Double numbers
2010jbw | Pavlov D.G., Garasko G.I.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia, geom2004@mail.ru, gri9z@mail.ru

There is an attempt to show that there is much more in common between the complex numbers and the double (hyperbolically complex) numbers than it is usually thought to be. With this the new and non-trivial properties of the analytical functions of the double number variable are discovered. For example, there is a relation between these functions and the hyperbolic potential and solenoidal vector fields on the pseudo Euclidean plane. Besides, it is shown how many structures on the complex plane can be one-to-one mapped at their hyperbolical analogues. This repudiates the magic properties of the complex numbers, and particularly, leads to the understanding that the analytical functions of complex numbers can be given by two scalar functions not of two but of one real variable each.

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