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If r is the inradius of a circle inscribed in a right triangle with sides a and b and hypotenuse c, then r=1/2(a+b-c). (1) A Sangaku problem dated 1803 from the Gumma ...

A circular pattern obtained by superposing parallel equally spaced lines on a set of concentric circles of increasing radii, then coloring the regions in chessboard fashion. ...

The circular points at infinity, also called the isotropic points, are the pair of (complex) points on the line at infinity through which all circles pass. The circular ...

A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

The circum-medial triangle DeltaA^'B^'C^' is the circumcevian triangle of a reference triangle DeltaABC with respect to the triangle centroid G of DeltaABC (Kimberling 1998, ...

Given a triangle DeltaABC and a point P not a vertex of DeltaABC, define the A^'-vertex of the circumcevian triangle as the point other than A in which the line AP meets the ...

A circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...

The circumsphere of given set of points, commonly the vertices of a solid, is a sphere that passes through all the points. A circumsphere does not always exist, but when it ...

Let O be an order of an imaginary quadratic field. The class equation of O is the equation H_O=0, where H_O is the extension field minimal polynomial of j(O) over Q, with ...

The clique covering number theta(G) of a graph G is the minimum number of cliques in G needed to cover the vertex set of G. Since theta(G) involves the minimum number of ...