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Let i_k(G) be the number of irredundant sets of size k in a graph G, then the irredundance polynomial R_G(x) of G in the variable x is defined as ...

The Stammler circles are the three circles (apart from the circumcircle), that intercept the sidelines of a reference triangle DeltaABC in chords of lengths equal to the ...

The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

Riddell's formula for unlabeled graphs is the Euler transform relating the number of unlabeled connected graphs on n nodes satisfying some property with the corresponding ...

The first Neuberg circle is the circumcircle of the first Neuberg triangle. The center has center function (1) which is not a Kimberling center. Its radius is ...

The biconnected graph theta_0 on seven nodes and seven edges illustrated above. It has chromatic polynomial pi_(theta_0)(z)=z^7-8z^6+28z^5-56z^4+68z^3-47z^2+14z and chromatic ...

A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each ...

The inverse curve of the Archimedean spiral r=atheta^(1/n) with inversion center at the origin and inversion radius k is the Archimedean spiral r=k/atheta^(-1/n).