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An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

The "witch of Agnesi" is a curve studied by Maria Agnesi in 1748 in her book Instituzioni analitiche ad uso della gioventù italiana (the first surviving mathematical work ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

A repunit prime is a repunit (i.e., a number consisting of copies of the single digit 1) that is also a prime number. The base-10 repunit (possibly probable) primes ...

A highly structured geometric object used to study groups which act upon them.

The set of roots of a polynomial f(x,y,z)=0. An algebraic surface is said to be of degree n=max(i+j+k), where n is the maximum sum of powers of all terms ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

A B-spline is a generalization of the Bézier curve. Let a vector known as the knot vector be defined T={t_0,t_1,...,t_m}, (1) where T is a nondecreasing sequence with t_i in ...

Lockwood (1957) terms the ellipse negative pedal curve with pedal point at the focus "Burleigh's oval" in honor of his student M. J. Burleigh, who first drew his attention to ...