That's Maths E-Book

Peter Lynch

• Herausgeber: Gill Books
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2016

Seitenzahl: 297

Beschreibung

From atom bombs to rebounding slinkies, open your eyes to the mathematical magic in the everyday. Mathematics isn't just for academics and scientists, a fact meteorologist and blogger Peter Lynch has spent the past several years proving through his Irish Times newspaper column and blog, That's Maths.Here, he shows how maths is all around us, with chapters on the beautiful equations behind designing a good concert venue, predicting the stock market and modelling the atom bomb, as well as playful meditations on everything from coin-stacking to cartography. If you left school thinking maths was boring, think again!

Leseprobe

THAT’SMATHS

Peter Lynch

Gill Books

CONTENTS

Cover

Title Page

Preface

Introduction

You Can Do Maths

Instant Information

Napier’s Nifty Rules

Sproutology

Why Don’t Clouds Fall Down?

Packing Oranges and Stacking Cannonballs

Modelling Epidemics

A Falling Slinky

A ‘Mersennery’ Quest

Shackleton’s Spectacular Boat Journey

Where in the World?

Srinivasa Ramanujan

Sharing a Pint

Pons Asinorum

Lost and Found: The Secrets of Archimedes

Subterranean Topology

The Earth’s Vast Orb

More Equal than Others

Maths and CAT Scans

Bayes Rules OK

Pythagoras goes Global

Dozenal Digits: From Dix to Douze

How Leopards get their Spots

Monster Symmetry and the Forces of Nature

Kelvin Wakes

Gauss Misses a Trick

Prime Secrets Revealed

Amazing Normal Numbers

Heavy Metal or Blue Jeans?

The School of Athens

Hailstone Numbers

The Remarkable BBP Formula

The Atmospheric Railway

A Hole through the Earth

Sofia Kovalevskaya

The Simpler the Better

Geometry out of this World

Euler’s Gem

The Watermelon Puzzle

The Antikythera Mechanism: The First Computer

World Population

Ireland’s Fractal Coast

Santa’s Fractal Journey

Interesting Bores

Pythagorean (or Babylonian) Triples

Bézout’s Theorem

French Curves and Bézier Splines

Astronomical Perturbations

The Predictive Power of Maths

Highway Geometry

Breaking Weather Records

The Faraday of Statistics

The Chaos Game

Fibonacci Numbers are Good for Business

Biscuits, Books, Coins and Cards: Severe Hangovers

Gauss’s Great Triangle and the Shape of Space

Degrees of Infinity

A Swinging Way to See the Spinning Globe

Do You Remember Venn?

Mathematics is Coming to Life in a Big Way

Temperamental Tuning

Cartoon Curves

How Big was the Bomb?

Algebra in the Golden Age

Old Octonions May Rule the World

Light Weight

Falling Bodies

Earth’s Shape and Spin Won’t Make You Thin

The Tangled Tale of Knots

Plateau’s Problem: Soap Bubbles and Soap Films

The Steiner Minimal Tree Problem

Who Wants to be a Millionaire?

The Klein 4-Group

Tracing Our Mathematical Ancestry: The Mathematics Genealogy Project

Café Mathematics in Lvov

The King of Infinite Space: Euclid and his Elements

Golden Moments

Mode-S EHS: A Novel Source of Weather Data

For Good Communications, Leaky Cables are Best

Tap-tap-tap the Cosine Button

The Black–Scholes Equation

Eccentric Pizza Slices

Mercator’s Marvellous Map

The Remarkable Power of Symmetry

Increasingly Abstract Algebra

Acoustic Excellence and RT-60

The Bridges of Paris

Buffon Was No Buffoon

James Joseph Sylvester

Holbein’s Anamorphic Skull

The Ubiquitous Cycloid

Hamming’s Smart Error-correcting Codes

Mowing the Lawn in Spirals

Melencolia I: An Enigma for Half a Millennium

Mathematics Can Solve Crimes

Life’s a Drag Crisis

The Flight of a Golf Ball

Factorial 52: A Stirling Problem

Richardson’s Fantastic Forecast Factory

The Analemmatic Sundial

Further Reading

Acknowledgements

Copyright

About the Author

About Gill Books

PREFACE

This book is a collection of articles covering all major aspects of mathematics. It is written for people who have a keen interest in science and mathematics but who may not have the technical knowledge required to study mathematical texts and journals. The articles are accessible to anyone who has studied mathematics at secondary school.

Mathematics can be enormously interesting and inspiring, but its beauty and utility are often hidden. Many of us did not enjoy mathematics at school and have negative memories of slogging away, trying to solve pointless and abstruse problems. Yet we realise that mathematics is essential for modern society and plays a key role in our economic welfare, health and recreation.

Mathematics can be demanding on the reader because it requires active mental effort. Recognising this, the present book is modular in format. Each article can be read as a self-contained unit. I have resisted the temptation to organise the articles into themes, presenting them instead in roughly the order in which they were written. Each article tells its own story, whether it is a biography of some famous mathematician, a major problem (solved or unsolved), an application of maths to technology or a cultural connection to music or the visual arts.

I have attempted to maintain a reasonably uniform mathematical level throughout the book. You may have forgotten the details of what you learned at school, but what remains should be sufficient to enable you to understand the articles. If you find a particular article abstruse or difficult to understand, just skip to the next one, which will be easier. You can always return later if you wish.

The byline of my blog, thatsmaths.com, is ‘Beautiful, Useful and Fun’. I have tried to bring out these three aspects of mathematics in the articles. Beauty can be subjective, but, as you learn more, you cannot fail to be impressed by the majesty and splendour of the intellectual creations of some of the world’s most brilliant minds. The usefulness of maths is shown by its many applications to modern technology, and its growing role in medicine, biology and the social sciences. The fun aspect will be seen in the field known as recreational mathematics, aspects of maths that no longer attract active professional research but that still hold fascination.

About half the articles have appeared in The Irish Times over the past four years. The remainder are newly written pieces and postings from thatsmaths.com. If you have a general interest in scientific matters and wish to be inspired by the beauty and power of mathematics, this book should serve you well.

INTRODUCTION

BEAUTIFUL, USEFUL AND FUN: THAT’S MATHS

Type a word into Google: a billion links come back in a flash. Tap a destination into your satnav: distances, times and highlights of the route appear. Get cash from an ATM, safe from prying eyes. Choose a tune from among thousands squeezed onto a tiny chip. How are these miracles of modern technology possible? What is the common basis underpinning them? The answer is mathematics.

Maths now reaches into every corner of our lives. Our technological world would be impossible without it. Electronic devices like smartphones and iPods, which we use daily, depend on the application of maths, as do computers, communications and the internet. International trade and the financial markets rely critically on secure communications, using encryption methods that spring directly from number theory, once thought to be a field of pure mathematics without ‘useful’ applications.

We are living longer and healthier lives, partly due to the application of maths to medical imaging, automatic diagnosis and modelling the cardiovascular system. The pharmaceuticals that cure us and control disease are made possible through applied mathematics. Agricultural production is more efficient thanks to maths; forensic medicine and crime detection depend on it. Control and operation of air transport would be impossible without maths. Sporting records are broken by studying and modelling performance and designing equipment mathematically. Maths is everywhere.

THE LANGUAGE OF NATURE

Galileo is credited with quantifying the study of the physical world, and his philosophy is encapsulated in the oft-quoted aphorism, ‘The Book of Nature is written in the language of mathematics.’ This development flourished with Isaac Newton, who unified terrestrial and celestial mechanics in a grand theory of universal gravitation, showing that the behaviour of a projectile like a cannonball and the trajectory of the moon are governed by the same dynamics.

Mechanics and astronomy were the first subjects to be ‘mathematicised’, but over the past century the influence of quantitative methods has spread to many other fields. Statistical analysis now pervades the social sciences. Computers enable us to simulate complex systems and predict their behaviour. Modern weather forecasting is an enormous arithmetical calculation, underpinned by mathematical and physical principles. With the recent untangling of the human genome, mathematical biology is a hot topic.

The mathematics that we learned at school was developed centuries ago, so it is easy to get the idea that maths is static, frozen in the seventeenth century or fossilised since ancient Greece. In fact, the vast bulk of mathematics has emerged in the past hundred years, and the subject continues to blossom. It is a vibrant and dynamic field of study. The future health of our technological society depends on this continuing development.

While a deep understanding of advanced mathematics requires intensive study over a long period, we can appreciate some of the beauty of maths without detailed technical knowledge, just as we can enjoy music without being performers or composers. It is a goal of this book to assist readers in this appreciation. It is hoped that, through this collection of articles, you may come to realise that mathematics is beautiful, useful and fun.

THE TWO CULTURES

‘Of course I’ve heard of Beethoven, but who is this guy Gauss?’

The ‘Two Cultures’, introduced by the British scientist and novelist C. P. Snow in an influential Rede Lecture in 1959, are still relevant today.

Ludwig van Beethoven and Carl Friedrich Gauss were at the height of their creativity in the early nineteenth century. Beethoven’s music, often of great subtlety and intricacy, is accessible even to those of us with limited knowledge and understanding of it. Gauss, the master of mathematicians, produced results of singular genius, great utility and deep aesthetic appeal. But, although the brilliance and beauty of his work is recognised and admired by experts, it is hidden from most of us, requiring much background knowledge and technical facility for a true appreciation of it.

There is a stark contrast here. There are many parallels between music and mathematics: both are concerned with structure, symmetry and pattern; but while music is accessible to all, maths presents greater obstacles. Perhaps it’s a left versus right brain issue. Music gets into the soul on a high-speed emotional autobahn, while maths has to follow a rational, step-by-step route. Music has instant appeal; maths takes time.

It is regrettable that public attitudes to mathematics are predominantly unsympathetic. The beauty of maths can be difficult to appreciate, and its significance in our lives is often underestimated. But mathematics is an essential thread in the fabric of modern society. We all benefit from the power of maths to model our world and facilitate technological advances. It is arguable that the work of Gauss has a greater impact on our daily lives than the magnificent creations of Beethoven.

In addition to utility and aesthetic appeal, maths has great recreational value, with many surprising and paradoxical results that are a source of amusement and delight. The goal of this book is to elucidate the beauty, utility and fun of mathematics by examining some of its many uses in modern society and to illustrate how it benefits our lives in so many ways.