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Robert Solomon - The Little Book of Mathematical Principles, Theories, & Things

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Book:
The Little Book of Mathematical Principles, Theories, & Things
Author:
Robert Solomon
Publisher:
IMM Lifestyle Books
Genre:
Books / Science
Year:
2016
City:
Lincolnshire
Rating:
3 / 5
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This little book makes serious math simple!

Over 120 concepts including laws, principles, equations, paradoxes, and theorems
Simplifies mathematics, providing fascinating answers to intriguing questions
Jargon-free text provides accessible explanations for famous principles such as chaos theory, Fibonacci numbers, Euclids Elements, Zenos paradoxes, and more
The perfect gift for students, scholars, deep thinkers, armchair intellectuals, and anyone who is interested in math

The Little Book of Mathematical Principles provides simple, clear explanations for over 120 principles, equations, paradoxes, laws, and theorems that form the basis of modern mathematics.

Making serious math simple, this book explains Fibonacci numbers, Euclids Elements, and Zenos paradoxes, as well as other fundamental principles such as chaos theory, game theory, and the game of life.

This book simplifies the ancient discipline of mathematics and provides fascinating answers to intriguing questions, such as: What is the greatest pyramid?, What is a perfect number?, and Is there a theory for stacking oranges?

Written by the author of CCEA GCSE Mathematics Higher 2 and Advanced Level Mathematics: Mechanics, this book is excellent either for dipping into or for reading from cover to cover for a more thorough and engaging understanding of mathematics.

A great coffee table book or gift for anyone interested in math, The Little Book of Mathematical Principles, Theories, & Things provides just enough information for each foundational principle that you will understand the underlying issues. Use it to impress your friends with your knowledge of paradoxes, theories, and more!

Robert Solomon: author's other books

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Published 2016 IMM Lifestyle Books

www.IMMLifestyleBooks.com

IMM Lifestyle Books are distributed

in the United Kingdom by Grantham Book Service,

Trent Road, Grantham, Lincolnshire, NG31 7XQ.

Text 2016 by Dr Bob Solomon

Illustrations 2016 by IMM Lifestyle Books

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission from the publisher.

eISBN 978-1-6076-5222-9

Manufactured in China

Contents

Writing Numbers

Fractions

Quadratic Equations

The Greatest Pyramid

The Pythagoreans

Pythagorass Theorem

Irrational Numbers

Perfect Numbers

Regular Polygons

Platonic Solids

The Golden Ratio

Trisecting the Angle

Doubling the Cube

Squaring the Circle

Zenos Paradoxes

Plato and Platonism

Conic Sections

Euclids Elements

The Fifth Postulate

Sum of the Angles in a Triangle

The Fundamental Theorem of Arithmetic

The Infinity of Prime Numbers

Measurement of a Sphere

Quadrature of the Parabola

The Sand Reckoner

Trigonometry

Negative Numbers

The Earth-Centered Universe

Zero

Kitab wa al jabr wa al muqabalah (The Book of Shifting and Balancing)

Cubic Equations Geometric Solutions

Fibonacci Numbers

Perspective

Cubic Equations Algebraic Solution

Quartic Equations

The Sun-Centered Universe

Mathematical Induction

Falling Bodies

The Sun-Centered Universe Again

Logarithms

Tessellations

Regular Solids Revisited

Calculating Machines

Analytic Geometry

A Formula for Prime Numbers

The Problem of the Points

Pascals Triangle

The Binomial Distribution

Pascals Wager

Differentiation

Integration

The Fundamental Theorem of Calculus

Three Laws of Motion

The Law of Gravity

The Precession of the Equinoxes

The Law of Large Numbers

The Normal Distribution

The Seven Bridges of Knigsberg

Goldbachs Conjecture

V + F = E +

The Gamblers Fallacy

Complex Numbers

Regular Polygons Revisited

Arithmetic and Geometric Progressions

The Fundamental Theorem of Algebra

Fourier Series

The Difference and Analytic Engines

Quintic Equations

Non-Euclidean Geometry

Galois Theory

Constructible Lengths

Doubling the Cube and Trisecting the Angle Revisited

Quaternions

Transcendental Numbers

Kirkmans Schoolgirl Problem

The Laws of Thought

Twisted Shapes

The Riemann Hypothesis

Maxwells Equations

The Countability of Fractions

The Uncountability of the Reals

Squaring the Circle Revisited

The Correlation Coefficient

The Continuum Hypothesis

Space-Filling Curves

Wallpaper Patterns

Doughnuts and Coffee Cups

What the Tortoise Said to Achilles

The Prime Number Theorem

Hilberts Problems

Quantum Mechanics

The Central Limit Theorem

Russells Paradox

Mathematics as Part of Logic

The Snowflake Curve

Axiom of Choice

The Jordan Curve Theorem

Special Relativity

Intuitionism

ZermeloFraenkel Set Theory

The Hairy-Ball Theorem

General Relativity

The Hilbert Program

Gdels Theorem

The Travelling Salesman

Turing Machines

Binary Numbers

The Ham Sandwich Theorem

The Enigma Machine

Colossus

Game Theory

ENIAC

The Prisoners Dilemma

Electronic Calculators

Polyas Principles

Erds Number

Chaos Theory

The Secretary Problem

Catastrophe Theory

Life

Matiyasevichs Theorem

P = NP?

Public Key Codes

Fractals

The Four-Color Theorem

The Logistic Model

Stacking Oranges

Fermats Last Theorem

The Seven Millennium Prize Problems

Appendix

Glossary

Acknowledgements

Index

HOW TO USE THIS BOOK

The Little Book of Mathematical Principles, Theories, & Things is an easy-to-use comprehensive guide to mathematics. It features over entries on key principles or theories essential to understanding the subject. Written in an easily accessible manner, the Little Book explains sometimes very difficult concepts and theories, putting them in their historical context, giving background information on the experts who proposed them in the first place, analysing influences and proposing, where relevant, links to other related entries. The book also features tables, equations and illustrations, and ends with a glossary, and a comprehensive index.

The Little Book of Mathematical Principles, Theories, & Things is arranged chronologically and the country of origin is listed, where appropriate. Each entry includes a clear main heading, the person or people responsible for the discovery, birth and death dates, where relevant, followed by a short introductory paragraph explaining the concept concisely. In some cases, the main essay is also cross referenced to linked subjects. The key on the opposite page explains the order of information in each entry.

3000 BC Global

Writing Numbers

The place value system uses only a finite number of symbols to write any number.

_______________

In some number systems, there are different symbols for each power of In a place value system, only a small number of symbols are used.

In the Ancient Egyptian number system, dating from about 3000 there were symbols for units, symbols for 10s, and so on. The number was written:

where | represents a unit, represents and represents

The Chinese system writes numbers much as we say them. We say three hundred and sixty-five: in other words, so many hundreds, so many tens, and so many units. The number is written as shown below.

It represents x + x +

In both these systems there is no limit to the number of symbols required. We need a different symbol for millions, another symbol for millions, and so on. The modern system uses precisely symbols: the digits to

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