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The outer Vecten circle is the circumcircle of the outer Vecten triangle. It has center at Kimberling center X_(641), which is the complement of the outer Vecten point ...

Let A be a C^*-algebra. An element a in A is called positive if a=a* and sp(a) subset= R^+, or equivalently if there exists an element b in A such that a=bb^*. For example, ...

Let A be a C^*-algebra. An element a in A is called self-adjoint if a^*=a. For example, the real functions of the C^*-algebra of C([a,b]) of continuous complex-valued ...

Let K be a class of topological spaces that is closed under homeomorphism, and let X be a topological space. If X in K and for every Y in K such that X subset= Y, X is a ...

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 ...

Gauge theory studies principal bundle connections, called gauge fields, on a principal bundle. These connections correspond to fields, in physics, such as an electromagnetic ...

A map u:M->N, between two compact Riemannian manifolds, is a harmonic map if it is a critical point for the energy functional int_M|du|^2dmu_M. The norm of the differential ...

Miller's rules, originally devised to restrict the number of icosahedron stellations to avoid, for example, the occurrence of models that appear identical but have different ...

A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p. 61) is a four-sided polygon. If not explicitly stated, all four polygon vertices are ...

An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of ...