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A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...

The Nevanlinna Prize is awarded by the International Mathematical Union to outstanding contributors to the mathematical aspects of information science. The International ...

The nine-point center N (sometimes instead denoted F) is the center of the nine-point circle. It has equivalent triangle center functions alpha_5 = cos(B-C) (1) alpha_5 = ...

Given a positive integer m>1, let its prime factorization be written m=p_1^(a_1)p_2^(a_2)p_3^(a_3)...p_k^(a_k). (1) Define the functions h(n) and H(n) by h(1)=1, H(1)=1, and ...

A noncayley graph is a graph which is not a Cayley graph. All graphs that are not vertex-transitive are noncayley graphs. However, some vertex-transitive graph are noncayley. ...

An extremely fast factorization method developed by Pollard which was used to factor the RSA-130 number. This method is the most powerful known for factoring general numbers, ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

Orthogonal circles are orthogonal curves, i.e., they cut one another at right angles. By the Pythagorean theorem, two circles of radii r_1 and r_2 whose centers are a ...

If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square ...

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a ...