close this window

# The Infinite in the Finite

## Contents

- Symphonies of stone
- The pyramid builders
- The Theban Mysteries
- Babylon

Babylonian mathematics
- The Middle Kingdom

Chinese mathematics
- The Achaeans
- A world made of numbers

Pythagoras

The shapes of numbers

The regular polyhedra

Euler’s number

Polyhedra in the world
- The thoughts of Zeus

The symmetries of polygons

The symmetry groups of the regular polyhedra
- The philosopher’s criticism

Geometry

The Peloponnesian War

Socrates

Plato

Aristotle

Aristotle’s logic

The Stoics construct the truth
- The
*Elements* of Euclid

Euclid’s dream

Similar triangles

The angles of triangles

The area of a triangle

Pythagoras’ theorem

Triangles in circles
- An island interlude
- Proportion

The geometrical solution of *aha* problems

The theory of proportion

The construction of regular polygons

The uses of proportion

A problem of maxima
- The Divine Archimedes

Archimedes

The measurement of a circle

The method of exhaustion

The surface area of a sphere

The volume of a sphere

The volume of a cone

The quadrature of a spiral

The quadrature of a parabola

Archimedes’ principle

The Rancher’s Dilemma
- Apollonius the great geometer

Apollonius

Apollonius’ *Conics*

The three conic sections

Tangents to conic sections

The property of the parabola used by Archimedes

The centres of conics

The foci of a conic

Reflection properties of conic sections

The focal construction of conics
- The science of numbers

Pythagorean numerology

Prime numbers

Irrational numbers

Pythagorean triples

Patterns of primes
- The School of Alexandria

Alexandria

Heron

Diophantus

Pappus

The last of the Greeks

The Eudemian summary
- The dark subcontinent of India

The Aryans

Sanskrit and the Hindu numerals

Hindu astronomy

The mathematics of Brahmagupta and Mahavira

A pearl of number theory
- The contribution of Islam

The conquests of the Arabs

Trigonometry

The uses of trigonometry

The geometry of the sphere

The gnomon curve

Algebra

The summation of powers of integers

Spain under Islam

close this window