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A complete metric is a metric in which every Cauchy sequence is convergent. A topological space with a complete metric is called a complete metric space.

A concho-spiral, also known as a conchospiral, is a space curve with parametric equations r = mu^ua (1) theta = u (2) z = mu^uc, (3) where mu, a, and c are fixed parameters. ...

The envelope of refracted rays for a given curve.

A proof based on a dissection which shows the formula for the area of a plane figure or of the volume of a solid. Dozens of different dissection proofs are known for the ...

The Doppler spiral is the curve obtained from an Archimedes' spiral which is translated horizontally with speed k. It has parametric equations x(t) = a(tcost+kt) (1) y(t) = ...

A chord which is a normal at each end. A centrosymmetric set K subset R^d has d double normals through the center (Croft et al. 1991). For a curve of constant width, all ...

A quantity defined for a conic section which can be given in terms of semimajor a and semiminor axes b. interval curve e e=0 circle 0 0<e<1 ellipse sqrt(1-(b^2)/(a^2)) e=1 ...

In two dimensions, the curve known as an "egg' is an oval with one end more pointed than the other.

An ellipsoidal section is the curve formed by the intersection of a plane with an ellipsoid. An ellipsoidal section is always an ellipse.

The epispiral is a plane curve with polar equation r=asec(ntheta). There are n sections if n is odd and 2n if n is even. A slightly more symmetric version considers instead ...