THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA

Year 2019, Volume: 20 , 170 - 180, 16.12.2019

Şadiye Çakmak Abidin Kılıç

https://doi.org/10.18038/estubtda.649511

Cited By: 2

Abstract

Geometric
algebras known as a generalization of Grassmann algebras complex numbers and
quaternions are presented by Clifford (1878). 
Geometric algebra describing the geometric symmetries of both physical
space and spacetime is a strong language for physics. Groups generated from
`Clifford numbers` are firstly defined by Lipschitz (1886).  They are used for defining rotations in a
Euclidean space. In this work, Clifford algebra is identified. The energy of
classic particles with Clifford algebra are defined. This calculations are
applied to some Archimedean solids. Also, the vertices of Archimedean solids
presented in the Cartesian coordinates are calculated.

Keywords

Clifford Algebra, Archimedes Solids, Platonic Solids

References

• [1] C. Doran, A. Lasenby, Geometric Algebra for Physicists.
• [2] M. Kline, Mathematical Thought from Ancient to Modern Times. Oxford University Press, Oxford (1972).
• [3] W. K. Clifford, Am. J. Math. 1(1878) 350.
• [4] S. L. Altmann, Rotations, quaternions, and double groups. Clarendon Press, Oxford (1994).
• [5] A. Kilic, K. Ozdas, M. Tanisli, An Investigation of Symmetry Operations with Clif¬ford Algebra 54(3) (2004).
• [6] P. R. Girard, Quaternions, Clifford Algebra, and Relativistic Physics.
• [7] J. Funda, R. P. Paul, A Comparison of Transforms and Quaternions in Physics, Proc. of 1988 IEEE Int. Conference on Robotics and Automation, Philadelphia, 1988, p.886.
• [8] M. Tanışlı, Acta Physica Slovaca, 53(3) (2003) 253. Turkey, 2012.
• [9] O. Rodriques, Journal de Mathematiques Pures et Appliquees 5 (1840) 380.
• [10] P. Lounesto, Lectures on Clifford Geometric Algebras. TTU Press, Cookeville, TN, USA (2002)
• [11] B. Jancewicz, Multivectors and Clifford Algebra in Electrodynamics. [12] J. Snygg: Clifford Algebra.
• [13] A. Pokorny, P. Herzig, S. L. Altman, Spectrochimica Acta A 57 (2001) 1931.
• [14] R. Williams, The Geometrical Foundation of Natural Structure.
• [15] S. J. R. Anderson, G. C. Joshi: Physics Essays 6 (1993), 308.