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A hyperstring is a simple semi-Hamiltonian acyclic digraph (V,E) with a labeling of the edges in E such that, for all vertices i,j,p,q in V, either pi(i,j)=pi(p,q) or pi(i,j) ...

A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is ...

For x(0)=a, x = a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)] (1) y = a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)]. (2) If a/b=n, then x = 1/(n-2)[(n-1)cosphi-cos[(n-1)phi]a (3) y = ...

The hypocycloid x = a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)] (1) y = a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)] (2) has involute x = (a-2b)/a[(a-b)cosphi+bcos((a-b)/bphi)] (3) y = ...

The pedal curve for an n-cusped hypocycloid x = a((n-1)cost+cos[(n-1)t])/n (1) y = a((n-1)sint-sin[(n-1)t])/n (2) with pedal point at the origin is the curve x_p = ...

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m<2. If n/m>2, the curve is a hyperellipse.

The evolute of a hypotrochoid is a complicated equation. Examples are illustrated above.

The term "ice fractal" refers to a fractal (square, triangle, etc.) that is based on a simple generating motif. The above plots show the ice triangle, antitriangle, square, ...

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 ...