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A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

Consider the family of ellipses (x^2)/(c^2)+(y^2)/((1-c)^2)-1=0 (1) for c in [0,1]. The partial derivative with respect to c is -(2x^2)/(c^3)+(2y^2)/((1-c)^3)=0 (2) ...

In general, a tetrakis hexahedron is a non-regular icositetrahedron that can be constructed as a positive augmentation of a cube. Such a solid is also known as a ...

The Bailey mod 9 identities are a set of three Rogers-Ramanujan-like identities appearing as equations (1.6), (1.8), and (1.7) on p. 422 of Bailey (1947) given by A(q) = ...

The conjecture that there are only finitely many triples of relatively prime integer powers x^p, y^q, z^r for which x^p+y^q=z^r (1) with 1/p+1/q+1/r<1. (2) Darmon and Merel ...

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

The nth cubic number n^3 is a sum of n consecutive odd numbers, for example 1^3 = 1 (1) 2^3 = 3+5 (2) 3^3 = 7+9+11 (3) 4^3 = 13+15+17+19, (4) etc. This identity follows from ...

What space-filling arrangement of similar cells of equal volume has minimal surface area? This questions arises naturally in the theory of foams when the liquid content is ...

A moving average using 15 points having weights -3, -6, -5, 3, 21, 46, 67, 74, 67, 46, 21, 3, -5, -6, and -3. It is sometimes used by actuaries.

The latus rectum of a conic section is the chord through a focus parallel to the conic section directrix (Coxeter 1969). "Latus rectum" is a compound of the Latin latus, ...