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The Euler-Gergonne-Soddy triangle is the right triangle DeltaZFlEv created by the pairwise intersections of the Euler line L_E, Soddy line L_S, and Gergonne line L_G. (The ...

A surface which a monkey can straddle with both legs and his tail. A simple Cartesian equation for such a surface is z=x(x^2-3y^2), (1) which can also be given by the ...

An n-dimensional disk (sometimes spelled "disc") of radius r is the collection of points of distance <=r (closed disk) or <r (open disk) from a fixed point in Euclidean ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the local discrepancy is defined as D(J,P)=|(number of x_n in J)/N-Vol(J)|, Vol(J) is the ...

A locally finite space is one for which every point of a given space has a neighborhood that meets only finitely many elements of any cover.

A vector field is a section of its tangent bundle, meaning that to every point x in a manifold M, a vector X(x) in T_xM is associated, where T_x is the tangent space.

Extend the symmedians of a triangle DeltaA_1A_2A_3 to meet the circumcircle at P_1, P_2, P_3. Then the symmedian point K of DeltaA_1A_2A_3 is also the symmedian point of ...

Let H be a Hilbert space and M a closed subspace of H. Corresponding to any vector x in H, there is a unique vector m_0 in M such that |x-m_0|<=|x-m| for all m in M. ...

A removable singularity is a singular point z_0 of a function f(z) for which it is possible to assign a complex number in such a way that f(z) becomes analytic. A more ...