The Gentle Art of Mathematics

Dan Pedoe

Publisher:

Dover Publications

Publication Date:

1974

Number of Pages:

143

Format:

Paperback

Price:

6.95

ISBN:

0486229491

Category:

General

MAA Review
Table of Contents

We do not plan to review this book.

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