Nice Numbers

Nice Numbers
Author: John Barnes
Pages: 329 pages
Edition: 1st ed. 2016
Language: English
Publisher: Birkhäuser
Publication Date: 2016-11-27
ISBN-10: 3319468308
ISBN-13: 9783319468303
1 Measures 1
Favourite numbers, Prime numbers, Factors,
Weights and measures, Musical notes, Currencies,
Further reading, Exercises.
2 Amicable Numbers 25
Perfect numbers, Modular arithmetic, Mersenne the
monk, Amicable numbers, Amicable multiplets,
Sociable cycles, Fermat numbers, Fibonacci
numbers, Further reading, Exercises.
3 Probability 43
Heads or tails, Distributions, Shake, rattle, and roll,
The normal distribution, An abnormal distribution,
Tossing for π, Double or quits, A medical problem,
Which box has the prize?, Craps and poker, Further
reading, Exercises.
4 Fractions 69
Real numbers, Vulgar fractions, Egyptian fractions,
Dividing loaves, The table of 2/n, The method of
false position, Decimal fractions, Roots, Continued
fractions, The eye of Horus, Further reading,
Exercises.
5 Time 97
Basic rhythms, The Roman calendar, The Gregorian
calendar, Start of the year and quarters, The week,
Time of day, Sunshine, Further reading, Exercises.
6 Notations 115
Types of notation, Roman numbers, Babylonian
system, Place systems and bases, Divisibility,
Fractions and bases, Fermat’s Little Theorem,
Further reading, Exercises.

7 Bells 137
Rounds and plain hunting, Plain Bob Minimus,
Plain Bob Doubles, Stedman, Grandsire, Groups,
Further reading, Exercises.
8 Primes 161
Greatest Common Divisor, Prime factors, Fermat’s
method, Eratosthenes revisited, Complex numbers,
Complex primes, Polynomials, Further reading,
Exercises.
9 Music 179
Frequency and vibrations, The Pythagorean scale,
Cents, Just intonation, Minor scales, Meantone
temperament, Equal temperament, Other
arrangements, Dividing the octave, Further reading.
10 Finale 205
The RSA algorithm, Linear congruences, Euler’s
function, Encryption and decryption, Code blocks,
Animal gaits, Towers and rings, Further reading.
A Ackermann 227
Recursion and iteration, Further reading.
B Pascal’s Triangle 231
Basic properties, Fibonacci numbers, Squares and
pyramids, Further reading.
C Stochastics 239
War games, Queuing, Further reading.
D Polydivisibility 245
The problem, Other bases.
E Groups 249
Basics, Subgroups, Generators, Cosets,
Permutations, Polyhedral groups, Direct products,
The quaternion group, Further reading.
F Rubik 265
Basics, Restoring a cube, Summary of restoration,
The cube group, Cosets, Finally, Further reading.

G Differences 287
Rings, Towers, Fibonacci numbers, Hats, Further
reading.
H Chinese Remainders 295
Linear congruences, Simultaneous equations,
Pirates, Eggs, Squares.
J Mersenne 303
Mersenne’s 31-note keyboard, A schema, The 12-
note keyboards, An 18-note keyboard, A 26-note
keyboard, The 31-note keyboard, Intervals, A better
keyboard, Modulation, Tonnetz revisited, Further
reading.
Bibliography 325
Index 327

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