A Motif of Mathematics

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Docent Press, 2011 - Mathematics - 243 pages
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The curious property that John Farey observed in one of Henry Goodwyn's tables has enduring pratical and theoretic interest. This book traces the curious property, the mediant, from its initial sighting by Nicolas Chuquet and Charles Haros to its connection to the Riemann hypothesis by Jerome Franel.
 

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Contents

The Mediant
1
12 Ratio Proportion and Fraction
3
13 Definition of the Mediant
5
14 A Sequence of Vulgar Fractions
7
15 Nicolas Chuquet and the Regle des Nombres Moyens
14
16 Rational Approximation
16
17 The Mediant and the Continued Fraction
19
18 John Wallis Savilian Chair of Geometry
22
225 Historys Grudge Against John Farey Sr
112
The Table Makers
115
31 Archibalds Mathematical Table Makers
120
32 Lehmers Guide to the Tables in the Theory of Numbers
122
33 Tables of Tables
124
34 Nevilles Tables
128
35 The Farey Series of Order 1025
129
36 Reviews of The Farey Series of Order 1025
133

19 Digit Generation
23
110 The Möbius Transformation
24
111 Mediant Convergents
25
112 The Simpson Paradox
32
113 A Motif of Mathematics
35
History of the Farey Sequence
39
22 Charles Haros Géometre
44
23 Tables pour évaluer une fraction ordinaire
45
24 Tables for evaluating a common fraction
49
25 The Farey Sequence as the Argument of a Mathematical Table
56
26 Instruction abrégée sur les nouvelles mesures
58
27 Computing Logarithms
61
28 General Purpose Root Finder
64
29 Haros Publications
65
210 The Bureau du Cadastre
69
211 Grandes Tables du Cadastre
76
212 Sources of Inspiration
77
213 Bookends on the Era of Organized Scientific Computation
79
214 Henry Goodwyn Brewer and Table Maker
80
215 The Dispersal of Goodwyns Archive
84
216 Goodwyns Publications
88
218 Goodwyn and the Mediant Property
90
219 Decimalization of the Pound Sterling
95
220 John Farey Geologist and Musicologist
98
222 Proof of a Curious Theorem Regarding Numbers
102
223 Delambre and Tilloch Weigh In
105
224 Fareys Publications
108
37 Solving Diophantine Equations
135
38 RectangularPolar Conversion Tables
137
39 Reviews of RectangularPolar Conversion Tables
141
310 Moritz Stern and Achille Brocot
144
311 Gears and Rational Approximation
146
Inventions and Applications
151
41 Sampling Algorithm
153
42 Dithering Algorithm
155
43 DecimaltoFraction Conversion
158
45 Slash Arithmetic and Mediant Rounding
160
46 Patterns for Weaving
165
47 Networks of Resistors
169
The Mediant and the Riemann Hypothesis
173
51 Jérôme Franel Chair for Mathematics in the French Language
175
52 The Farey Series and the Prime Numbers Problem
177
53 A Synopsis of Franels Proof
182
54 Remarks Concerning the Earlier Paper by Mr Franel
186
55 Nevilles Search for Structure
191
56 Capturing Regularization
195
Explorations and Peregrinations
201
62 Mediant Factorization
206
63 The MayerErdös Constant
208
64 Ocagnes Recursion
210
65 Primes and Twin Primes
212
66 The Fractional Part Function
214
67 Final Words
220
Copyright

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About the author (2011)

Scott Guthery has a PhD. in Probability and Statistics and is the holder of over 35 U.S. Patents. He has co-authored books on smart cards and mobile applications.

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