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Also called the ménage problem. In how many ways can n married couples be seated around a circular table in such a manner than there is always one man between two women and ...

The Mertens function is the summary function M(n)=sum_(k=1)^nmu(k), (1) where mu(n) is the Möbius function (Mertens 1897; Havil 2003, p. 208). The first few values are 1, 0, ...

The points of intersection of the adjacent angle trisectors of the angles of any triangle DeltaABC are the polygon vertices of an equilateral triangle DeltaDEF known as the ...

In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the ...

Given a triangle DeltaABC, the triangle DeltaH_AH_BH_C whose vertices are endpoints of the altitudes from each of the vertices of DeltaABC is called the orthic triangle, or ...

The intersection H of the three altitudes AH_A, BH_B, and CH_C of a triangle is called the orthocenter. The name was invented by Besant and Ferrers in 1865 while walking on a ...

Starting with the circle P_1 tangent to the three semicircles forming the arbelos, construct a chain of tangent circles P_i, all tangent to one of the two small interior ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

A knot is called prime if, for any decomposition as a connected sum, one of the factors is unknotted (Livingston 1993, pp. 5 and 78). A knot which is not prime is called a ...

The branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called "higher ...