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A fallacy is an incorrect result arrived at by apparently correct, though actually specious reasoning. The great Greek geometer Euclid wrote an entire book on geometric ...

Euler (1738, 1753) considered the series s_a(x)=sum_(n=1)^infty[1/(1-a^n)product_(k=0)^(n-1)(1-xa^(-k))]. He showed that just like log_a(a^n)=n, s_a(a^n)=n for nonnegative ...

Fano's geometry is a finite geometry attributed to Fano from around the year 1892. This geometry comes with five axioms, namely: 1. There exists at least one line. 2. Every ...

The far-out point F of a triangle DeltaABC is the inverse point of the triangle centroid with respect to the circumcircle of DeltaABC. For a triangle with side lengths a, b, ...

For a general second-order linear recurrence equation f_(n+1)=xf_n+yf_(n-1), (1) define a multiplication rule on ordered pairs by (A,B)(C,D)=(AD+BC+xAC,BD+yAC). (2) The ...

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).

Given a sequence of independent random variates X_1, X_2, ..., if sigma_k^2=var(X_k) and rho_n^2=max_(k<=n)((sigma_k^2)/(s_n^2)), then lim_(n->infty)rho_n^2=0. This means ...

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 ...

A self-avoiding polygon containing three corners of its minimal bounding rectangle. The anisotropic area and perimeter generating function G(x,y) and partial generating ...

A circumconic hyperbola, which therefore passes through the orthocenter, is a rectangular hyperbola, and has center on the nine-point circle. Its circumconic parameters are ...