Non-Euclidean geometry
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In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geo
On a sphere, the sum of the angles of a triangle is not equal to 180°. The surface of a sphere is not a Euclidean space, but locally the laws of the Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is very near 180°.
Hyperbolic geometry
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In mathematics, hyperbolic geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
Non-Euclidean geometry
…alternative, or consideration of quadratic forms other than the definite quadratic forms associated with metric geometry. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When isotropic quadratic forms are admitted, then there are affine planes associated…
A collection of crocheted hyperbolic planes, in imitation of a coral reef, by Institute For Figuring
The "hyperbolic soccerball", a paper model which approximates (part of) the hyperbolic plane as a truncated icosahedron approximates the sphere.