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There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...

The points of tangency of the Lucas inner circle with the Lucas circles are the inverses of the vertices A, B, and C in the Lucas circles radical circle. These form the Lucas ...

A Lucas polynomial sequence is a pair of generalized polynomials which generalize the Lucas sequence to polynomials is given by W_n^k(x) = ...

The Lucas tangents triangle (a term coined here for the first time) is the triangle DeltaT_AT_BT_C formed by the pairwise tangents of the Lucas circles of a given reference ...

A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions. For an abstract algebraic curve, if x and y are nonconstant ...

MANOVA ("multiple analysis of variance") is a procedure for testing the equality of mean vectors of more than two populations. The technique is analogous to ANOVA for ...

The M'Cay cubic Z(X_3) is a self-isogonal cubic given by the locus of all points whose pedal circle touches the nine-point circle, or equivalently, the locus of all points P ...

where Gamma(z) is the gamma function and other details are discussed by Gradshteyn and Ryzhik (2000).

A macron is a bar placed over a single symbol or character, such as x^_. The symbol z^_ is sometimes used to denote the following operations: 1. The complex conjugate z^_. 2. ...

If one looks inside a flat origami without unfolding it, one sees a zigzagged profile, determined by an alternation of "mountain-creases" and "valley-creases." The numbers of ...