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Several prizes are awarded periodically for outstanding mathematical achievement. There is no Nobel Prize in mathematics, and the most prestigious mathematical award is known ...

Martin Gardner (1975) played an April Fool's joke by asserting that the map of 110 regions illustrated above (left figure) required five colors and constitutes a ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method (MINRES) and ...

The modified bessel function of the second kind is the function K_n(x) which is one of the solutions to the modified Bessel differential equation. The modified Bessel ...

The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

In the technical combinatorial sense, an a-ary necklace of length n is a string of n characters, each of a possible types. Rotation is ignored, in the sense that b_1b_2...b_n ...

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 ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

Circumscribe a triangle about a circle, another circle around the triangle, a square outside the circle, another circle outside the square, and so on. The circumradius and ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...