Two-dimensional hypercomplex numbers and related trigonometries and geometries

Advances in Applied Clifford Algebras

Volumn 14, Issue 1, 2004, Pages 47-68

  Catoni, Francesco ^a   Cannata, Roberto ^a   Catoni, Vincenzo ^a   Zampetti, Paolo ^a  

^a ENEA C R CASACCIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748923094     PISSN: 01887009     EISSN: 16614909     Source Type: Journal    
DOI: 10.1007/s00006-004-0008-2     Document Type: Article

References (20)

1. Yaglom I. M., “Complex numbers in geometry”, Academic Press, New York (1968)
2. Lavrentiev M. and B. Chabat, “Effets Hydrodynamiques et modèles mathématiques”, Mir, Moscou (1980)
3. Yaglom I. M., “A simple non-euclidean geometry and its physical basis”, Springer-Verlag, New York (1979)
4. Sobczyk G., Hyperbolic number plane, The College Mathematics Journal, 26 (4), 268 (1995)
5. Fjelstad P., Extending relativity via the perplex numbers Am. J. Phys., 54, 416 (1986)
6. Catoni F., P. Zampetti, Two-dimensional space-time simmetry in hyperbolic functions, N. Cim. B, 115 B, 1433 (2000)
7. Catoni F., R. Cannata, V. Catoni, P. Zampetti, Hyperbolic trigonometry in two-dimensional space-time geometry, N. Cim. B, 118 B, 475 (2003)
8. Hestenes D., G. Sobczyk, “Clifford algebra to geometric calculus: a unified language for mathematics and physics”, Reidel, Dordrecht (1984)
9. Hestenes D., P. Reany, G. Sobczyk, Unipodal algebra and roots of polynomials: report, Advances in Applied Clifford Algebras, 1 (1), 51 (1991)
10. Keller J., Complex, duplex and real Clifford algebras, Advances in Applied Clifford Algebras, 4 (1), 1 (1994)
11. Calvet R. G., Treatise of plane geometry through geometric algebra, published at the Internet site http://campus.uab.es/ PC00018/ (2001)
12. Casanova G., L’Algebre de Clifford et ses applications, Advances in Applied Clifford Algebras, 12 (S1), 1 (2002)
13. Fjelstad P., S. G. Gal, Two-dimensional geometries, topologies, trigonometries and physics generated by complex-type numbers, Advances in Applied Clifford Algebras, 11 (1), 81 (2001)
14. Lie S., M. G. Scheffers, “Vorlesungen über continuerliche Gruppen”, Kap. 21 (Taubner, Leipzig) (1893)
15. Catoni F., R. Cannata, E. Nichelatti, Matrix representation of hypercomplex numbers and analytical functions of hypercomplex variable (in Italian), ENEA report RT/ERG/1997/10 (1997)
16. Catoni F., R. Cannata, E. Nichelatti, P. Zampetti, Analytical functions in non-canonical two-dimensional algebras (in Italian), ENEA report RT/ERG/1997/9 (1997)
17. Catoni F., Hypercomplex numbers, analytical functions of hypercomplex variable and physical fields (in Italian), ENEA report RT/ERG/94/18 (1994)
18. Chabat B., “Introduction à l’analyse complexe”, Vol. 1 Mir, Moscou (1990)
19. Naber G. L., “The Geometry of Minkowski Spacetime. An Introduction to the Mathematics of the Special Theory of Relativity”, Springer-Verlag, New York (1992)
20. Wolfram S., “Mathematica: a system for doing mathematics by computer”, Addison Wesley, Reading (1992)