Catoni, F., Boccaletti, D., Cannata, R., Catoni, V., Nichelatti, E., Zampetti, P.
2008, XIX, 256 p.
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Simplest extension of complex numbers, an immediate and complete formalization of two-dimensional space-time geometry and trigonometry
Results extended for studying non-flat varieties in space-time
Stimulating the investigation of multidimensional systems of numbers
Commutative systems with four unities are studied
This book arose out of original research by the authors on the extension of well-established applications of complex numbers related to Euclidean geometry and to the space-time symmetry of two-dimensional Special Relativity.
The system of hyperbolic numbers (the simplest extension of complex numbers) is extensively studied and applied to typical instances such as the ‘twin-paradox’, and a plain exposition of space-time geometry and trigonometry is given.
The application of hyperbolic numbers to Special Relativity suggests trying the possible application of multidimensional hypercomplex systems.
Commutative hypercomplex systems with four unities are studied and attention is drawn to their interesting properties.