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The Cantor diagonal method, also called the Cantor diagonal argument or Cantor's diagonal slash, is a clever technique used by Georg Cantor to show that the integers and ...

Let {a_i}_(i=1)^n be a set of positive numbers. Then sum_(i=1)^n(a_1a_2...a_i)^(1/i)<=esum_(i=1)^na_i (which is given incorrectly in Gradshteyn and Ryzhik 2000). Here, the ...

The dual polyhedra of the Archimedean solids, given in the following table. They are known as Catalan solids in honor of the Belgian mathematician who first published them in ...

Catastrophe theory studies how the qualitative nature of equation solutions depends on the parameters that appear in the equations. Subspecializations include bifurcation ...

Let f(x,y)=u(x,y)+iv(x,y), (1) where z=x+iy, (2) so dz=dx+idy. (3) The total derivative of f with respect to z is then (df)/(dz) = ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object, for example ...

(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+alpha^2y=0 (1) for |x|<1. The Chebyshev differential equation has regular singular points at -1, 1, and infty. It can be solved by series ...

The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi ...

A series is said to be conditionally convergent iff it is convergent, the series of its positive terms diverges to positive infinity, and the series of its negative terms ...