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A complex vector bundle is a vector bundle pi:E->M whose fiber bundles pi^(-1)(m) are a copy of C^k. pi is a holomorphic vector bundle if it is a holomorphic map between ...

The van der Grinten projection is a map projection given by the transformation x = (1) y = sgn(phi)(pi|PQ-Asqrt((A^2+1)(P^2+A^2)-Q^2)|)/(P^2+A^2), (2) where A = ...

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle ...

Although the inner shaded region has the same area as the outer shaded annulus, it appears to be larger. Since the rings are equally spaced, A_(inner) = pi·3^2=9pi (1) ...

A circle bundle pi:E->M is a fiber bundle whose fibers pi^(-1)(x) are circles. It may also have the structure of a principal bundle if there is an action of SO(2) that ...

Laplace's integral is one of the following integral representations of the Legendre polynomial P_n(x), P_n(x) = 1/piint_0^pi(du)/((x+sqrt(x^2-1)cosu)^(n+1))du (1) = ...

Niven's theorem states that if x/pi and sinx are both rational, then the sine takes values 0, +/-1/2, and +/-1. Particular cases include sin(pi) = 0 (1) sin(pi/2) = 1 (2) ...

A constant appearing in formulas for the efficiency of the Euclidean algorithm, B = (12ln2)/(pi^2)[-1/2+6/(pi^2)zeta^'(2)]+C-1/2 (1) = 0.06535142... (2) (OEIS A143304), where ...

The second de Villiers point is the perspector of the reference triangle and the excenter analog of the BCI triangle, which is Kimberling center X_(1128) has triangle center ...

A catenary of revolution. The catenoid and plane are the only surfaces of revolution which are also minimal surfaces. The catenoid can be given by the parametric equations x ...