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The sum over all external (square) nodes of the lengths of the paths from the root of an extended binary tree to each node. For example, in the tree above, the external path ...

If a function f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and a minimum on [a,b]. If f(x) has an extremum on an open interval (a,b), then the ...

The determination of a set of factors (divisors) of a given integer ("prime factorization"), polynomial ("polynomial factorization"), etc., which, when multiplied together, ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...

An efficient version of the Walsh transform that requires O(nlnn) operations instead of the n^2 required for a direct Walsh transform (Wolfram 2002, p. 1072).

The Fermat axis is the central line connecting the first and second Fermat points. It has line function l=a(b^2-c^2)(a^2-b^2-bc-c^2)(a^2-b^2+bc-c^2), corresponding to ...

There are so many theorems due to Fermat that the term "Fermat's theorem" is best avoided unless augmented by a description of which theorem of Fermat is under discussion. ...

The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles (Kimberling 1998, p. 158). (The fact that the ...

A place nu of a number field k is an isomorphism class of field maps k onto a dense subfield of a nondiscrete locally compact field k_nu. In the function field case, let F be ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...