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Circular points at infinity

Index Circular points at infinity

In projective geometry, the circular points at infinity (also called cyclic points or isotropic points) are two special points at infinity in the complex projective plane that are contained in the complexification of every real circle. [1]

9 relations: Cassini oval, Circle, Circular algebraic curve, Conic section, Focus (geometry), Homogeneous coordinates, Isotropic line, Jean-Victor Poncelet, Line at infinity.

Cassini oval

A Cassini oval is a quartic plane curve defined as the set (or locus) of points in the plane such that the product of the distances to two fixed points is constant.

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Circle

A circle is a simple closed shape.

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Circular algebraic curve

In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y).

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Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Focus (geometry)

In geometry, focuses or foci, singular focus, are special points with reference to which any of a variety of curves is constructed.

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Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.

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Isotropic line

In the geometry of quadratic forms, an isotropic line or null line is a line for which the quadratic form applied to the displacement vector between any pair of its points is zero.

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Jean-Victor Poncelet

Jean-Victor Poncelet (1 July 1788 – 22 December 1867) was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique.

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Line at infinity

In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane.

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Redirects here:

Cyclic points.

References

[1] https://en.wikipedia.org/wiki/Circular_points_at_infinity

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