spherical geometry

mathematics

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July 14, 2026

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Spherical geometry is the study of figures on the surface of a sphere. It is a type of non-Euclidean geometry, meaning it differs from the standard Euclidean geometry we learn in school.12

In spherical geometry, the "straight lines" are actually arcs of great circles, which are the largest circles that can be drawn on a sphere's surface. For example, the shortest distance between two points on Earth follows a great circle route. Unlike Euclidean geometry, where parallel lines never meet, in spherical geometry, there are no parallel lines; any two great circles will eventually intersect. Also, the sum of the interior angles of a triangle on a sphere is always greater than 180 degrees. This type of geometry is fundamental to understanding concepts like terrestrial geography and navigation.32

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mathematics
Greek trigonometry and mensuration
…geometry of the sphere (called spherics) were compiled into textbooks, such as the one by Theodosius (3rd or 2nd century bce) that consolidated the earlier work by Euclid and the work of Autolycus of Pitane (flourished c. 300 bce) on spherical astronomy. More significant, in the 2nd century bce the…
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…geometry of the sphere (called spherics) were compiled into textbooks, such as the one by Theodosius (3rd or 2nd century bce) that consolidated the earlier work by Euclid and the work of Autolycus of Pitane (flourished c. 300 bce) on spherical astronomy. More significant, in the 2nd century bce the…
Read More

non-Euclidean geometry
Spherical geometry
From early times, people noticed that the shortest distance between two points on Earth were great circle routes. For example, the Greek astronomer Ptolemy wrote in Geography (c. 150 ce):
Read More
From early times, people noticed that the shortest distance between two points on Earth were great circle routes. For example, the Greek astronomer Ptolemy wrote in Geography (c. 150 ce):
Read More