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A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

The trigonometric formulas for pi/5 can be derived using the multiple-angle formula sin(5theta)=5sintheta-20sin^3theta+16sin^5theta. (1) Letting theta=pi/5 and x=sintheta ...

Over a small neighborhood U of a manifold, a vector bundle is spanned by the local sections defined on U. For example, in a coordinate chart U with coordinates (x_1,...,x_n), ...

A Trott constant is a real number whose decimal digits are equal to the terms of its continued fraction. The first Trott constant (OEIS A039662) was discovered by M. Trott in ...

Let G(V,E) be a graph with graph vertices V and graph edges E on n graph vertices without a (k+1)-clique. Then t(n,k)<=((k-1)n^2)/(2k), where t(n,k) is the edge count. (Note ...

The Weibull distribution is given by P(x) = alphabeta^(-alpha)x^(alpha-1)e^(-(x/beta)^alpha) (1) D(x) = 1-e^(-(x/beta)^alpha) (2) for x in [0,infty), and is implemented in ...

Let B_n(r) be the n-dimensional closed ball of radius r>1 centered at the origin. A function which is defined on B(r) is called an extension to B(r) of a function f defined ...

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is ...

A diagram lemma which states that every short exact sequence of chain complexes and chain homomorphisms 0-->C-->^phiD-->^psiE-->0 gives rise to a long exact sequence in ...

The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...