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Given a curve C and O=(x_0,y_0) a fixed point called the pedal point, then for a point P on C, draw a line perpendicular to OP. The envelope of these lines as P describes the ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...

A connex is a geometric form introduced by Clebsch (1872) that included as special cases the curve considered as a point locus and the curve considered as a line envelope ...

The path traced out by a point P on the edge of a circle of radius b rolling on the outside of a circle of radius a. An epicycloid is therefore an epitrochoid with h=b. ...

The 2-cusped epicycloid is called a nephroid. The name nephroid means "kidney shaped" and was first used for the two-cusped epicycloid by Proctor in 1878 (MacTutor Archive). ...

Consider a set A_n={a_1,a_2,...,a_n} of n positive integer-denomination postage stamps sorted such that 1=a_1<a_2<...<a_n. Suppose they are to be used on an envelope with ...

A list of five properties of a topological space X expressing how rich the "population" of open sets is. More precisely, each of them tells us how tightly a closed subset can ...

The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the the product of distances from two fixed points (-a,0) ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The one-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the ...

A theory is decidable iff there is an algorithm which can determine whether or not any sentence r is a member of the theory.