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The "perp dot product" a^_|_·b for a and b vectors in the plane is a modification of the two-dimensional dot product in which a is replaced by the perpendicular vector ...

A knot equivalent to a polygon in R^3, also called a tame knot. For a polygonal knot K, there exists a plane such that the orthogonal projection pi on it satisfies the ...

At each point on a given a two-dimensional surface, there are two "principal" radii of curvature. The larger is denoted R_1, and the smaller R_2. The "principal directions" ...

The rectifiable sets include the image of any Lipschitz function f from planar domains into R^3. The full set is obtained by allowing arbitrary measurable subsets of ...

An algorithm that can always be used to decide whether a given polynomial is free of zeros in the closed unit disk (or, using an entire linear transformation, to any other ...

Let theta be the angle between two vectors. If 0<theta<pi, the vectors are positively oriented. If pi<theta<2pi, the vectors are negatively oriented. Two vectors in the plane ...

A smooth two-dimensional surface given by embedding the projective plane into projective 5-space by the homogeneous parametric equations v(x,y,z)=(x^2,y^2,z^2,xy,xz,yz). The ...

The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b ...

A board covered by a lattice of pegs around which one can span rubber bands to form segments and polygons. It was invented by the Egyptian mathematician and pedagogist Caleb ...

The Gershgorin circle theorem (where "Gershgorin" is sometimes also spelled "Gersgorin" or "Gerschgorin") identifies a region in the complex plane that contains all the ...