Elliptic geometry

Elliptic geometry is an example of a <a href="/facts/Geometry/wTQf5ffQ">geometry</a> in which Euclid's <a href="/facts/Parallel_postulate/xhSxUX4u">parallel postulate</a> does not hold. Instead, as in <a href="/facts/Spherical_geometry/WGLQb1Ys">spherical geometry</a>, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.
The appearance of this geometry in the nineteenth century stimulated the development of <a href="/facts/Non-Euclidean_geometry/efKa7De2">non-Euclidean geometry</a> generally, including <a href="/facts/Hyperbolic_geometry/DjTMKdgy">hyperbolic geometry</a>.
Elliptic geometry has a variety of properties that differ from those of classical Euclidean plane geometry. For example, the sum of the interior <a href="/facts/Angle/gFUTEQYq">angles</a> of any <a href="/facts/Triangle/cRXUwsMn">triangle</a> is always greater than 180°.

Elliptic geometry open-in-new

Elliptic geometry