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The Gentle Art of Mathematics

Publisher: 
Dover Publications
Number of Pages: 
143
Price: 
6.95
ISBN: 
0486229491
Date Received: 
Saturday, January 28, 2006
Reviewable: 
No
Include In BLL Rating: 
Yes
Reviewer Email Address: 
Dan Pedoe
Publication Date: 
1974
Format: 
Paperback
Audience: 
Category: 
General

 

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
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