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A "beam detector" for a given curve C is defined as a curve (or set of curves) through which every line tangent to or intersecting C passes. The shortest 1-arc beam detector, ...

A finite geometry is a geometry with a finite number of points. When confined to a plane, all finite geometries are either projective plane geometries (with no parallel ...

A curve also known as the Gerono lemniscate. It is given by Cartesian coordinates x^4=a^2(x^2-y^2), (1) polar coordinates, r^2=a^2sec^4thetacos(2theta), (2) and parametric ...

A semicubical parabola is a curve of the form y=+/-ax^(3/2) (1) (i.e., it is half a cubic, and hence has power 3/2). It has parametric equations x = t^2 (2) y = at^3, (3) and ...

Let f be a real-valued function defined on an interval [a,b] and let x_0 in (a,b). The four one-sided limits D^+f(x_0)=lim sup_(x->x_0+)(f(x)-f(x_0))/(x-x_0), (1) ...

A lune is a plane figure bounded by two circular arcs of unequal radii, i.e., a crescent. (By contrast, a plane figure bounded by two circular arcs of equal radius is known ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

A right triangle whose legs are in the ratio 2:1 is sometimes known as a "dom," a name derived from "half a domino." The name was suggested by Andrew Clarke and preferred in ...

A golden rhombus is a rhombus whose diagonals are in the ratio p/q=phi, where phi is the golden ratio. The faces of the acute golden rhombohedron, Bilinski dodecahedron, ...

Given an original triangle (thick line), find the medial triangle (outer thin line) and its incircle. Take the pedal triangle (inner thin line) of the medial triangle with ...