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An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in K. A nonsingular algebraic curve is an algebraic curve ...

Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n)=n,s^1(n)=s(n),s^2(n)=s(s(n)),... ...

Consider decomposition the factorial n! into multiplicative factors p_k^(b_k) arranged in nondecreasing order. For example, 4! = 3·2^3 (1) = 2·3·4 (2) = 2·2·2·3 (3) and 5! = ...

The Brocard axis is the line KO passing through the symmedian point K and circumcenter O of a triangle, where the segment OK is the Brocard diameter (Kimberling 1998, p. ...

An official chessboard is an 8×8 board containing squares alternating in color between olive green and buff (where "buff" is a color variously defined as a moderate orange ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also ...

Cube duplication, also called the Delian problem, is one of the geometric problems of antiquity which asks, given the length of an edge of a cube, that a second cube be ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

A cylindrical wedge, also called a cylindrical hoof or cylindrical ungula, is a wedge cut from a cylinder by slicing with a plane that intersects the base of the cylinder. ...