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Draw the perpendicular line from the intersection of the two small semicircles in the arbelos. The two circles C_1 and C_2 tangent to this line, the large semicircle, and ...

A basis vector in an n-dimensional vector space is one of any chosen set of n vectors in the space forming a vector basis, i.e., having the property that every vector in the ...

A cubic lattice is a lattice whose points lie at positions (x,y,z) in the Cartesian three-space, where x, y, and z are integers. The term is also used to refer to a regular ...

The polyhedron compound consisting of the cuboctahedron and its dual, the rhombic dodecahedron, illustrated in the left figure above. The right figure shows the solid common ...

One of the eight convex deltahedra built up from 16 equilateral triangles. It consists of two oppositely faced square pyramids rotated 45 degrees to each other and separated ...

The Heilbronn triangle problem is to place n>=3 points in a disk (square, equilateral triangle, etc.) of unit area so as to maximize the area Delta(n) of the smallest of the ...

A 20-sided polygon. The regular icosagon is a constructible polygon, and the regular icosagon of unit side length has inradius r, circumradius R, and area A given by r = ...

The polyhedron compound of the icosidodecahedron and its dual, the rhombic triacontahedron. The compound can be constructed from an icosidodecahedron of unit edge length by ...

The winding number W(theta) of a map f(theta) with initial value theta is defined by W(theta)=lim_(n->infty)(f^n(theta)-theta)/n, which represents the average increase in the ...

The metabidiminished icosahedron is a convex equilateral solid that is Johnson solid J_(62). The unit metabidiminished icosahedron has volume V=1/6(5+2sqrt(5)) (1) and Dehn ...