This is a book about the mathematical nature of our Universe. Armed with no more than basic high school mathematics, Dr. Joel L. Schiff takes you on a foray through some of the most intriguing aspects of the world around us. Along the way, you will visit the bizarre world of subatomic particles, honey bees and ants, galaxies, black holes, infinity, and more. Included are such goodies as measuring the speed of light with your microwave oven, determining the size of the Earth with a stick in the ground and the age of the Solar System from meteorites, understanding how the Theory of Relativity makes your everyday GPS system possible, and so much more. These topics are easily accessible to anyone who has ever brushed up against the Pythagorean Theorem and the symbol p, with the lightest dusting of algebra. Through this book, science-curious readers will come to appreciate the patterns, seeming contradictions, and extraordinary mathematical beauty of our Universe.

Autorentext
Joel Schiff  has a PhD in Mathematics from the University of California Los Angeles and spent his academic career at the University of Auckland, New Zealand. He is the author of seven other books, four of which are mathematical in nature. He and his wife discovered the asteroid 12926 Brianmason from their own observatory. Schiff was also the publisher of the international quarterly, Meteorite, for many years.  

Zusammenfassung
I first had a quick look, then I started reading it. I couldn't stop. -Gerard 't Hooft (Nobel Prize, in Physics 1999)
This is a book about the mathematical nature of our Universe. Armed with no more than basic high school mathematics, Dr. Joel L. Schiff takes you on a foray through some of the most intriguing aspects of the world around us. Along the way, you will visit the bizarre world of subatomic particles, honey bees and ants, galaxies, black holes, infinity, and more. Included are such goodies as measuring the speed of light with your microwave oven, determining the size of the Earth with a stick in the ground and the age of the Solar System from meteorites, understanding how the Theory of Relativity makes your everyday GPS system possible, and so much more. These topics are easily accessible to anyone who has ever brushed up against the Pythagorean Theorem and the symbol , with the lightest dusting of algebra. Through this book, science-curious readers will come to appreciate the patterns, seeming contradictions, and extraordinary mathematical beauty of our Universe.
      

Inhalt

Dedication

Acknowledgements

About the Author

Prologue

Preface

1. The Mystery of Mathematics

Let us be reasonable

All set

Where is Mathematics?

Fine tuning

A blast from the past: Euclid's geometry

Taking the Fifth further

Pi in the sky

Off to Monte Carlo

Smashed pi

The divine Isoperimetric Inequality

2. From Here to Infinity

Zeno's Paradox

Summing Up

In what Universe is this true?

The power of e

Fast money

What is normal? Multiplying ad infinitum

3. Imaginary Worlds The Strange Case of

The ' 's have it

The God-like Euler identity

Even more imaginaries - quaternions

But wait, there is more - octonians

The world's hardest problem - the Riemann Hypothesis

4. Random Universe

Going steady

Brownian Motion

Life is a gamble

The dating game The world of entropy - order to chaos

Information entropy

5. Order from Chaos

Cellular Automata

Life as a game

Infectious disease model - SIR

Mimicking Darwin One-dimensional CA

The whole is greater than the sum of its parts

Bees and termites

... And ants

Bacteria count

A hive of Mathematics: Fibonacci

Dynamical systems

Messrs. Fatou, Julia and Mandelbrot

The fractal Universe

6. Mathematics in Space Faster than a speeding bullet

Down to Earth

Heavens above

Light-years

The great recession

The Universe is flat

Measuring the invisible: Black holes

A galaxy far, far away 7. The Unreality of Reality

Miniature Universe

Quantum world

Infinite space

Qubits It is all relative, Albert

That equation

What time is it anyway?

Matters of gravity

Time in motion

Radiation

Symmetry and groups

8. The Unknowable Universe

Gödel incompleteness

Halting problem

EMX

Where is it, Dr. Heisenberg?

Summing up

Appendix I: Being Reasonable

Appendix II: Hyperbolic Geometry and Minkowski Spacetime

Appendix III: The Uncountable Real Numbers

Appendix IV: c2 = c: Square and Line have Same Cardinality

Appendix V: Geometric Series

Appendix VI: Cesàro Sums

Appendix VII: Rotating a Vector via a Quaternion

Appendix VIII: Quaternions q2 = -1

Appendix IX: Riemann Zeta Function

Appendix X: Random Walk Code

Appendix XI: Age of the Solar System

Appendix XII: Chelyabinsk Meteoroid

Appendix XIII: Logic Gates

Appendix XIV: Galaxy Distance via Cepheids

Appendix XV: Time Dilation

Appendix XVI: Expansion of the Universe

Bibliography

Index