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Pythagorean Vectors and Clifford Numbers |
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| Authors: | G. Arag��n-Gonz��lez J. L. Arag��n M. A. Rodr��guez-Andrade |
| Affiliation: | 1. Programa de Desarrollo Profesional en Automatizaci??n, Universidad Aut??noma Metropolitana, Azcapotzalco, San Pablo 180, Colonia Reynosa-Tamaulipas, 02200, D. F., M??xico 2. Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford, OX1 3LB, U.K. 3. Centro de F??sica Aplicada y Tecnolog??a Avanzada, Universidad Nacional Aut??noma de M??xico, Apartado Postal 1-1010, 76000, Quer??taro, M??xico 4. Departamento de Matem??ticas, Escuela Superior de F??sica y Matem??ticas, Instituto Polit??cnico Nacional, Unidad Profesional Adolfo L??pez Mateos, Edificio 9, 07300, D. F., M??xico 5. Departamento de Matem??tica Educativa, CINVESTAV-IPN, Avenida Instituto Polit??cnico Nacional 2508, Colonia San Pedro Zacatenco, 07360, D.F., M??xico |
| Abstract: | In this work simple reflections or rotations of canonical vectors are used to generate all Pythagorean vectors, i.e. vectors in mathbbQn{mathbb{Q}^{n}} that satisfy the Pythagoras generalized equation. By using Clifford algebra we develop a constructive method that explicitly provides an algorithm to generate generalized Pythagorean numbers. |
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