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Infinity, most often denoted as infty, is an unbounded quantity that is greater than every real number. The symbol infty had been used as an alternative to M (1000) in Roman ...

Let three similar isosceles triangles DeltaA^'BC, DeltaAB^'C, and DeltaABC^' be constructed on the sides of a triangle DeltaABC. Then DeltaABC and DeltaA^'B^'C^' are ...

Let z be defined as a function of w in terms of a parameter alpha by z=w+alphaphi(z). (1) Then Lagrange's inversion theorem, also called a Lagrange expansion, states that any ...

Minkowski's question mark function is the function y=?(x) defined by Minkowski for the purpose of mapping the quadratic surds in the open interval (0,1) into the rational ...

A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right ...

The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid, a fact first discovered and ...

The one-dimensional wave equation is given by (partial^2psi)/(partialx^2)=1/(v^2)(partial^2psi)/(partialt^2). (1) In order to specify a wave, the equation is subject to ...

An algebraic equation in n variables is an polynomial equation of the form f(x_1,x_2,...,x_n)=sum_(e_1,...,e_n)c_(e_1,e_2,...,e_n)x_1^(e_1)x_2^(e_2)...x_n^(e_n)=0, where the ...

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball. n random tetrahedra can ...

Four or more points P_1, P_2, P_3, P_4, ... which lie on a circle C are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a ...