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The second Brocard Cevian triangle is the Cevian triangle of the second Brocard point. It has area Delta_2=(2a^2b^2c^2)/((a^2+b^2)(b^2+c^2)(c^2+a^2))Delta, where Delta is the ...

A quantity which takes on the value zero is said to vanish. For example, the function f(z)=z^2 vanishes at the point z=0. For emphasis, the term "vanish identically" is ...

If three circles A, B, and C are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one ...

Given any straight line and a point not on it, there "exists one and only one straight line which passes" through that point and never intersects the first line, no matter ...

Let a Gram point g_n be called "good" if (-1)^nZ(g_n)>0, and "bad" otherwise (Rosser et al. 1969; Edwards 2001, p. 180). Then the interval between two consecutive good Gram ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

Let f be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then if f(a)=f(b), then there is at least one point c in (a,b) where f^'(c)=0. ...

A symbol used to distinguish a third quantity x^('') ("x double prime") from two other related quantities x and x^' ("x prime). Double primes are most commonly used to denote ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

The neighborhood graph of a given graph from a vertex v is the subgraph induced by the neighborhood of a graph from vertex v, most commonly including v itself. Such graphs ...