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Regulus (geometry)

Index Regulus (geometry)

In three-dimensional space, a regulus R is a set of skew lines, every point of which is on a transversal which intersects an element of R only once, and such that every point on a transversal lies on a line of R The set of transversals of R forms an opposite regulus S. In ℝ3 the union R ∪ S is the ruled surface of a hyperboloid of one sheet. [1]

17 relations: Albrecht Beutelspacher, Brianchon's theorem, Bulletin of the American Mathematical Society, Cambridge University Press, Charlotte Scott, Finite geometry, Harold Scott MacDonald Coxeter, Henry Forder, Hyperboloid, John Wiley & Sons, Pascal's theorem, Proceedings of the Royal Society, Ruled surface, Skew lines, Transversal (combinatorics), Transversal (geometry), William Edge (mathematician).

Albrecht Beutelspacher

Albrecht Beutelspacher (born 5 June 1950) is a German mathematician.

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Brianchon's theorem

In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point.

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Bulletin of the American Mathematical Society

The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Charlotte Scott

Charlotte Angas Scott (8 June 1858, Lincoln, England – 10 November 1931, Cambridge, England) was a British mathematician who made her career in the United States and was influential in the development of American mathematics, including the mathematical education of women.

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Finite geometry

A finite geometry is any geometric system that has only a finite number of points.

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Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

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Henry Forder

Henry George Forder (27 September 1889 – 21 September 1981) was a New Zealand mathematician.

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Hyperboloid

In geometry, a hyperboloid of revolution, sometimes called circular hyperboloid, is a surface that may be generated by rotating a hyperbola around one of its principal axes.

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John Wiley & Sons

John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.

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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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Proceedings of the Royal Society

Proceedings of the Royal Society is the parent title of two scientific journals published by the Royal Society.

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Ruled surface

In geometry, a surface S is ruled (also called a scroll) if through every point of S there is a straight line that lies on S. Examples include the plane, the curved surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space.

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Skew lines

In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel.

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Transversal (combinatorics)

In mathematics, given a family of sets, here called a collection C, a transversal (also called a cross-section) is a set containing exactly one element from each member of the collection.

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Transversal (geometry)

In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points.

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William Edge (mathematician)

Prof William Leonard Edge FRSE (8 November 1904 – 27 September 1997) was a British mathematician most known for his work in finite geometry.

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References

[1] https://en.wikipedia.org/wiki/Regulus_(geometry)

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