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A map u:M->N, between two compact Riemannian manifolds, is a harmonic map if it is a critical point for the energy functional int_M|du|^2dmu_M. The norm of the differential ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler, states "at least it seems that every number ...

A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., to an n-gon for n an arbitrary positive integer. The above diagrams ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...

The line on which the orthocenter H, triangle centroid G, circumcenter O, de Longchamps point L, nine-point center N, and a number of other important triangle centers lie. ...

The Lucas numbers are the sequence of integers {L_n}_(n=1)^infty defined by the linear recurrence equation L_n=L_(n-1)+L_(n-2) (1) with L_1=1 and L_2=3. The nth Lucas number ...

The Möbius function is a number theoretic function defined by mu(n)={0 if n has one or more repeated prime factors; 1 if n=1; (-1)^k if n is a product of k distinct primes, ...

The Möbius strip, also called the twisted cylinder (Henle 1994, p. 110), is a one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving ...