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Conic section and Pappus's hexagon theorem

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

Difference between Conic section and Pappus's hexagon theorem

Conic section vs. Pappus's hexagon theorem

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 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.

Similarities between Conic section and Pappus's hexagon theorem

Conic section and Pappus's hexagon theorem have 8 things in common (in Unionpedia): Collinearity, Degenerate conic, Duality (projective geometry), Euclid, Line (geometry), Pappus of Alexandria, Pascal's theorem, Projective plane.

Collinearity

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

Collinearity and Conic section · Collinearity and Pappus's hexagon theorem · See more »

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.

Conic section and Degenerate conic · Degenerate conic and Pappus's hexagon theorem · See more »

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.

Conic section and Duality (projective geometry) · Duality (projective geometry) and Pappus's hexagon theorem · See more »

Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of 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.

Conic section and Line (geometry) · Line (geometry) and Pappus's hexagon theorem · See more »

Pappus of Alexandria

Pappus of Alexandria (Πάππος ὁ Ἀλεξανδρεύς; c. 290 – c. 350 AD) was one of the last great Greek mathematicians of Antiquity, known for his Synagoge (Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry.

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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.

Conic section and Pascal's theorem · Pappus's hexagon theorem and Pascal's theorem · See more »

Projective plane

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

Conic section and Projective plane · Pappus's hexagon theorem and Projective plane · See more »

The list above answers the following questions

Conic section and Pappus's hexagon theorem Comparison

Conic section has 141 relations, while Pappus's hexagon theorem has 28. As they have in common 8, the Jaccard index is 4.73% = 8 / (141 + 28).

References

This article shows the relationship between Conic section and Pappus's hexagon theorem. To access each article from which the information was extracted, please visit:

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