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A transformation T (a.k.a., map, function) over a domain D takes the elements X in D to elements Y in T(D), where the range (a.k.a., image) of T is defined as ...

Rather surprisingly, trigonometric functions of npi/17 for n an integer can be expressed in terms of sums, products, and finite root extractions because 17 is a Fermat prime. ...

Let s_i be the sum of the products of distinct polynomial roots r_j of the polynomial equation of degree n a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the roots are taken ...

As defined by Gray (1997, p. 201), Viviani's curve, sometimes also called Viviani's window, is the space curve giving the intersection of the cylinder of radius a and center ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

There are many mathematical and recreational problems related to folding. Origami, the Japanese art of paper folding, is one well-known example. It is possible to make a ...

The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value ...

A matchstick graph is a simple graph which has a graph embedding that is planar, for which all distances between vertices have unit distance, and which is non-degenerate (so ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

The regular icosahedron (often simply called "the" icosahedron) is the regular polyhedron and Platonic solid illustrated above having 12 polyhedron vertices, 30 polyhedron ...