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Since |(a+ib)(c+id)| = |a+ib||c+di| (1) |(ac-bd)+i(bc+ad)| = sqrt(a^2+b^2)sqrt(c^2+d^2), (2) it follows that (a^2+b^2)(c^2+d^2) = (ac-bd)^2+(bc+ad)^2 (3) = e^2+f^2. (4) This ...

A full angle, also called a complete angle, round angle, or perigon, is an angle equal to 2pi radians =360 degrees corresponding to the central angle of an entire circle. ...

A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any ...

The geometric span is largest possible distance between two points drawn from a finite set of points. It is therefore closely related to the generalized diameter of a closed ...

A half-space is that portion of an n-dimensional space obtained by removing that part lying on one side of an (n-1)-dimensional hyperplane. For example, half a Euclidean ...

A metric on a bunch of segments with a common endpoint O, which defines the distance between two points P_1 and P_2 as the length of the shortest path connecting them inside ...

A Heegaard splitting of a connected orientable 3-manifold M is any way of expressing M as the union of two (3,1)-handlebodies along their boundaries. The boundary of such a ...

A hendecagon is an 11-sided polygon, also variously known as an undecagon or unidecagon. The term "hendecagon" is preferable to the other two since it uses the Greek prefix ...

A hexagrammic prism is a prism formed by two regular hexagrams offset along their symmetry axis and with corresponding edges connected by lateral faces. For an equilateral ...

A shell bounded by two similar ellipsoids having a constant ratio of axes. Given a chord passing through a homeoid, the distance between inner and outer intersections is ...