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An amazing pandigital approximation to e that is correct to 18457734525360901453873570 decimal digits is given by (1+9^(-4^(7·6)))^(3^(2^(85))), (1) found by R. Sabey in 2004 ...

A Cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension). The condition for three general Cevians from the three ...

Homogeneous barycentric coordinates are barycentric coordinates normalized such that they become the actual areas of the subtriangles. Barycentric coordinates normalized so ...

The point Ko of concurrence in Kosnita theorem, i.e., the point of concurrence of the lines connecting the vertices A, B, and C of a triangle DeltaABC with the circumcenters ...

Whitehead and Russell (1927) devised a hierarchy of "types" in order to eliminate self-referential statements from Principia Mathematica, which purported to derive all of ...

A Proth number that is prime, i.e., a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. Factors of Fermat numbers are of this form as long as they ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

The Fritsch graph is the 9-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

There are several related series that are known as the binomial series. The most general is (x+a)^nu=sum_(k=0)^infty(nu; k)x^ka^(nu-k), (1) where (nu; k) is a binomial ...