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The first Brocard point Omega is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the ...

Let D be a set of positive numbers containing 1, then the D-distance graph X(D) on a nonempty subset X of Euclidean space is the graph with vertex set X and edge set ...

If a univariate real function f(x) has a single critical point and that point is a local maximum, then f(x) has its global maximum there (Wagon 1991, p. 87). The test breaks ...

A point traced out twice as a closed curve is traversed. The maximum number of double points for a nondegenerate quartic curve is three. An ordinary double point is also ...

For n points in the plane, there are at least N_1=sqrt(n-3/4)-1/2 different distances. The minimum distance can occur only <=3n-6 times, and the maximum distance can occur ...

While the pedal point, Cevian point, and even pedal-Cevian point are commonly used concepts in triangle geometry, there seems to be no established term to describe the ...

The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...

A number x such that for all epsilon>0, there exists a member of the set y different from x such that |y-x|<epsilon. The topological definition of limit point P of A is that ...

The spherical distance between two points P and Q on a sphere is the distance of the shortest path along the surface of the sphere (paths that cut through the interior of the ...

A point x_0 is said to be a periodic point of a function f of period n if f^n(x_0)=x_0, where f^0(x)=x and f^n(x) is defined recursively by f^n(x)=f(f^(n-1)(x)).