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Publisher:

Dover Publications

Publication Date:

1974

Number of Pages:

143

Format:

Paperback

Price:

6.95

ISBN:

0486229491

Category:

General

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 | ||||||||

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