geometry

Table of Contents

Introduction
Major branches of geometry
- Euclidean geometry
- Analytic geometry
- Projective geometry
- Differential geometry
- Non-Euclidean geometries
- Topology
History of geometry
- Ancient geometry: practical and empirical
  - Finding the right angle
  - Locating the inaccessible
  - Estimating the wealth
- Ancient geometry: abstract and applied
  - The three classical problems
    - Doubling the cube
    - Trisecting the angle
    - Squaring the circle
  - Idealization and proof
  - The Euclidean synthesis
  - Gnomonics and the cone
  - Astronomy and trigonometry
    - Calculation
    - Epistemology
- Ancient geometry: cosmological and metaphysical
  - Pythagorean numbers and Platonic solids
  - Measuring the Earth and heavens
- The post-classical period
  - Passage through Islam
  - Europe rediscovers the classics
  - Linear perspective
- Transformation
  - French circles
    - Projective geometry
    - Cartesian geometry
  - Geometrical calculus
  - The world system
- Relaxation and rigour
  - Projection again
  - Non-Euclidean geometries
  - A grand synthesis
  - The real world

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Topics

topology Euclidean geometry differential geometry analytic geometry projective geometry non-Euclidean geometry algebraic geometry Pappus’s theorem catastrophe theory Ceva’s theorem analysis probability theory cryptology computer science combinatorics algebra statistics automata theory set theory information theory

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Key People

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Greek mathematician

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Egyptian astronomer, mathematician, and geographer

Fermat, portrait by Roland Lefèvre; in the Narbonne City Museums, France

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Bernhard Riemann, lithograph after a portrait, artist unknown, 1863.

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German mathematician

Paul Erdős

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Hungarian mathematician

Leonhard Euler

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Swiss mathematician

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Ibn al-Haytham

Arab astronomer and mathematician

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Heron of Alexandria

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Isaac Barrow, pencil drawing by David Loggan, 1676; in the National Portrait Gallery, London

Isaac Barrow

English mathematician

James Gregory.

James Gregory

Scottish mathematician and astronomer

Thales of Miletus

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Girard Desargues

French mathematician

Colin Maclaurin, engraving by S. Freeman; in the British Museum.

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Giovanni Ceva

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Quiz

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