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Pi: A Source Book
Overview of attention for book
Table of Contents
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Book Overview
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Chapter 1
The Rhind Mathematical Papyrus-Problem 50 (~ 1650 B.C.)
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Chapter 2
Quadrature of the Circle in Ancient Egypt
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Chapter 3
Measurement of a Circle
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Chapter 4
Archimedes the Numerical Analyst
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Chapter 5
Circle Measurements in Ancient China
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Chapter 6
The Measurement of Plane and Solid Figures (~850)
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Chapter 7
The Power Series of Arctan and Pi (~1400)
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Chapter 8
Ludolph (or Ludolff or Lucius) van Ceulen
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Chapter 9
Variorum de Rebus Mathematicis Reponsorum Liber VII (1593)
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Chapter 10
Computation of π by Successive Interpolations
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Chapter 11
Arithmetica Infinitorum (1655)
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Chapter 12
De Circuli Magnitudine Inventa
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Chapter 13
Correspondence with John Collins (1671)
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Chapter 14
The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha
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Chapter 15
The First Use of π for the Circle Ratio
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Chapter 16
Of the Method of Fluxions and Infinite Series (1737)
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Chapter 17
On the Use of the Discovered Factors to Sum Infinite Series
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Chapter 18
Mémoire Sur Quelques Propriétés Remarquables des Quantités Transcendentes Circulaires et Logarithmiques
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Chapter 19
Lambert. Irrationality of π
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Chapter 20
Contributions to Mathematics Comprising Chiefly the Rectification of the Circle to 607 Places of Decimals
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Chapter 21
Sur La Fonction Exponentielle
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Chapter 22
Ueber die Zahl π
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Chapter 23
Zu Lindemann’s Abhandlung: „Über die Ludolph’sche Zahl“
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Chapter 24
Ueber die Transcendenz der Zahlen e und π
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Chapter 25
Quadrature of the Circle
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Chapter 26
House Bill No. 246, Indiana State Legislature, 1897
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Chapter 27
The Legal Values of Pi
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Chapter 28
Squaring the Circle
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Chapter 29
Modular Equations and Approximations to π
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Chapter 30
The Marquis and the Land-Agent; A Tale of the Eighteenth Century
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Chapter 31
The Best (?) Formula for Computing π to a Thousand Places
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Chapter 32
An Algorithm for the Construction of Arctangent Relations
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Chapter 33
A Simple Proof that π is Irrational
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Chapter 34
An ENIAC Determination of π and e to more than 2000 Decimal Places
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Chapter 35
The Chronology of Pi
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Chapter 36
On the Approximation of π
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Chapter 37
The evolution of extended decimal approximations to π
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Chapter 38
Calculation of π to 100,000 Decimals
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Chapter 39
On the Computation of Euler’s Constant
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Chapter 40
Approximations to the logarithms of certain rational numbers
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Chapter 41
Asymptotic Diophantine Approximations to E
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Chapter 42
Applications of Some Formulae by Hermite to the Approximation of Exponentials and Logarithms
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Chapter 43
In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969)
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Chapter 44
Mathematical Circles Revisited ; A Selection Collection of Mathematical Stories and Anecdotes (excerpt) (1971)
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Chapter 45
The Lemniscate Constants
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Chapter 46
Computation of π Using Arithmetic-Geometric Mean
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Chapter 47
Fast Multiple-Precision Evaluation of Elementary Functions
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Chapter 48
A Note on the Irrationality of ζ(2) and ζ(3)
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Chapter 49
A Proof that Euler Missed...
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Chapter 50
Some New Algorithms for High-Precision Computation of Euler’s Constant
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Chapter 51
A Proof that Euler Missed: Evaluating ζ(2) the Easy Way
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Chapter 52
Putting God Back In Math
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Chapter 53
A remarkable approximation to π
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Chapter 54
On a Sequence Arising in Series for π
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Chapter 55
The Arithmetic-Geometric Mean of Gauss
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Chapter 56
The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
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Chapter 57
A Simplified Version of the Fast Algorithms of Brent and Salamin
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Chapter 58
Is π Normal?
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Chapter 59
Circle Digits A Self-Referential Story
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Chapter 60
The Computation of π to 29,360,000 Decimal Digits Using Borweins’ Quartically Convergent Algorithm
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Chapter 61
Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of π Calculation
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Chapter 62
Ramanujan and Pi
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Chapter 63
Approximations and complex multiplication according to Ramanujan
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Chapter 64
Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
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Chapter 65
Pi, Euler Numbers, and Asymptotic Expansions
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Chapter 66
An Alternative Proof of the Lindemann-Weierstrass Theorem
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Chapter 67
The Tail of π
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Chapter 68
An excerpt from Foucault’s Pendulum (1993)
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Chapter 69
Pi Mnemonics and the Art of Constrained Writing
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Chapter 70
On the Rapid Computation of Various Polylogarithmic Constants
Overall attention for this book and its chapters
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Mentioned by
twitter
2
X users
syllabi
4
institutions with syllabi
wikipedia
2
Wikipedia pages
Book overview
1. The Rhind Mathematical Papyrus-Problem 50 (~ 1650 B.C.)
2. Quadrature of the Circle in Ancient Egypt
3. Measurement of a Circle
4. Archimedes the Numerical Analyst
5. Circle Measurements in Ancient China
6. The Measurement of Plane and Solid Figures (~850)
7. The Power Series of Arctan and Pi (~1400)
8. Ludolph (or Ludolff or Lucius) van Ceulen
9. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593)
10. Computation of π by Successive Interpolations
11. Arithmetica Infinitorum (1655)
12. De Circuli Magnitudine Inventa
13. Correspondence with John Collins (1671)
14. The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha
15. The First Use of π for the Circle Ratio
16. Of the Method of Fluxions and Infinite Series (1737)
17. On the Use of the Discovered Factors to Sum Infinite Series
18. Mémoire Sur Quelques Propriétés Remarquables des Quantités Transcendentes Circulaires et Logarithmiques
19. Lambert. Irrationality of π
20. Contributions to Mathematics Comprising Chiefly the Rectification of the Circle to 607 Places of Decimals
21. Sur La Fonction Exponentielle
22. Ueber die Zahl π
23. Zu Lindemann’s Abhandlung: „Über die Ludolph’sche Zahl“
24. Ueber die Transcendenz der Zahlen e und π
25. Quadrature of the Circle
26. House Bill No. 246, Indiana State Legislature, 1897
27. The Legal Values of Pi
28. Squaring the Circle
29. Modular Equations and Approximations to π
30. The Marquis and the Land-Agent; A Tale of the Eighteenth Century
31. The Best (?) Formula for Computing π to a Thousand Places
32. An Algorithm for the Construction of Arctangent Relations
33. A Simple Proof that π is Irrational
34. An ENIAC Determination of π and e to more than 2000 Decimal Places
35. The Chronology of Pi
36. On the Approximation of π
37. The evolution of extended decimal approximations to π
38. Calculation of π to 100,000 Decimals
39. On the Computation of Euler’s Constant
40. Approximations to the logarithms of certain rational numbers
41. Asymptotic Diophantine Approximations to E
42. Applications of Some Formulae by Hermite to the Approximation of Exponentials and Logarithms
43. In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969)
44. Mathematical Circles Revisited ; A Selection Collection of Mathematical Stories and Anecdotes (excerpt) (1971)
45. The Lemniscate Constants
46. Computation of π Using Arithmetic-Geometric Mean
47. Fast Multiple-Precision Evaluation of Elementary Functions
48. A Note on the Irrationality of ζ(2) and ζ(3)
49. A Proof that Euler Missed...
50. Some New Algorithms for High-Precision Computation of Euler’s Constant
51. A Proof that Euler Missed: Evaluating ζ(2) the Easy Way
52. Putting God Back In Math
53. A remarkable approximation to π
54. On a Sequence Arising in Series for π
55. The Arithmetic-Geometric Mean of Gauss
56. The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
57. A Simplified Version of the Fast Algorithms of Brent and Salamin
58. Is π Normal?
59. Circle Digits A Self-Referential Story
60. The Computation of π to 29,360,000 Decimal Digits Using Borweins’ Quartically Convergent Algorithm
61. Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of π Calculation
62. Ramanujan and Pi
63. Approximations and complex multiplication according to Ramanujan
64. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
65. Pi, Euler Numbers, and Asymptotic Expansions
66. An Alternative Proof of the Lindemann-Weierstrass Theorem
67. The Tail of π
68. An excerpt from Foucault’s Pendulum (1993)
69. Pi Mnemonics and the Art of Constrained Writing
70. On the Rapid Computation of Various Polylogarithmic Constants
Summary
X
Syllabi
Wikipedia
This data is correct as of December 2015 - for more up to date information, please visit
https://opensyllabus.org/
So far, Altmetric has seen this research output assigned in
5
syllabi from
4
institutions on Open Syllabus Project.
Institution
Syllabi count
Course subject areas covered
Nottingham Trent University
2
Unknown
Denison University
1
Business, Engineering, Kinesiology
Simon Fraser University
1
Unknown
Unknown
1
Unknown