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An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

Regular tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround each polygon vertex are called semiregular ...

Consider the circle map. If K is nonzero, then the motion is periodic in some finite region surrounding each rational Omega. This execution of periodic motion in response to ...

If an integrable quasiperiodic system is slightly perturbed so that it becomes nonintegrable, only a finite number of n-map cycles remain as a result of mode locking. One ...

A polar zonohedron is a convex zonohedron derived from the star which joins opposite vertices of any right n-gonal prism (for n even) or antiprism (for n odd). The faces of ...

The illusion due to psychologist Edward Bradford Titchener that a circle surrounded by other circles will appear smaller if the surrounding circles are enlarged. This effect ...

A curvature such as Gaussian curvature which is detectable to the "inhabitants" of a surface and not just outside observers. An extrinsic curvature, on the other hand, is not ...

A linear functional on a real vector space V is a function T:V->R, which satisfies the following properties. 1. T(v+w)=T(v)+T(w), and 2. T(alphav)=alphaT(v). When V is a ...

If f is a continuous function that satisfies the Lipschitz condition |f(x,t)-f(y,t)|<=L|x-y| (1) in a surrounding of (x_0,t_0) in Omega subset ...

A circle surrounded by a square looks larger than the same circle surrounding a square.