Araştırma Makalesi

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

Yıl 2019, Cilt 20, Sayı , 170 - 180, 16.12.2019

### Öz

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.

### Kaynakça

• [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.
Yıl 2019, Cilt 20, Sayı , 170 - 180, 16.12.2019

### Kaynakça

• [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.

### Ayrıntılar

Birincil Dil İngilizce Fen Makaleler Şadiye ÇAKMAK Bu kişi benim ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ 0000-0001-9256-0571 Abidin KILIÇ (Sorumlu Yazar) Eskişehir Teknik Üniversitesi 0000-0003-4567-5207 Türkiye 16 Aralık 2019 Yıl 2019, Cilt 20, Sayı

### Kaynak Göster

 Bibtex @araştırma makalesi { estubtda649511, journal = {Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering}, issn = {2667-4211}, address = {btda@anadolu.edu.tr}, publisher = {Eskişehir Teknik Üniversitesi}, year = {2019}, volume = {20}, pages = {170 - 180}, doi = {10.18038/estubtda.649511}, title = {THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA}, key = {cite}, author = {Çakmak, Şadiye and Kılıç, Abidin} } APA Çakmak, Ş. & Kılıç, A. (2019). THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA . Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering , Vol:20 - ICONAT 2019 Special Issue , 170-180 . DOI: 10.18038/estubtda.649511 MLA Çakmak, Ş. , Kılıç, A. "THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA" . Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 20 (2019 ): 170-180 Chicago Çakmak, Ş. , Kılıç, A. "THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA". Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 20 (2019 ): 170-180 RIS TY - JOUR T1 - THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA AU - Şadiye Çakmak , Abidin Kılıç Y1 - 2019 PY - 2019 N1 - doi: 10.18038/estubtda.649511 DO - 10.18038/estubtda.649511 T2 - Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering JF - Journal JO - JOR SP - 170 EP - 180 VL - 20 IS - SN - 2667-4211- M3 - doi: 10.18038/estubtda.649511 UR - https://doi.org/10.18038/estubtda.649511 Y2 - 2019 ER - EndNote %0 Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA %A Şadiye Çakmak , Abidin Kılıç %T THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA %D 2019 %J Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering %P 2667-4211- %V 20 %N %R doi: 10.18038/estubtda.649511 %U 10.18038/estubtda.649511 ISNAD Çakmak, Şadiye , Kılıç, Abidin . "THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA". Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 20 / (Aralık 2019): 170-180 . https://doi.org/10.18038/estubtda.649511 AMA Çakmak Ş. , Kılıç A. THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering. 2019; 20: 170-180. Vancouver Çakmak Ş. , Kılıç A. THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering. 2019; 20: 170-180. IEEE Ş. Çakmak ve A. Kılıç , "THE STUDY OF CLASSICS PARTICLES' ENERGY AT ARCHIMEDEAN SOLIDS WITH CLIFFORD ALGEBRA", Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, c. 20, ss. 170-180, Ara. 2019, doi:10.18038/estubtda.649511
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