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It is conjectured that any convex body in n-dimensional Euclidean space has an interior point lying on normals through 2n distinct boundary points (Croft et al. 1991). This ...

A cross section of a solid is a plane figure obtained by the intersection of that solid with a plane. The cross section of an object therefore represents an infinitesimal ...

The term diamond is another word for a rhombus. The term is also used to denote a square tilted at a 45 degrees angle. The diamond shape is a special case of the superellipse ...

A number of points on a line segment. The term was first used by Desargues (Cremona 1960, p. x). If the points A, B, C, ... lie on a line segment with the coordinates of the ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

The set of all lines through a point. The term was first used by Desargues (Cremona 1960, p. x). The six angles of any pencils of four rays O{ABCD} are connected by the ...

A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

A circle packing is called rigid (or "stable") if every circle is fixed by its neighbors, i.e., no circle can be translated without disturbing other circles of the packing ...

A sphericon is the solid formed from a bicone with opening angle of 90 degrees (and therefore with a=r=h) obtained by slicing the solid with a plane containing the rotational ...

A trip-let is a three-dimensional solid that is shaped in such a way that its projections along three mutually perpendicular axes are three different letters of the alphabet. ...