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The equation of a line ax+by+c=0 in slope-intercept form is given by y=-a/bx-c/b, (1) so the line has slope -a/b. Now consider the distance from a point (x_0,y_0) to the ...

A polyabolo is an analog of the polyomino composed of n isosceles right triangles joined along edges of the same length. Polyaboloes are sometimes also called polytans ...

A number n is practical if for all k<=n, k is the sum of distinct proper divisors of n. Defined in 1948 by A. K. Srinivasen. All even perfect numbers are practical. The ...

The quadratrix was discovered by Hippias of Elias in 430 BC, and later studied by Dinostratus in 350 BC (MacTutor Archive). It can be used for angle trisection or, more ...

A random closed set (RACS) in R^d is a measurable function from a probability space (Omega,A,P) into (F,Sigma) where F is the collection of all closed subsets of R^d and ...

The regular octagon is the regular polygon with eight sides, as illustrated above. The inradius r, circumradius R, and area A of the regular octagon can be computed directly ...

A surface of constant Gaussian curvature that can be given parametrically by x = a(Ucosu-U^'sinu) (1) y = -a(Usinu+U^'cosu) (2) z = v-aV^', (3) where U = ...

A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length, i.e., an equilateral parallelogram. The word rhomb is sometimes used ...

A rotation group is a group in which the elements are orthogonal matrices with determinant 1. In the case of three-dimensional space, the rotation group is known as the ...

A Saunders graphic is a plot of the dth base-b digits of a function f(x,y) as a function of x and y. The plots above show Saunders graphics for the functions ...