The Gentle Art of Mathematics

The Gentle Art of Mathematics

3.33 (9 ratings by Goodreads)
By (author) 

List price: US$7.95

Currently unavailable

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

Description

This lighthearted work uses a variety of practical applications and puzzles to take a look at today's mathematical trends. In nine chapters, Professor Pedoe covers mathematical games; chance and choice; where does it end; automatic thinking; two-way stretch; rules of play; an accountant's nightmare; and double talk. Practical examples and problems are featured throughout.
show more

Product details

  • Paperback | 160 pages
  • 137 x 215 x 9mm | 176g
  • New York, United States
  • English
  • New edition
  • New edition
  • 42 figures
  • 0486229491
  • 9780486229492
  • 1,908,740

Table of contents

CHAPTER I MATHEMATICAL GAMES
  The fascination of ordinary numbers
  Why fifteen Fellows of the Royal Society?
  The scale of ten
  A problem involving ordinary numbers
  A very long division
  A much shorter solution of the digital problem
  "Sixteen months in the year, and their names"
  "The binary scale, or scale of two"
  A magic table of numbers
  The game of Nim
  As played by an electronic brain against humans
  The theory behind the game
  Winning positions in the game
  Punched cards and automatic rearrangement of twelve cards
  The twelve-coin problem
  Can it be done without the use of mathematics?
  "The ternary scale, or scale of three"
  A solution of the twelve-coin problem
  Weighing up to forty pounds with only four weights
  There is an infinity of prime numbers
  The square root of two is not a rational number
CHAPTER II CHANCE AND CHOICE
  A coin is spun
  Dr. Joad and the law of averages
  Historical background to theory of probability
  What is random behaviour?
  Scattering seed at random
  Urns and dice
  Addition law of probabilities
  Multiplication law
  Errors of mathematicians
  Eliza Doolittle
  Odds that a head turns up in tossing a penny
  A problem of Samuel Pepys
  Two letters from Isaac Newton to Samuel Pepys
  Expectation of a prize in a football pool
  Expectation of eternal bliss
  The St. Petersburg problem
  Moral criticism of mathematical results
  "Buffon's test, using child labour"
  The courageous Bertrand
  Anything which can happen will happen
  Buffon's needle theorem and the evaluation of p
  The giddy Lazzerini
  Extra-sensory perception and psycho-kinesis
  Why does heads turn up when you pray for tails?
CHAPTER III WHERE DOES IT END?
  Is infinity greater than infinity?
  Can you count?
  Definition of an infinite class
  Countable infinities
  The positive rationals can be counted
  The decimals greater than zero and less than one cannot be counted
  A great unsolved problem of mathematics
  The terrible Cantor
CHAPTER IV AUTOMATIC THINKING
  Classes
  One class contained in another
  Syllogisms
  Socrates was mortal
  Universal class and null class
  Some laws are unsatisfactory
  Writers and Shakespeare
  Another Lewis Carroll teaser
  Algebra of classes and propositions
  "Alice, Brenda, Cissie and Doreen"
  Who won the scholarship?
CHAPTER V TWO-WAY STRETCH
  Ballon d'essai
  Rubber-sheet geometry
  Topological transformation defined
  Deformations
  The escape-artist's trick
  Supplying three houses with main services
  Is topology worth while?
  Multiply-connected figures
  Sphere and torus
  The Moebius band
  "Fun with paper, gum and scissors"
  Rotating ring of tetrahedra
  Modern art and the Klein bottle
  Simple polyhedra and Euler's formula
  The four-colour theorem
  Can you prove it?
  Disdainful doggerel
CHAPTER VI RULES OF PLAY
  Laws of addition
  A double negative gives a positive
  Additive groups
  "What every airman knows, or how to add vectors"
  Rotation is addition
  Finite groups
  How to multiply
  Rings (not of commercial firms)
  The Pascal triangle
  The binomial theorem
  "Perms. and combs., or how to arrange and select"
  No help with football-pools
  How to divide
  Why exclude division by zero?
  The group postulates
  Do you put your shirt on before your tie?
  A plane slides over itself
  Symmetry investigated
  Inkblots rationalised
  Rotational symmetry
  Ornaments
  Point-lattices and curtain materials
  The symmetries in Arabic art
CHAPTER VII AN ACCOUNTANT'S NIGHTMARE
  The gullible Emperor
  A fable of a slowly but surely divergent series
  A well-behaved series
  Can you rub out this line?
  Decimals which come to an end
  Those which do not
  What kind of decimals arise from rational numbers
  The uniqueness of infinite decimals
  Irrational numbers
  The number p
  Shanks and p
  A mystic rhyme for p
  Why should seven suffer?
  "Sir your superior mathematics"
  Trouble with series
  Pinning them down
  More fuss and bother
  Safety first
  Achilles and the tortoise
  Is he still running?
CHAPTER VIII DOUBLE TALK
  Mathematicians not logical
  The uncertainty of logic
  Paradoxes galore
  Class of all classes paradox
  A humble mathematician
  Mathematics not logic
  Infinite collections of shoes
  Of socks
  Can you choose?
  Intuitionism
  Law of the excluded middle
  Right or wrong?
  Formalist view
  No neurosis amongst mathematicians
CHAPTER IX WHAT IS MATHEMATICS?
  What mathematicians do
  International conferences
  Mathematicians as human beings
  What mathematics is not
  Poincaré to the rescue
show more

Rating details

9 ratings
3.33 out of 5 stars
5 11% (1)
4 33% (3)
3 44% (4)
2 0% (0)
1 11% (1)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X