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The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. A complete quadrangle is therefore a ...

Let H be a heptagon with seven vertices given in cyclic order inscribed in a conic. Then the Pascal lines of the seven hexagons obtained by omitting each vertex of H in turn ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

The point at which the three lines connecting the vertices of two perspective triangles concur, sometimes also called the perspective center, homology center, or pole. In the ...

A nonuniform rational B-spline curve defined by C(t)=(sum_(i=0)^(n)N_(i,p)(t)w_iP_i)/(sum_(i=0)^(n)N_(i,p)(t)w_i), where p is the order, N_(i,p) are the B-spline basis ...

Families of surfaces which are mutually orthogonal. Up to three families of surfaces may be orthogonal in three dimensions. The simplest example of three orthogonal surfaces ...

The MacBeath circumconic is the dual conic to the MacBeath inconic, introduced in Dec. 2004 by P. Moses (Kimberling). It has circumconic parameters x:y:z=cosA:cosB:cosC, (1) ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

A self-isogonal cubic us a triangle cubic that is invariant under isogonal conjugation. The term is commonly applied to mean a pivotal isogonal cubic, in which points P lying ...