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A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the x-axis, ...

Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

A d-repdigit is a number composed of repetition of a single digit (in a given base, generally taken as base 10 unless otherwise specified). For example, the beast number 666 ...

Consider the sequence defined by w_1=01 and w_(n+1)=w_nw_nw_n^R, where l^R denotes the reverse of a sequence l. The first few terms are then 01, 010110, 010110010110011010, ...

A rolling polyhedron graph is a graph obtained by rolling a polyhedral solid along a board whose tiles match up with the faces of the polyhedron being rolled. The vertices of ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

A ruled surface is a surface that can be swept out by moving a line in space. It therefore has a parameterization of the form x(u,v)=b(u)+vdelta(u), (1) where b is called the ...

Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. ...

A solitary number is a number which does not have any friends. Solitary numbers include all primes, prime powers, and numbers for which (n,sigma(n))=1, where (a,b) is the ...

Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...