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An s-route of a graph G is a sequence of vertices (v_0,v_1,...,v_s) of G such that v_iv_(i+1) in E(G) for i=0, 1, ..., s-1 (where E(G) is the edge set of G) and ...

257 is a Fermat prime, and the 257-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. An illustration of the 257-gon is not included ...

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 ...

An amphichiral knot is a knot that is capable of being continuously deformed into its own mirror image. More formally, a knot K is amphichiral (also called achiral or ...

Bertelsen's number is an erroneous name erroneously given to the erroneous value of pi(10^9)=50847478, where pi(x) is the prime counting function. This value is 56 lower than ...

A catenary of revolution. The catenoid and plane are the only surfaces of revolution which are also minimal surfaces. The catenoid can be given by the parametric equations x ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

There are two theorems commonly known as Feuerbach's theorem. The first states that circle which passes through the feet of the perpendiculars dropped from the polygon ...

The Frucht graph is smallest cubic identity graph (Skiena 1990, p. 185). It is implemented in the Wolfram Language as GraphData["FruchtGraph"]. It has 12 vertices and 18 ...