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A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...

The Moses circle is defined as the circle with center at the Brocard midpoint X_(39) that is tangent to the nine-point circle at the center of the Kiepert hyperbola X_(115). ...

Draw an initial circle, and arrange six circles tangent to it such that they touch both the original circle and their two neighbors. Then the three lines joining opposite ...

The sine function sinx is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let theta be an ...

A plane shape constructed by Reinhardt (1934) that is conjectured to be the "worst" packer of all centrally-symmetric plane regions. It has a packing density of ...

Given a triangle DeltaABC with inner and outer Soddy centers S and S^', respectively, the inner Soddy triangle DeltaPQR (respectively, outer Soddy triangle DeltaP^'Q^'R^') is ...

For a scalar function f over a surface parameterized by u and v, the surface integral is given by Phi = int_Sfda (1) = int_Sf(u,v)|T_uxT_v|dudv, (2) where T_u and T_v are ...

A quadrilateral which has an incircle, i.e., one for which a single circle can be constructed which is tangent to all four sides. Opposite sides of such a quadrilateral ...

A geometric implement discovered in a 19th century book, and whose inventor is unknown. It essentially consists of a semicircle, a segment SR which prolongs its diameter and ...