The Infinite in the Finite

Contents

  1. Symphonies of stone
  2. The pyramid builders
  3. The Theban Mysteries
  4. Babylon
    Babylonian mathematics
  5. The Middle Kingdom
    Chinese mathematics
  6. The Achaeans
  7. A world made of numbers
    Pythagoras
    The shapes of numbers
    The regular polyhedra
    Euler’s number
    Polyhedra in the world
  8. The thoughts of Zeus
    The symmetries of polygons
    The symmetry groups of the regular polyhedra
  9. The philosopher’s criticism
    Geometry
    The Peloponnesian War
    Socrates
    Plato
    Aristotle
    Aristotle’s logic
    The Stoics construct the truth
  10. The Elements of Euclid
    Euclid’s dream
    Similar triangles
    The angles of triangles
    The area of a triangle
    Pythagoras’ theorem
    Triangles in circles
  11. An island interlude
  12. Proportion
    The geometrical solution of aha problems
    The theory of proportion
    The construction of regular polygons
    The uses of proportion
    A problem of maxima
  13. 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
  14. 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
  15. The science of numbers
    Pythagorean numerology
    Prime numbers
    Irrational numbers
    Pythagorean triples
    Patterns of primes
  16. The School of Alexandria
    Alexandria
    Heron
    Diophantus
    Pappus
    The last of the Greeks
    The Eudemian summary
  17. 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
  18. 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