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The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

Given any triangle ABC, the signed sum of perpendicular distances from the circumcenter O to the sides (i.e., signed lengths of the pedal lines from O) is OO_A+OO_B+OO_C=R+r, ...

The circum-medial triangle DeltaA^'B^'C^' is the circumcevian triangle of a reference triangle DeltaABC with respect to the triangle centroid G of DeltaABC (Kimberling 1998, ...

A circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...

A cyclic polygon is a polygon with vertices upon which a circle can be circumscribed. Since every triangle has a circumcircle, every triangle is cyclic. It is conjectured ...

The Darboux integral, also called a Darboux-Stieltjes integral, is a variant of the Stieltjes integral that is defined as a common value for the lower and upper Darboux ...

The detour matrix Delta, sometimes also called the maximum path matrix or maximal topological distances matrix, of a graph is a symmetric matrix whose (i,j)th entry is the ...

The maximum number of disjoint dominating sets in a domatic partition of a graph G is called its domatic number d(G). The domatic number should not be confused with the ...

The edge connectivity, also called the line connectivity, of a graph is the minimum number of edges lambda(G) whose deletion from a graph G disconnects G. In other words, it ...

Euler's series transformation is a transformation that sometimes accelerates the rate of convergence for an alternating series. Given a convergent alternating series with sum ...