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There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane ax+by+cz+d=0 (1) by defining the ...

The largest area of intersection of a solid body by a plane parallel to a given plane, also called the "HA measurement."

A bijective map between two metric spaces that preserves distances, i.e., d(f(x),f(y))=d(x,y), where f is the map and d(a,b) is the distance function. Isometries are ...

A level set in two dimensions. Phase curves are sometimes also known as level curves (Tabor 1989, p. 14).

A fractal curve, also called the C-curve (Gosper 1972). The base curve and motif are illustrated below. Duvall and Keesling (1999) proved that the Hausdorff dimension of the ...

A nonnegative function g(x,y) describing the "distance" between neighboring points for a given set. A metric satisfies the triangle inequality g(x,y)+g(y,z)>=g(x,z) (1) and ...

The unknotting number for a torus knot (p,q) is (p-1)(q-1)/2. This 40-year-old conjecture was proved (Adams 1994) by Kronheimer and Mrowka (1993, 1995).

The point of concurrence of the six planes in Monge's tetrahedron theorem.

The six planes through the midpoints of the edges of a tetrahedron and perpendicular to the opposite edges concur in a point known as the Monge point.