274-275
Calculation of π to 100,000 Decimals....Pages 276-276
On the Computation of Euler’s Constant....Pages 277-281
Approximations to the logarithms of certain rational numbers....Pages 282-305
Asymptotic Diophantine Approximations to E....Pages 306-318
Applications of Some Formulae by Hermite to the Approximation of Exponentials and Logarithms....Pages 319-325
In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969)....Pages 326-349
Mathematical Circles Revisited ; A Selection Collection of Mathematical Stories and Anecdotes (excerpt) (1971)....Pages 350-358
The Lemniscate Constants....Pages 359-367
Computation of π Using Arithmetic-Geometric Mean....Pages 368-371
Fast Multiple-Precision Evaluation of Elementary Functions....Pages 372-399
A Note on the Irrationality of ζ(2) and ζ(3)....Pages 400-401
A Proof that Euler Missed.......Pages 402-411
Some New Algorithms for High-Precision Computation of Euler’s Constant....Pages 412-417
A Proof that Euler Missed: Evaluating ζ(2) the Easy Way....Pages 418-423
Putting God Back In Math....Pages 424-433
The Arithmetic-Geometric Mean of Gauss....Pages 434-438
The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions....Pages 439-447
A Simplified Version of the Fast Algorithms of Brent and Salamin....Pages 448-455
Is π Normal?....Pages 456-457
Circle Digits A Self-Referential Story....Pages 458-459
The Computation of π to 29,360,000 Decimal Digits Using Borweins’ Quartically Convergent Algorithm....Pages 460-461
Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of π Calculation....Pages 462-480
Ramanujan and Pi....Pages 481-536
Approximations and complex multiplication according to Ramanujan....Pages 537-552
Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi....Pages 553-556
Pi, Euler Numbers, and Asymptotic Expansions....Pages 557-559
An Alternative Proof of the Lindemann-Weierstrass Theorem....Pages 560-561
The Tail of π....Pages 562-575
An excerpt from Foucault’s Pendulum (1993)....Pages 576-587
Pi Mnemonics and the Art of Constrained Writing....Pages 588-595
On the Rapid Computation of Various Polylogarithmic Constants....Pages 596-622
Back Matter....Pages 623-641
....Pages 642-648