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A derived polygon with side ratios chosen as r=1/2 so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle P, the ...

The sum of sets A and B in a vector space, equal to {a+b:a in A,b in B}.

The operation of subtraction, i.e., a minus b. The operation is denoted a-b. The minus sign "-" is also used to denote a negative number, i.e., -x.

∡A_2MA_3=∡A_2A_1A_3+∡P_2P_1P_3, where ∡ is a directed angle.

Spherical triangles into which a sphere is divided by the planes of symmetry of a uniform polyhedron.

(b-c)/a = (sin[1/2(B-C)])/(cos(1/2A)) (1) (c-a)/b = (sin[1/2(C-A)])/(cos(1/2B)) (2) (a-b)/c = (sin[1/2(A-B)])/(cos(1/2C)). (3)

A branch of mathematics which attempts to formalize the nature of the set using a minimal collection of independent axioms. Unfortunately, as discovered by its earliest ...

A natural transformation Phi={Phi_C:F(C)->D(C)} between functors F,G:C->D of categories C and D is said to be a natural isomorphism if each of the components is an ...

where del is the backward difference.

Let N be a nilpotent, connected, simply connected Lie group, and let D be a discrete subgroup of N with compact right quotient space. Then N/D is called a nilmanifold.