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Draw lines P_AQ_A, P_BQ_B, and P_CQ_C through the symmedian point K and parallel to the sides of the triangle DeltaABC. The points where the parallel lines intersect the ...

A curve which has at least multiplicity r_i-1 at each point where a given curve (having only ordinary singular points and cusps) has a multiplicity r_i is called the adjoint ...

The point of concurrence of the four maltitudes of a cyclic quadrilateral. Let M_(AC) and M_(BD) be the midpoints of the diagonals of a cyclic quadrilateral ABCD, and let P ...

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the P-anticomplementary conjugate of U is the point where h(a,b,c,p,q,r,u,v,w) ...

Barycentric coordinates (t_1,t_2,t_3) normalized so that they become the areas of the triangles PA_1A_2, PA_1A_3, and PA_2A_3, where P is the point whose coordinates have ...

If a is a point in the open unit disk, then the Blaschke factor is defined by B_a(z)=(z-a)/(1-a^_z), where a^_ is the complex conjugate of a. Blaschke factors allow the ...

In a cyclic quadrilateral ABCD having perpendicular diagonals AC_|_BD, the perpendiculars to the sides through point T of intersection of the diagonals (the anticenter) ...

A section of a fiber bundle gives an element of the fiber over every point in B. Usually it is described as a map s:B->E such that pi degreess is the identity on B. A ...

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...

A circle bundle pi:E->M is a fiber bundle whose fibers pi^(-1)(x) are circles. It may also have the structure of a principal bundle if there is an action of SO(2) that ...