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A curve of order n is generally determined by n(n+3)/2 points. So a conic section is determined by five points and a cubic curve should require nine. But the Maclaurin-Bézout ...

The 60 Pascal lines of a hexagon inscribed in a conic section intersect three at a time through 20 Steiner points. There is a dual relationship between the 15 Plücker lines ...

A RAT-free ("right angle triangle-free") set is a set of points, no three of which determine a right triangle. Let f(n) be the largest integer such that a RAT-free subset of ...

A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

The desmic configuration is three-dimensional configuration of points consisting of three tetrads of points, each two of the tetrads of which are perspective from the four ...

The symbol ∡ABC denotes the directed angle from AB to BC, which is the signed angle through which AB must be rotated about B to coincide with BC. Four points ABCD lie on a ...

On the Clebsch diagonal cubic, all 27 of the complex lines present on a general smooth cubic surface are real. In addition, there are 10 points on the surface where three of ...

An arrangement of points with no three collinear, or of lines with no three concurrent.

The happy end problem, also called the "happy ending problem," is the problem of determining for n>=3 the smallest number of points g(n) in general position in the plane ...

Three concurrent homologous lines pass respectively through three fixed points on the similitude circle which are known as the invariable points.