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A projective plane in which every line is a translation line is called a Moufang plane.

A polygon whose vertices do not all lie in a plane.

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance ...

Given an arrangement of points, a line containing just two of them is called an ordinary line. Dirac (1951) conjectured that every sufficiently set of n noncollinear points ...

The octahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider an ...

The tetrahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider a ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...