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A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

The path covering number (or path-covering number; Slater 1972) of a graph G, variously denoted as summarized below, is the minimum number of vertex-disjoint paths that cover ...

A perpendicular bisector CD of a line segment AB is a line segment perpendicular to AB and passing through the midpoint M of AB (left figure). The perpendicular bisector of a ...

Suppose that f is an analytic function which is defined in the upper half-disk {|z|^2<1,I[z]>0}. Further suppose that f extends to a continuous function on the real axis, and ...

The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...

The Tschirnhausen cubic is a plane curve given by the polar equation r=asec^3(1/3theta). (1) Letting theta=3tan^(-1)t gives the parametric equations x = a(1-3t^2) (2) y = ...

The volume of a solid body is the amount of "space" it occupies. Volume has units of length cubed (i.e., cm^3, m^3, in^3, etc.) For example, the volume of a box (cuboid) of ...

A symbol consisting of three rational numbers that can be used to describe uniform polyhedra based on how a point C in a spherical triangle can be selected so as to trace the ...

The shortest circular sequence of length sigma^n such that every string of length n on the alphabet a of size sigma occurs as a contiguous subrange of the sequence described ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...