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Conic section and Line at infinity

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Conic section and Line at infinity

Conic section vs. Line at infinity

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

Similarities between Conic section and Line at infinity

Conic section and Line at infinity have 11 things in common (in Unionpedia): Circular points at infinity, Curve, Homogeneous coordinates, Hyperbola, Incidence (geometry), Parabola, Parallel (geometry), Plane (geometry), Point at infinity, Projective plane, Real projective plane.

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.

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Curve

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.

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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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Hyperbola

In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

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Incidence (geometry)

In geometry, an incidence relation is a binary relation between different types of objects that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used.

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Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

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Parallel (geometry)

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

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Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

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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 plane

In mathematics, a projective plane is a geometric structure that extends the concept of a plane.

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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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The list above answers the following questions

Conic section and Line at infinity Comparison

Conic section has 141 relations, while Line at infinity has 27. As they have in common 11, the Jaccard index is 6.55% = 11 / (141 + 27).

References

This article shows the relationship between Conic section and Line at infinity. To access each article from which the information was extracted, please visit:

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