geometry

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

References & Edit History Related Topics

Images & Videos

Map of the Greco-Roman world highlighting the birthplaces of notable ancient mathematicians, marked with the pi symbol and labeled with their names. Cities such as Athens, Alexandria, Syracuse, and Miletus are shown around the Mediterranean, with modern country boundaries outlined. An inset provides detail for the region of Greece and western Anatolia.

Chinese and Greek geometric theorems

Diagram showing four types of polygonal numbers with colored dots arranged in geometric patterns: blue triangles for triangular numbers, green squares for square numbers, red pentagons for pentagonal numbers, and purple hexagons for hexagonal numbers, each illustrating how numbers like 1, 3, 6, 10, 4, 9, 16, 5, 12, 22, 6, 15, and 28 can be visually represented.

A diagram on aged parchment illustrates Eratosthenes' method for measuring Earth's circumference, showing sunlight rays striking Alexandria and Syene at different angles, with labeled lines and angles representing the geometric calculation.

Map showing the birthplaces of prominent mathematicians from the Islamic world, marked with city names and mathematician names across the Middle East and Central Asia. Cities such as Baghdad, Basra, Harran, and others are labeled, each associated with a historical mathematician. Modern country boundaries and a locator inset of the region are included.

Two geometric solids of equal height are shown side by side, each sliced horizontally at the same levels. Corresponding cross sections are highlighted and connected by arrows, illustrating Cavalieri's principle that solids with equal heights and equal cross-sectional areas at every level have equal volumes.

A geometric diagram illustrating Fermat's tangent method, showing a curve intersecting a triangle with labeled points, axes, and segments representing variables x, epsilon, y, and y1.

Pascal's hexagon

A blue quadrilateral labeled ABCD with diagonals intersecting inside, forming four triangles; right angles are marked at corners A and B, and tick marks indicate equal side lengths. Text explains triangle congruence and angle equality within the quadrilateral.

Related Questions

Map of the Greco-Roman world highlighting the birthplaces of notable ancient mathematicians, marked with the pi symbol and labeled with their names. Cities such as Athens, Alexandria, Syracuse, and Miletus are shown around the Mediterranean, with modern country boundaries outlined. An inset provides detail for the region of Greece and western Anatolia. — mathematicians of the Greco-Roman world This map spans a millennium of prominent Greco-Roman mathematicians, from Thales of Miletus (c. 600 bce) to Hypatia of Alexandria (c. 400 ce).

geometry

mathematics

Written by

J.L. Heilbron

Fact-checked by

Britannica Editors

Last updated

Oct. 30, 2026 •History

geometry, the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space. It is one of the oldest branches of mathematics, having arisen in response to such practical problems as those found in surveying, and its name is derived from Greek words meaning “Earth measurement.” Eventually it was realized that geometry need not be limited to the study of flat surfaces (plane geometry) and...

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