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great circle

Circle on the surface of a sphere whose center coincides with that of the sphere itself. On the globe, the equator is a great circle, while every meridian corresponds to half of a great circle.

If you want to move on a spherical surface in the straightest possible way, choose a path along a great circle – in the language of mathematics this is equivalent to saying: great circles are geodesics of a spherical surface.

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surface

Geometric space with two dimensions. Examples include the plane or the surface of a sphere.

sphere

A spherical surface is a simple example for a curved surface. It is easily pictured as a surface embedded in three-dimensional space: a spherical surface is the set of all points at a certain fixed distance from a given point (the point being the centre of the sphere). Mathematically, a spherical surface can be described without recourse to three-dimensional space - when mathematicians talk of the geometry of such a surface, they (almost) always mean the "inner geometry": Those properties of the surface noticeable to two-dimensional beings, living and working in that surface, capable of measuring distances and angles in it. Sphere is regularly used as a synonym for spherical surface (instead of describing a solid, three-dimensional ball). And not only for the two-dimensional spherical surface described above, but also for its analogues in lower and higher dimensions. A one-sphere, for instance, is the same as a circle, a two-sphere is the spherical surface defined above, a three-sphere its three-dimensional analogue.

great circle

Circle on the surface of a sphere whose center coincides with that of the sphere itself. On the globe, the equator is a great circle, while every meridian corresponds to half of a great circle.

If you want to move on a spherical surface in the straightest possible way, choose a path along a great circle - in the language of mathematics this is equivalent to saying: great circles are geodesics of a spherical surface.

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great circle

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