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Ueber die Zahl π
other
Author(s):
F. Lindemann
Publication date
(Print):
2004
Publisher:
Springer New York
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Author and book information
Book Chapter
Publication date (Print):
2004
Pages
: 194-206
DOI:
10.1007/978-1-4757-4217-6_22
SO-VID:
9d0bc2a1-62d9-4235-9dc7-597443334c67
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Book chapters
pp. 1
Extract from the Rhind Papyrus
pp. 3
Quadrature of the Circle in Ancient Egypt
pp. 7
Measurement of a Circle
pp. 15
Archimedes the Numerical Analyst
pp. 20
Circle Measurements in Ancient China
pp. 36
[V.] The Ratio of the Diameter of any Circle to its Circumference is One [That is, is The Same for All Circles].
pp. 45
Appendix
pp. 51
Correspondence. Ludolph (or Ludolff or Lucius) van Ceulen
pp. 53
Capvt XVIII
pp. 68
Wallis. Computation of π by Successive Interpolations
pp. 78
Wallis. Arithmetica Infinitorum
pp. 81
Huygens. De Circuli Magnitudine Inventa (1654)
pp. 87
Gregory. Correspondence with John Collins (1671)
pp. 92
The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha
pp. 108
The First Use of π for the Circle Ratio
pp. 110
Newton. Of the Method of Fluxions and Infinite Series (1737)
pp. 112
On the Use of the Discovered Factors to Sum Infinite Series
pp. 129
Mémoire sur Quelques Propriétés Remarquables des Quantités Transcendentes Circulaires et Logarithmiques
pp. 141
Lambert. Irrationality of π
pp. 147
Contributions to Mathematics Comprising Chiefly the Rectification of the Circle to 607 Places of Decimals
pp. 162
Sur La Fonction Exponentielle
pp. 194
Ueber die Zahl π
pp. 207
Zu Lindemann’s Abhandlung: „Über die Ludolph’sche Zahl”
pp. 226
Ueber die Transcendenz der Zahlen e und π
pp. 230
Quadrature of the Circle
pp. 231
House Bill No. 246, Indiana State Legislature, 1897
pp. 236
The Legal Values of Pi
pp. 240
Squaring the Circle
pp. 241
Modular Equations and Approximations to π
pp. 258
The Marquis and the Land-Agent; A Tale of the Eighteenth Century
pp. 271
The Best (?) Formula for Computing π to a Thousand Places
pp. 274
An Algorithm for the Construction of Arctangent Relations
pp. 276
A Simple Proof that π is Irrational
pp. 277
An ENIAC Determination of π and e to more than 2000 Decimal Places
pp. 282
The Chronology of P I
pp. 306
On the Approximation of π
pp. 319
The evolution of extended decimal approximations to π
pp. 326
Calculation of π to 100,000 Decimals
pp. 350
On the Computation of Euler’s Constant
pp. 359
Approximations to the logarithms of certain rational numbers
pp. 368
Asymptotic Diophantine Approximations to E
pp. 372
Applications of Some Formulae by Hermite to the Approximation of Exponentials and Logarithms
pp. 400
In Mathematical Circles: A Selection of Mathematical Stories and Anecdotes
pp. 402
In Mathematical Circles: A Selection of Mathematical Stories and Anecdotes
pp. 412
The Lemniscate Constants
pp. 418
Computation of π Using Arithmetic-Geometric Mean
pp. 424
Fast Multiple-Precision Evaluation of Elementary Functions
pp. 434
A Note on the Irrationality of ζ(2) and ζ(3)
pp. 439
A Proof that Euler Missed ...
pp. 448
Some New Algorithms for High-Precision Computation of Euler’s Constant
pp. 456
A Proof that Euler Missed: Evaluating ζ(2) the Easy Way
pp. 458
Putting God Back In Math
pp. 460
69.30 A remarkable approximation to π
pp. 462
On a Sequence Arising in Series for π
pp. 481
The Arithmetic-Geometric Mean of Gauss
pp. 537
The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
pp. 553
A Simplified Version of the Fast Algorithms of Brent and Salamin
pp. 557
Is π Normal?
pp. 560
Circle Digits A Self-Referential Story
pp. 562
The Computation of π to 29,360,000 Decimal Digits Using Borweins’ Quartically Convergent Algorithm
pp. 576
Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of π Calculation
pp. 588
Ramanujan and Pi
pp. 596
Approximations and complex multiplication according to Ramanujan
pp. 623
Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
pp. 642
Pi, Euler Numbers, and Asymptotic Expansions
pp. 649
An Alternative Proof of the Lindemann-Weierstrass Theorem
pp. 654
The Tail of π
pp. 658
The Deconstruction of Pi
pp. 659
Pi Mnemonics and the Art of Constrained Writing
pp. 663
On the Rapid Computation of Various Polylogarithmic Constants
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