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A (finite, circular) conical surface is a ruled surface created by fixing one end of a line segment at a point (known as the vertex or apex of the cone) and sweeping the ...

The self-intersection of a one-sided surface. The word "cross-cap" is sometimes also written without the hyphen as the single word "crosscap." The cross-cap can be thought of ...

The term "cylinder" has a number of related meanings. In its most general usage, the word "cylinder" refers to a solid bounded by a closed generalized cylinder (a.k.a. ...

The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by (x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1, (1) where ...

In finding the average area A^__R of a triangle chosen from a closed, bounded, convex region R of the plane, then A^__(T(R))=A^__R, for T any nonsingular affine ...

The first Strehl identity is the binomial sum identity sum_(k=0)^n(n; k)^3=sum_(k=0)^n(n; k)^2(2k; n), (Strehl 1993, 1994; Koepf 1998, p. 55), which are the so-called Franel ...

Two distinct theorems are referred to as "the de Bruijn-Erdős theorem." One of them (de Bruijn and Erdős 1951) concerns the chromatic number of infinite graphs; the other (de ...

A composite number n is a positive integer n>1 which is not prime (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes called ...

As proved by Sierpiński (1960), there exist infinitely many positive odd numbers k such that k·2^n+1 is composite for every n>=1. Numbers k with this property are called ...

Hardy and Littlewood (1914) proved that the sequence {frac(x^n)}, where frac(x) is the fractional part, is equidistributed for almost all real numbers x>1 (i.e., the ...