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For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...

The Nagel line is the term proposed for the first time in this work for the line on which the incenter I, triangle centroid G, Spieker center Sp, and Nagel point Na lie. ...

The negative binomial distribution, also known as the Pascal distribution or Pólya distribution, gives the probability of r-1 successes and x failures in x+r-1 trials, and ...

The geodesic on an oblate spheroid can be computed analytically, although the resulting expression is much more unwieldy than for a simple sphere. A spheroid with equatorial ...

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 y-axis ...

A number of attractive polyhedron compounds consisting of three octahedra. The first (left figues) is the polyhedron dual of the cube 3-compound. These compounds will be ...

One of the symbols ( or ) used to denote grouping. Parentheses have a great many specialized meanings in mathematics. A few of these are described below. 1. Parentheses are ...

Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation. (1) The ...

A system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...