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In a given acute triangle DeltaABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of DeltaABC. The problem was ...

Successive points dividing a golden rectangle into squares lie on a logarithmic spiral (Wells 1991, p. 39; Livio 2002, p. 119) which is sometimes known as the golden spiral. ...

Jung's theorem states that the generalized diameter D of a compact set X in R^n satisfies D>=Rsqrt((2(n+1))/n), where R is the circumradius of X (Danzer et al. 1963). This ...

A surface of revolution defined by Kepler. It consists of less than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

There are at least two distinct notions of linear space throughout mathematics. The term linear space is most commonly used within functional analysis as a synonym of the ...

Möbius tetrahedra, also called Möbius tetrads (Baker 1922, pp. 61-62) are a pair of tetrahedra, each of which has all the vertices lying on the faces of the other: in other ...

The six planes through the midpoints of the edges of a tetrahedron and perpendicular to the opposite edges concur in a point known as the Monge point.

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 ...

If the faces of a convex polyhedron were made of metal plates and the polyhedron edges were replaced by hinges, the polyhedron would be rigid. The theorem was stated by ...

Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...