Hyperbolic geometry
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In mathematics, hyperbolic geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
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.
Euclidean geometry
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Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a sma
Hyperbolic geometry
…hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate…
Detail from Raphael's The School of Athens featuring a Greek mathematician – perhaps representing Euclid or Archimedes – using a compass to draw a geometric construction.
3D CAD model
PCB of a DVD player
NASA Cassegrain, extremely high gain ~70 dBi.