great circle

mathematics

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June 29, 2026

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In mathematics, a great circle is formed on the surface of a sphere by the intersection of a plane that passes through the sphere's center. An arc of a great circle connecting two points on a sphere represents the shortest distance between them.123

The Earth's Equator is an example of a great circle, dividing the planet into the Northern and Southern hemispheres. Ancient Greek philosophers like Aristotle and Eratosthenes recognized that Earth was spherical and even attempted to calculate its circumference using principles related to great circles.45

Great circle routes are crucial in navigation, particularly for long-distance travel by air and sea, as they offer the most efficient path between two points.36

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non-Euclidean geometry
Spherical geometry
Great circles are the “straight lines” of spherical geometry. This is a consequence of the properties of a sphere, in which the shortest distances on the surface are great circle routes. Such curves are said to be “intrinsically” straight. (Note, however, that intrinsically straight and…
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Great circles are the “straight lines” of spherical geometry. This is a consequence of the properties of a sphere, in which the shortest distances on the surface are great circle routes. Such curves are said to be “intrinsically” straight. (Note, however, that intrinsically straight and…
Read More

trigonometry
Spherical trigonometry
…by the intersection of three great circle arcs on the surface of a sphere. Spherical triangles were subject to intense study from antiquity because of their usefulness in navigation, cartography, and astronomy. (See above Passage to Europe.)
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…by the intersection of three great circle arcs on the surface of a sphere. Spherical triangles were subject to intense study from antiquity because of their usefulness in navigation, cartography, and astronomy. (See above Passage to Europe.)
Read More