physics. Möbius geometries and their transformations generalize this case to any number of dimensions over other fields. Möbius transformations are named...
70 KB (10,554 words) - 05:55, 8 August 2024
d, and z are complex numbers (in which case the transformation is also called a Möbius transformation), or more generally elements of a field. The invertibility...
12 KB (1,679 words) - 18:03, 7 June 2024
named after him, including the Möbius plane, the Möbius transformations, important in projective geometry, and the Möbius transform of number theory. His...
8 KB (685 words) - 00:10, 25 August 2024
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist...
88 KB (9,611 words) - 15:13, 22 August 2024
Conformal geometry (redirect from Möbius geometry)
locally conformal to a Möbius geometry, meaning that there exists an angle preserving local diffeomorphism from the manifold into a Möbius geometry. In two...
21 KB (3,351 words) - 09:08, 12 December 2023
Examples of Möbius transformations include dilations, rotations, translations, and complex inversion. In fact, any Möbius transformation can be written...
21 KB (3,313 words) - 05:25, 16 August 2024
Lorentz group (redirect from Parabolic transformation)
isomorphism to the Möbius group. The following table lists the six generators, in which The first column gives a generator of the flow under the Möbius action (after...
65 KB (9,740 words) - 16:15, 2 February 2024
Conformal map (redirect from Conformal transformation)
itself is conformal if and only if it is a Möbius transformation. The complex conjugate of a Möbius transformation preserves angles, but reverses the orientation...
22 KB (2,511 words) - 19:47, 30 May 2024
Zhegalkin polynomial (section Möbius transformation)
polynomial. This is the partial order version of the Möbius formula, not the number theoretic. The Möbius inversion formula for partial orders is: g ( x )...
33 KB (5,153 words) - 14:47, 4 July 2024