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Parallel postulate
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In geometry, the parallel postulate is the fifth postulate in Euclid's Elements and a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
The page containing the Parallel Postulate from the 1747 Latin edition of Euclid’s Elements, originally Euclid’s 5th Postulate, here reclassified and
The page containing the Parallel Postulate from the 1747 Latin edition of Euclid’s Elements, originally Euclid’s 5th Postulate, here reclassified and presented as Axiom XII by the editor.
Hyperbolic geometry
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In mathematics, hyperbolic geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
Parallel postulate
…including the parallel postulate and its converse. Non-Euclidean geometries are geometries that do not satisfy the second form of the postulate. A hyperbolic geometry is a geometry that does not satisfy the original postulate. An elliptic geometry is geometry that does not satisfy the converse of the postulate. In…
A collection of crocheted hyperbolic planes, in imitation of a coral reef, by Institute For Figuring
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.
The "hyperbolic soccerball", a paper model which approximates (part of) the hyperbolic plane as a truncated icosahedron approximates the sphere.