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Given a point P and a triangle DeltaABC, the Miquel triangle is the triangle DeltaP_AP_BP_C connecting the side points P_A, P_B, and P_C of DeltaABC with respect to which M ...

Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

The theorem of Möbius tetrads, also simply called Möbius's theorem by Baker (1925, p. 18), may be stated as follows. Let P_1, P_2, P_3, and P_4 be four arbitrary points in a ...

Möbius tetrahedra, also called Möbius tetrads (Baker 1922, pp. 61-62) are a pair of tetrahedra, each of which has all the vertices lying on the faces of the other: in other ...

A knot which is not alternating. Unlike alternating knots, flype moves are not sufficient to pass between all minimal diagrams of a given nonalternating knot (Hoste et al. ...

An orthogonal transformation is a linear transformation T:V->V which preserves a symmetric inner product. In particular, an orthogonal transformation (technically, an ...

A rational function P(x)/Q(x) can be rewritten using what is known as partial fraction decomposition. This procedure often allows integration to be performed on each term ...

Let Y^X be the set of continuous mappings f:X->Y. Then the topological space Y^X supplied with the compact-open topology is called a mapping space. If (Y,*) is a pointed ...

The pentagonal dipyramid is one of the convex deltahedra, and Johnson solid J_(13). It is also the dual polyhedron of the pentagonal prism U_(76) and is an isohedron. It is ...

Plancherel's theorem states that the integral of the squared modulus of a function is equal to the integral of the squared modulus of its spectrum. It corresponds to ...