Search Results for ""

Given a complete graph K_n which is two-colored, the number of forced monochromatic triangles is at least {1/3u(u-1)(u-2) for n=2u; 2/3u(u-1)(4u+1) for n=4u+1; ...

Morley's circle is the circumcircle of the first Morley triangle. Its center is the first Morley center, which has center function alpha_(356)=cos(1/3A)+2cos(1/3B)cos(1/3C), ...

Multisection of a mathematical quantity or figure is division of it into a number of (usually) equal parts. Division of a quantity into two equal parts is known as bisection, ...

The center of a Neuberg circle.

The radical circle of the Neuberg circles has circle function l=(a^2b^4-b^4c^2+a^2c^4-b^2c^4)/(bc(a^2b^2+a^2c^2+b^2c^2)), (1) which does not correspond to any Kimberling ...

Let a triangle have side lengths a, b, and c with opposite angles A, B, and C. Then (b+c)/a = (cos[1/2(B-C)])/(sin(1/2A)) (1) (c+a)/b = (cos[1/2(C-A)])/(sin(1/2B)) (2) ...

Given an acute angle in a right triangle, the opposite side is the leg of the triangle which is not incident on the angle. Lengths of opposite and adjacent sides appear ...

The orthoptic circle of the Steiner inellipse is the circle with center at alpha_2=1/a, (1) corresponding to the triangle centroid G and radius ...

Consider a reference triangle DeltaABC and any given point P. The perpendiculars to AP, BP and CP respectively meet BC, AC and AB in three collinear points defining line l. ...

The outer Vecten circle is the circumcircle of the outer Vecten triangle. It has center at Kimberling center X_(641), which is the complement of the outer Vecten point ...