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The sign of a real number, also called sgn or signum, is -1 for a negative number (i.e., one with a minus sign "-"), 0 for the number zero, or +1 for a positive number (i.e., ...

Take the Helmholtz differential equation del ^2F+k^2F=0 (1) in spherical coordinates. This is just Laplace's equation in spherical coordinates with an additional term, (2) ...

The Grötzsch graph is smallest triangle-free graph with chromatic number four. It is identical to the Mycielski graph of order four, and is implemented as ...

Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

A ternary diagram is a triangular diagram which displays the proportion of three variables that sum to a constant and which does so using barycentric coordinates. The ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...

An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...

A general type of statistical distribution which is related to the gamma distribution. Beta distributions have two free parameters, which are labeled according to one of two ...