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The envelope of the plane lx+my+nz=c, (1) where c is the speed of propagation of a wave in the direction (l,m,n) (i.e., l, m, and n are the direction cosines) is known as the ...

Let three similar isosceles triangles DeltaA^'BC, DeltaAB^'C, and DeltaABC^' be constructed on the sides of a triangle DeltaABC. Then DeltaABC and DeltaA^'B^'C^' are ...

An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance ...

The cornoid is the curve illustrated above given by the parametric equations x = acost(1-2sin^2t) (1) y = asint(1+2cos^2t), (2) where a>0. It is a sextic algebraic curve with ...

The class of curve known as Dürer's conchoid appears in Dürer's work Instruction in Measurement with Compasses and Straight Edge (1525) and arose in investigations of ...

The locus of a point P (or the envelope of a line) fixed in relation to a curve C which slides between fixed curves. For example, if C is a line segment and P a point on the ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the ...

The polynomials defined by B_(i,n)(t)=(n; i)t^i(1-t)^(n-i), (1) where (n; k) is a binomial coefficient. The Bernstein polynomials of degree n form a basis for the power ...

Guilloché patterns are spirograph-like curves that frame a curve within an inner and outer envelope curve. They are used on banknotes, securities, and passports worldwide for ...