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The Euler triangle of a triangle DeltaABC is the triangle DeltaE_AE_BE_C whose vertices are the midpoints of the segments joining the orthocenter H with the respective ...

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 ...

The conjecture that there are only finitely many triples of relatively prime integer powers x^p, y^q, z^r for which x^p+y^q=z^r (1) with 1/p+1/q+1/r<1. (2) Darmon and Merel ...

Given triangle DeltaA_1A_2A_3, let the point of intersection of A_2Omega and A_3Omega^' be B_1, where Omega and Omega^' are the Brocard points, and similarly define B_2 and ...

Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...

Let G be a finite graph and v a vertex of G. The stabilizer of v, stab(v), is the set of group elements {g in Aut(G)|g(v)=v}, where Aut(g) is the graph automorphism group. ...

Let C^*(u) denote the number of nowhere-zero u-flows on a connected graph G with vertex count n, edge count m, and connected component count c. This quantity is called the ...

A graph is a forbidden minor if its presence as a graph minor of a given graph means it is not a member of some family of graphs. More generally, there may be a family of ...

Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional ...

The squared norm of a four-vector a=(a_0,a_1,a_2,a_3)=a_0+a is given by the dot product a^2=a_mua^mu=(a^0)^2-a·a, (1) where a·a is the usual vector dot product in Euclidean ...