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AW, AB, and AY in the above figure are in a harmonic range.

There are (at least) three different types of points known as Steiner points. The point S of concurrence of the three lines drawn through the vertices of a triangle parallel ...

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

Let G=SL(n,C). If lambda in Z^n is the highest weight of an irreducible holomorphic representation V of G, (i.e., lambda is a dominant integral weight), then the G-map ...

If all elements a_(ij) of an irreducible matrix A are nonnegative, then R=minM_lambda is an eigenvalue of A and all the eigenvalues of A lie on the disk |z|<=R, where, if ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

Two points are antipodal (i.e., each is the antipode of the other) if they are diametrically opposite. Examples include endpoints of a line segment, or poles of a sphere. ...

Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. ...

The Yff circles are the two triplets of congruent circle in which each circle is tangent to two sides of a reference triangle. In each case, the triplets intersect pairwise ...

Let H be a heptagon with seven vertices given in cyclic order inscribed in a conic. Then the Pascal lines of the seven hexagons obtained by omitting each vertex of H in turn ...