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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]

22 relations: Algebraic curve, Angle, Circle, Circular algebraic curve, Complex number, Complex projective plane, Complexification, Cross-ratio, Duncan Sommerville, Fixed point (mathematics), Homogeneous coordinates, Isotropic line, Natural logarithm, Point at infinity, Projective geometry, Real number, Real projective plane, Rotation, System of linear equations, Translation, University of Michigan, W. H. Freeman and Company.

Algebraic curve

In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.

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Angle

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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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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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Complex projective plane

In mathematics, the complex projective plane, usually denoted P2(C), is the two-dimensional complex projective space.

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Complexification

In mathematics, the complexification of a vector space V over the field of real numbers (a "real vector space") yields a vector space VC over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers.

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Cross-ratio

In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line.

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Duncan Sommerville

Duncan MacLaren Young Sommerville (1879–1934) was a Scottish mathematician and astronomer.

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Fixed point (mathematics)

In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.

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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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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

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Point at infinity

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

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Projective geometry

Projective geometry is a topic in mathematics.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Real projective plane

In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.

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Rotation

A rotation is a circular movement of an object around a center (or point) of rotation.

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System of linear equations

In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.

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Translation

Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text.

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University of Michigan

The University of Michigan (UM, U-M, U of M, or UMich), often simply referred to as Michigan, is a public research university in Ann Arbor, Michigan.

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W. H. Freeman and Company

W.

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Redirects here:

Cyclic points.

References

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

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