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A measure lambda is absolutely continuous with respect to another measure mu if lambda(E)=0 for every set with mu(E)=0. This makes sense as long as mu is a positive measure, ...

The ampersand curve is the name given by Cundy and Rowlett (1989, p. 72) to the quartic curve with implicit equation (y^2-x^2)(x-1)(2x-3)=4(x^2+y^2-2x)^2. (1) Although it is ...

The anticomplement of a point P in a reference triangle DeltaABC is a point P^' satisfying the vector equation P^'G^->=2GP^->, (1) where G is the triangle centroid of ...

Given a regular surface M, an asymptotic curve is formally defined as a curve x(t) on M such that the normal curvature is 0 in the direction x^'(t) for all t in the domain of ...

The Brocard inellipse is the inconic with parameters x:y:z=1/a:1/b:1/c, (1) giving the trilinear equation ...

Two geometric figures are said to be concentric if their centers coincide. The region between two concentric circles is called an annulus. The following table summarizes some ...

The pedal curve of an epicycloid x = (a+b)cost-b[((a+b)t)/b] (1) y = (a+b)sint-bsin[((a+b)t)/b] (2) with pedal point at the origin is x_p = 1/2(a+2b){cost-cos[((a+b)t)/b]} ...

Let a chord of constant length be slid around a smooth, closed, convex curve C, and choose a point on the chord which divides it into segments of lengths p and q. This point ...

The sphere with respect to which inverse points are computed (i.e., with respect to which geometrical inversion is performed). For example, the cyclides are inversions in a ...

The geometry resulting from the application of the inversion operation. It can be especially powerful for solving apparently difficult problems such as Steiner's porism and ...