Читать книгу The Little Book of Mathematical Principles, Theories & Things - Robert Solomon - Страница 4

Writing Numbers

Fractions

Quadratic Equations

The Greatest Pyramid

π

The Pythagoreans

Pythagoras’s Theorem

Irrational Numbers

Perfect Numbers

Regular Polygons

Platonic Solids

The Golden Ratio

Trisecting the Angle

Doubling the Cube

Squaring the Circle

Zeno’s Paradoxes

Plato and Platonism

Conic Sections

Euclid’s 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

Pascal’s Triangle

The Binomial Distribution

Pascal’s 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 Königsberg

Goldbach’s Conjecture

V + F = E + 2

The Gambler’s Fallacy

Complex Numbers

e

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

Kirkman’s Schoolgirl Problem

The Laws of Thought

Twisted Shapes

The Riemann Hypothesis

Maxwell’s 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

Hilbert’s Problems

Quantum Mechanics

The Central Limit Theorem

Russell’s Paradox

Mathematics as Part of Logic

The Snowflake Curve

Axiom of Choice

The Jordan Curve Theorem

Special Relativity

Intuitionism

Zermelo–Fraenkel Set Theory

The Hairy-Ball Theorem

General Relativity

The Hilbert Program

Gödel’s Theorem

The Travelling Salesman

Turing Machines

Binary Numbers

The Ham Sandwich Theorem

The Enigma Machine

Colossus

Game Theory

ENIAC

The Prisoner’s Dilemma

Electronic Calculators

Polya’s Principles

Erdös Number

Chaos Theory

The Secretary Problem

Catastrophe Theory

Life

Matiyasevich’s Theorem

P = NP?

Public Key Codes

Fractals

The Four-Color Theorem

The Logistic Model

Stacking Oranges

Fermat’s Last Theorem

The Seven Millennium Prize Problems

Appendix

Glossary

Acknowledgements

Index