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The centroid is center of mass of a two-dimensional planar lamina or a three-dimensional solid. The mass of a lamina with surface density function sigma(x,y) is ...

The decimal expansion of the Glaisher-Kinkelin constant is given by A=1.28242712... (OEIS A074962). A was computed to 5×10^5 decimal digits by E. Weisstein (Dec. 3, 2015). ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

Turing machines are defined by sets of rules that operate on four parameters: (state, tape cell color, operation, state). Let the states and tape cell colors be numbered and ...

Let A(n) denote the number of partitions of n into parts =2,5,11 (mod 12), let B(n) denote the number of partitions of n into distinct parts =2,4,5 (mod 6), and let C(n) ...

Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

Given a triangle DeltaABC and the excentral triangle DeltaJ_AJ_BJ_C, define the A^'-vertex of the hexyl triangle as the point in which the perpendicular to AB through the ...

p^x is an infinitary divisor of p^y (with y>0) if p^x|_(y-1)p^y, where d|_kn denotes a k-ary Divisor (Guy 1994, p. 54). Infinitary divisors therefore generalize the concept ...

Let omega_1 and omega_2 be periods of a doubly periodic function, with tau=omega_2/omega_1 the half-period ratio a number with I[tau]!=0. Then Klein's absolute invariant ...