geometry: Quick Facts

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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.

Know how civil and environmental engineers understand the mechanics of thin structures and how they use geometry to study the deformation process

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Topics

Menelaus’ theorem Atiyah-Singer index theorem Landen’s theorem Helly’s theorem topology Euclidean geometry differential geometry analytic geometry projective geometry non-Euclidean geometry analysis probability theory cryptology computer science combinatorics algebra statistics automata theory set theory information theory

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Key People

French philosopher Blaise Pascal

Blaise Pascal

French philosopher and scientist

Euclid

Euclid

Greek mathematician

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

Pierre de Fermat

French mathematician

How did Ptolemy explain retrograde motion?

Ptolemy

Egyptian astronomer, mathematician, and geographer

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

Bernhard Riemann

German mathematician

Paul Erdős

Paul Erdős

Hungarian mathematician

Leonhard Euler

Swiss mathematician

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Eudoxus of Cnidus

Greek mathematician and astronomer

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Apollonius of Perga

Greek mathematician

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Pappus of Alexandria

Greek mathematician

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Ibn al-Haytham

Arab astronomer and mathematician

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

Isaac Barrow

English mathematician

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Heron of Alexandria

Greek mathematician

Etching by Jacob de Gheyn III showing Thales of Miletus seated with a long beard, draped in robes, holding a compass over an open book with geometric diagrams.

Thales of Miletus

Greek philosopher

James Gregory.

James Gregory

Scottish mathematician and astronomer

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Girard Desargues

French mathematician

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

Colin Maclaurin

Scottish mathematician

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Giovanni Ceva

Italian mathematician and engineer

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Michel Chasles

French mathematician

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Archytas of Tarentum

Greek mathematician

Equations written on blackboard

All About Math Quiz

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

Define It: Math Terms

Equations written on blackboard

Numbers and Mathematics