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单词 Hyperoval
释义

Hyperoval

英语百科

Oval (projective plane)

(重定向自Hyperoval)
To the definition of an oval: 
p: exterior (passing) line, 
t: tangent, 
s: secant
projective conic in inhomogeneous coordinates: parabola plus point at infinity of the axis
projective conic in inhomogeneous coordinates: hyperbola plus points at infinity of the asymptotes
A hyperoval (the 4 red points) in the 7 point Fano plane.

In projective geometry an oval is a circle-like pointset (curve) in a plane that is defined by incidence propertes. The standard examples are the nondegenerate conics. However, a conic is only defined in a pappian plane, whereas an oval may exist in any type of projective plane. In the literature, there are many criteria which imply that an oval is a conic, but there are many examples, both infinite and finite, of ovals in pappian planes which are not conics.

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更新时间:2025/6/17 8:08:36