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The Euler points are the midpoints E_A, E_B, E_C of the segments which join the vertices A, B, and C of a triangle DeltaABC and the orthocenter H. They are three of the nine ...

The triangle of numbers A_(n,k) given by A_(n,1)=A_(n,n)=1 (1) and the recurrence relation A_(n+1,k)=kA_(n,k)+(n+2-k)A_(n,k-1) (2) for k in [2,n], where A_(n,k) are shifted ...

The trilinear coordinates alpha:beta:gamma of a point P relative to a reference triangle are proportional to the directed distances a^':b^':c^' from P to the side lines of ...

Define A^' to be the point (other than the polygon vertex A) where the triangle median through A meets the circumcircle of ABC, and define B^' and C^' similarly. Then the ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the B- and C-excircles (with centers J_B and J_C, respectively). Of these, three correspond to the ...

A circumconic hyperbola, which therefore passes through the orthocenter, is a rectangular hyperbola, and has center on the nine-point circle. Its circumconic parameters are ...

The first Fermat point X (or F_1) (sometimes simply called "the Fermat point," Torricelli point, or first isogonic center) is the point X which minimizes the sum of distances ...

The first Napoleon point N, also called the outer Napoleon point, is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of ...

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 ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...