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Conic section and Five points determine a conic

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

Difference between Conic section and Five points determine a conic

Conic section vs. Five points determine a conic

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 Euclidean and projective geometry, just as two (distinct) points determine a line (a degree-1 plane curve), five points determine a conic (a degree-2 plane curve).

Similarities between Conic section and Five points determine a conic

Conic section and Five points determine a conic have 14 things in common (in Unionpedia): Apollonian circles, Collinearity, Degenerate conic, Duality (projective geometry), General position, Jakob Steiner, Line (geometry), Line at infinity, Mathematical Association of America, Pappus's hexagon theorem, Pascal's theorem, Projective plane, Synthetic geometry, Two-dimensional space.

Apollonian circles

Apollonian circles are two families of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa.

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Collinearity

In geometry, collinearity of a set of points is the property of their lying on a single line.

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Degenerate conic

In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve.

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Duality (projective geometry)

In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept.

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General position

In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects.

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Jakob Steiner

Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry.

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Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

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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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Mathematical Association of America

The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.

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Pappus's hexagon theorem

In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear, lying on the Pappus line.

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Pascal's theorem

In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (i.e., ellipse, parabola or hyperbola) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet in three points which lie on a straight line, called the Pascal line of the hexagon.

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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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Synthetic geometry

Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.

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Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

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The list above answers the following questions

Conic section and Five points determine a conic Comparison

Conic section has 141 relations, while Five points determine a conic has 34. As they have in common 14, the Jaccard index is 8.00% = 14 / (141 + 34).

References

This article shows the relationship between Conic section and Five points determine a conic. To access each article from which the information was extracted, please visit:

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