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The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...

A sphericon is the solid formed from a bicone with opening angle of 90 degrees (and therefore with a=r=h) obtained by slicing the solid with a plane containing the rotational ...

The square knot, also called the reef knot, is a composite knot of six crossings consisting of a knot sum of a trefoil knot and its mirror image (Rolfsen 1976, p. 220). The ...

A flexagon made with square faces. Gardner (1961) shows how to construct a tri-tetraflexagon, tetra-tetraflexagon, and hexa-tetraflexagon.

In general, a tetrahedron is a polyhedron with four sides. If all faces are congruent, the tetrahedron is known as an isosceles tetrahedron. If all faces are congruent to an ...

The third Morley triangle is made by rotating line BC toward vertex A about vertex B by angle (B+4pi)/3. It is an equilateral triangle. It has trilinear vertex matrix [1 ...

The Thomson cubic Z(X_2) of a triangle DeltaABC is the locus the centers of circumconics whose normals at the vertices are concurrent. It is a self-isogonal cubic with pivot ...

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 torus with a hole that can eat another torus. The transformation is continuous, and so can be achieved by stretching only without tearing or making new holes in the tori.

A transformation of a polynomial equation f(x)=0 which is of the form y=g(x)/h(x) where g and h are polynomials and h(x) does not vanish at a root of f(x)=0. The cubic ...