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Consider a convex plane curve K with perimeter L, and the set of points P exterior to K. Further, let t_1 and t_2 be the perpendicular distances from P to K (with ...

A number is said to be cubefree if its prime factorization contains no tripled factors. All primes are therefore trivially cubefree. The cubefree numbers are 1, 2, 3, 4, 5, ...

A special case of Stokes' theorem in which F is a vector field and M is an oriented, compact embedded 2-manifold with boundary in R^3, and a generalization of Green's theorem ...

A cyclic pentagon is a not necessarily regular pentagon on whose polygon vertices a circle may be circumscribed. Let such a pentagon have edge lengths a_1, ..., a_5, and area ...

The map projection having transformation equations x = (lambda-lambda_0)cosphi_1 (1) y = phi, (2) and the inverse formulas are phi = y (3) lambda = lambda_0+xsecphi_1, (4) ...

Decimal is the base-10 notational system for representing real numbers. The expression of a number using the decimal system is called its decimal expansion, examples of which ...

Degen's eight-square identity is the incredible polynomial identity (1) found around 1818 by the Danish mathematician Ferdinand Degen (1766-1825). It was subsequently ...

Amazingly, the catacaustic of the deltoid when the rays are parallel in any direction is an astroid. In particular, for a deltoid with parametric equations x = 2cost+cos(2t) ...

The total angular defect is the sum of the angular defects over all polyhedron vertices of a polyhedron, where the angular defect delta at a given polyhedron vertex is the ...

7 7 6 6 3 1; 6 5 4 2 ; 3 3 ; 2 A descending plane partition of order n is a two-dimensional array (possibly empty) of positive integers less than or equal to n such that the ...