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In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a ...

Let lambda_1, ..., lambda_n in C be linearly independent over the rationals Q, then Q(lambda_1,...,lambda_n,e^(lambda_1),...,e^(lambda_n)) has transcendence degree at least n ...

The concurrence S of the Euler lines E_n of the triangles DeltaXBC, DeltaXCA, DeltaXAB, and DeltaABC where X is the incenter. It has equivalent triangle center functions ...

A conformal mapping from the upper half-plane to a polygon.

One of the beautiful arrangements of circles found at the Temple of Osiris at Abydos, Egypt (Rawles 1997). The pattern also appears in Italian art from the 13th century ...

A lattice polygon consisting of a closed self-avoiding walk on a square lattice. The perimeter, horizontal perimeter, vertical perimeter, and area are all well-defined for ...

The sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... (OEIS A002024) consisting of 1 copy of 1, 2 copies of 2, 3 copies of 3, and so on. Surprisingly, there exist simple formulas ...

The general sextic equation x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in ...

The silver constant is the algebraic number given by S = (x^3-5x^2+6x-1)_3 (1) = 2+2cos(2/7pi) (2) = 3.246979603... (3) (OEIS A116425), where (P(x))_n denotes a polynomial ...

A simple polyhedron, also called a simplicial polyhedron, is a polyhedron that is topologically equivalent to a sphere (i.e., if it were inflated, it would produce a sphere) ...