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A chamfered dodecahedron, inaccurately called a truncated rhombic triacontahedron or more accurately called a pentatruncated rhombic triacontahedron, is a polyhedron obtained ...

A chamfered octahedron, which could also know known as a tritruncated rhombic dodecahedron, is a polyhedron obtained by chamfering a regular octahedron. The illustration ...

A chamfered tertrahedron, also known as the alternate truncated cube, is a polyhedron obtained by chamfering a regular tetrahedron. The illustration above shows increasing ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

The pedal curve of a unit circle with parametric equation x = cost (1) y = sint (2) with pedal point (x,y) is x_p = cost-ycostsint+xsin^2t (3) y_p = ...

If V and W are Banach spaces and T:V->W is a bounded linear operator, the T is said to be a compact operator if it maps the unit ball of V into a relatively compact subset of ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

An improper use of the symbol sqrt(-1) for the imaginary unit leads to the apparent proof of a false statement. sqrt(-1) = sqrt(-1) (1) sqrt((-1)/1) = sqrt(1/(-1)) (2) ...

Let E be a simply connected compact set in the complex plane. By the Riemann mapping theorem, there is a unique analytic function ...

Consider the distribution of distances l between a point picked at random in the interior of a unit cube and on a face of the cube. The probability function, illustrated ...