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Consider a game, first proposed by Nicolaus Bernoulli, in which a player bets on how many tosses of a coin will be needed before it first turns up heads. The player pays a ...

The half-altitude circle is the circumcircle of the half-altitude triangle. The circle function is given by l=(f(a,b,c))/(128a^2b^3c^3cosAcosBcosC), (1) where (2) which is ...

1 0 1 0 1 1 0 1 2 2 0 2 4 5 5 (1) The Entringer numbers E(n,k) (OEIS A008281) are the number of permutations of {1,2,...,n+1}, starting with k+1, which, after initially ...

The perspector of the first Morley triangle with reference triangle DeltaABC is called the second Morley center. Its triangle center function is alpha_(357)=sec(1/3A), which ...

The Fuhrmann center Fu is the center of the Fuhrmann circle, given by the midpoint of the line joining the Nagel point and orthocenter (which forms a diameter of the Fuhrmann ...

In finding the average area A^__R of a triangle chosen from a closed, bounded, convex region R of the plane, then A^__(T(R))=A^__R, for T any nonsingular affine ...

For a triangle DeltaABC and three points A^', B^', and C^', one on each of its sides, the three Miquel circles are the circles passing through each polygon vertex and its ...

Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...

The line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspective axis or homology ...

There are two kinds of power sums commonly considered. The first is the sum of pth powers of a set of n variables x_k, S_p(x_1,...,x_n)=sum_(k=1)^nx_k^p, (1) and the second ...