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The smallest number of times u(K) a knot K must be passed through itself to untie it. Lower bounds can be computed using relatively straightforward techniques, but it is in ...

The Barth sextic is a sextic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 65. The surface was ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

A class formed by sets in R^n which have essentially the same structure, regardless of size, shape and dimension. The "essential structure" is what a set keeps when it is ...

Noncommutative topology is a recent program having important and deep applications in several branches of mathematics and mathematical physics. Because every commutative ...

A space-filling function which maps a one-dimensional interval into a two-dimensional area. Plane-filling functions were thought to be impossible until Hilbert discovered the ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

The Abel equation of the first kind is given by y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3+... (Murphy 1960, p. 23; Zwillinger 1997, p. 120), and the Abel equation of the second ...

An acnode, also called an isolated point or hermit point, of a curve is a point that satisfies the equation of the curve but has no neighboring points that also lie on the ...

An ordinary differential equation of the form x^my^'=f(x,y), where m is a positive integer, f is analytic at x=y=0, f(0,0)=0, and f_y^'(0,0)!=0. Zwillinger (1997, p. 120), ...