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If f(z) is analytic in some simply connected region R, then ∮_gammaf(z)dz=0 (1) for any closed contour gamma completely contained in R. Writing z as z=x+iy (2) and f(z) as ...

A double-toroidal graph is a graph with graph genus 2 (West 2000, p. 266). Planar and toroidal graphs are therefore not double-toroidal. Some known double-toroidal graphs on ...

If two perpendicular lines are drawn through the orthocenter H of any triangle, these lines intercept each side (or its extension) in two points (labeled P_(12), P_(12)^', ...

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 ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

The circumcircle of the Fuhrmann triangle. It has the line HNa, where H is the orthocenter and Na is the Nagel point, as its diameter. In fact, these points (Kimberling ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

Let G_1, G_2, ..., G_t be a t-graph edge coloring of the complete graph K_n, where for each i=1, 2, ..., t, G_i is the spanning subgraph of K_n consisting of all graph edges ...

The first and second isodynamic points of a triangle DeltaABC can be constructed by drawing the triangle's angle bisectors and exterior angle bisectors. Each pair of ...

An isolated singularity is a singularity for which there exists a (small) real number epsilon such that there are no other singularities within a neighborhood of radius ...