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Also known as the alternating series test. Given a series sum_(n=1)^infty(-1)^(n+1)a_n with a_n>0, if a_n is monotonic decreasing as n->infty and lim_(n->infty)a_n=0, then ...

A product of a reflection in a line and translation along the same line.

A number is said to be biquadratefree (or quarticfree) if its prime factorization contains no quadrupled factors. All primes and prime powers p^n with n<=3 are therefore ...

A number is said to be cubefree if its prime factorization contains no tripled factors. All primes are therefore trivially cubefree. The cubefree numbers are 1, 2, 3, 4, 5, ...

When all the points P on one line are related by an isometry to all points P^' on another, the midpoints of the segments PP^' are either distinct and collinear or coincident.

The Griewank function is a function widely used to test the convergence of optimization functions. The Griewank function of order n is defined by ...

The use of permil (a.k.a. parts per thousand) is a way of expressing ratios in terms of whole numbers. Given a ratio or fraction, it is converted to a permil-age by ...

The use of permil (a.k.a. parts per thousand) is a way of expressing ratios in terms of whole numbers. Given a ratio or fraction, it is converted to a permil-age by ...

A point of a function or surface which is a stationary point but not an extremum. An example of a one-dimensional function with a saddle point is f(x)=x^3, which has f^'(x) = ...

The classic treatise in geometry written by Euclid and used as a textbook for more than 1000 years in western Europe. An Arabic version The Elements appears at the end of the ...