Conic section
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A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circl
This diagram clarifies the different angles of the cutting planes that result in the different properties of the three types of conic section.
Types of conic sections: 1: Circle 2: Ellipse 3: Parabola 4: Hyperbola
Diagram from Apollonius' Conics, in a 9th-century Arabic translation
Table of conics, Cyclopaedia, 1728
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.