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The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

A geodesic on a paraboloid x = sqrt(u)cosv (1) y = sqrt(u)sinv (2) z = u (3) has differential parameters defined by P = ...

The integral kernel in the Poisson integral, given by K(psi)=1/(2pi)(1-|z_0|^2)/(|z_0-e^(ipsi)|^2) (1) for the open unit disk D(0,1). Writing z_0=re^(itheta) and taking ...

A polyomino-like object made by attaching squares joined either at sides or corners. Because neighboring squares can be in relation to one another as kings may move on a ...

A power mean is a mean of the form M_p(a_1,a_2,...,a_n)=(1/nsum_(k=1)^na_k^p)^(1/p), (1) where the parameter p is an affinely extended real number and all a_k>=0. A power ...

The power tower of order k is defined as a^^k=a^(a^(·^(·^(·^a))))_()_(k), (1) where ^ is Knuth up-arrow notation (Knuth 1976), which in turn is defined by ...

A presheaf C of categories consists of the following data: 1. For every local homeomorphism f:Y->X of topological spaces X, Y, a category C(f:Y->X); 2. For every diagram f ...

The previous prime function PP(n) gives the largest prime less than n. The function can be given explicitly as PP(n)=p_(pi(n-1)), where p_i is the ith prime and pi(n) is the ...

A positive proper divisor is a positive divisor of a number n, excluding n itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not. The number ...

The Pythagorean means are the three "classic" means A (the arithmetic mean), G (the geometric mean), and H (the harmonic mean) are sometimes known as the Pythagorean means. ...