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The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

Let the inner and outer Soddy triangles of a reference triangle DeltaABC be denoted DeltaPQR and DeltaP^'Q^'R^', respectively. Similarly, let the tangential triangles of ...

The turning of an object or coordinate system by an angle about a fixed point. A rotation is an orientation-preserving orthogonal transformation. Euler's rotation theorem ...

The second Brocard point is the interior point Omega^' (also denoted tau_2 or Z_2) of a triangle DeltaABC with points labeled in counterclockwise order for which the angles ...

Let c_1, c_2, and c_3 be the circles through the vertices A_2 and A_3, A_1 and A_3, and A_1 and A_2, respectively, which intersect in the first Brocard point Omega. ...

A smooth structure on a topological manifold (also called a differentiable structure) is given by a smooth atlas of coordinate charts, i.e., the transition functions between ...

The Spieker center is the center Sp of the Spieker circle, i.e., the incenter of the medial triangle of a reference triangle DeltaABC. It is also the center of the excircles ...

The word "star" is used in a number of different ways in mathematics. The term is commonly used to voice an asterisk when appearing in a mathematical expression. For example, ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...

The point T at which the lines through the polygon vertices of a triangle perpendicular to the corresponding sides of the first Brocard triangle, are concurrent. The Tarry ...