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Given a triangle, draw a Cevian to one of the bases that divides it into two triangles having congruent incircles. The positions and sizes of these two circumcircles can then ...

A surface of constant negative curvature obtained by twisting a pseudosphere and given by the parametric equations x = acosusinv (1) y = asinusinv (2) z = ...

In a graph G, contraction of an edge e with endpoints u,v is the replacement of u and v with a single vertex such that edges incident to the new vertex are the edges other ...

The Egawa graph with parameters (p,s) is a distance-regular but not distance-transitive graph on 16^p4^s nodes. These graphs generalize the Doob graphs and give (s,4)-Hamming ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...

The numbers 2^npq and 2^nr are an amicable pair if the three integers p = 2^m(2^(n-m)+1)-1 (1) q = 2^n(2^(n-m)+1)-1 (2) r = 2^(n+m)(2^(n-m)+1)^2-1 (3) are all prime numbers ...

The even part Ev(n) of a positive integer n is defined by Ev(n)=2^(b(n)), where b(n) is the exponent of the exact power of 2 dividing n. The values for n=1, 2, ..., are 1, 2, ...

Let f(z) = z+a_1+a_2z^(-1)+a_3z^(-2)+... (1) = zsum_(n=0)^(infty)a_nz^(-n) (2) = zg(1/z) (3) be a Laurent polynomial with a_0=1. Then the Faber polynomial P_m(f) in f(z) of ...

Let X(x)=X(x_1,x_2,...,x_n) be a random vector in R^n and let f_X(x) be a probability distribution on X with continuous first and second order partial derivatives. The Fisher ...

A graph is a forbidden subgraph if its presence as a subgraph of a given graph means it is not a member of some family of graphs. For example, a bipartite graph is a graph ...