A New Year’s Present from a Mathematician

201 Pages·68.508 MB·\201

by  Snezana Lawrence (Author)

A New Year’s Present from a

Mathematician
ii
A New Year’s Present from a

Mathematician
By
Snezana Lawrence
CRC Press
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To my Kit, who is constantly mathematizing

Contents

List of Figures, xi
Preface, xvii
Acknowledgments, xix
About the Author, xxi
Introduction 1

TWELVE DROPS OF MATHEMATICAL WISDOM 1

LET’S CREATE OUR MAP 4

WHY THE DESERT? 6

IS MATHEMATICS FOR YOU, OR ARE YOU FOR
MATHEMATICS? 6

Chapter 1 ◾ January 9
MATHEMATICAL TRIBES 9

I WROTE YOU A POEM 11

NEWTON’S INFINITELY IMPORTANT AND INFINITELY
SMALL QUANTITIES 13

THE SEARCH FOR THE PHILOSOPHER’S STONE 18

THAT DIVINE CLOCK 19

FRIENDS IN NEED 21

Chapter 2 ◾ February 31
THE HOLY MONTH OF WISDOM 31

GOING BACK TO THALES 35

ISIDORE, THE MILESIAN 40

vii
viii Contents
◾
APPROXIMATIONS IN MATHEMATICS,

ARCHITECTURE, AND LIFE 40

Chapter 3 ◾ March 45
HIDDEN DOMES AND HEAVENLY IDEAS 45
THE HANGING CHAIN CURVE 49
WREN AND OTHER CURVED SHAPES 51
BEAUTY IS IN THE EYE OF THE BEHOLDER – OR IN
MATHEMATICS? 52

SOME OTHER INTERESTING CURVES 53

Chapter 4 ◾ April 59
AN IDEAL AND EMMY 59
NOETHER’S ABSTRACT ART OF MATHEMATICS 60
NOETHER SET DOWN THE LAW 63
WHAT ABOUT THE IDEAL AND EMMY? 65
Chapter 5 ◾ May 69
THE WITCH THAT TURNED 69

NEWTON FOR, AND BY, LADIES 71
THE BOOK 71
THE SPECTACLE OF NEWTONIANISM 72
AGNESI AND THE WITCH 74
AND, BY A TURN IN THE STORYLINE… 76

Chapter 6 ◾ June 79

MATHEMATICS IS LIKE… A TRANSLUCENT OBJECT
FLOATING IN SPACE 79

SOLIDS NAMED AFTER A GREEK PHILOSOPHER 81
THE STRUCTURE OF THE FIFTH ELEMENT 85
THE TRANSLUCENT OBJECT FLOATING IN SPACE 89

Chapter 7 ◾ July 95
THE POWER OF (MATHEMATICAL) BOOKS 95

THE MATHEMATICAL PREFACE 98

BURNING BOOKS 99

AND THEN, ACROSS THE POND 100
Contents ix
  ◾     
Chapter 8 ◾ August 105
REVOLUTIONARY MATHEMATICS 105

THE REAL BIRTHDAY OF IMAGINARY BOURBAKI 107

THE MODERN ELEMENTS 108

THE ETERNAL APPEAL OF PYTHAGORAS 109

DANGEROUS BENDS 111

BOURBAKI’S THEOREM – EN FIN 112

Chapter 9 ◾ September 115
THE MATHEMATICAL TRAVELER IS AT HOME
EVERYWHERE 115

THE NUMBER THAT BEARS YOUR NAME 116

CAN I IMAGINE AN EVEN BIGGER NUMBER? 118

BIG NUMBERS IN ANTIQUITY 118

ERDŐS AND HIS MATHEMATICAL FRIENDS’ NUMBERS 120
A FAMOUS MISTAKE AND THE VALUE OF BIG NUMBERS 124

Chapter 10 ◾ October 127
THE ROUNDED LIFE AND MUSIC OF VIBRATING
STRINGS 127

THE FOURTH DIMENSION 129

THOUGHT EXPERIMENTS 130

SOME MORE DIFFICULT MATHS 132

A FULL CIRCLE BACK TO LE ROND AND HIS WAY OF
FINDING HAPPINESS 134

Chapter 11 ◾ November 137
WE MAY BE FRIENDS, BUT I STILL HAVE TO CHECK
WHETHER WHAT YOU ARE SAYING IS TRUE 137

NEW WORLDS ON THE HORIZON 139

THE BOOLE FAMILY AND THEIR FRIENDS 140

AS MATHEMATICAL FAMILIES GO… 141

THE LEGACY FOR THE FUTURE 145

Chapter 12 ◾ December 149
WHAT CAN A MATHEMATICIAN GIVE TO
THEIR FRIEND AS A NEW YEAR’S PRESENT? 149