Some Golden Objects in Geometry

Yıl 2014, Cilt: 11 Sayı: 1, - , 01.05.2014

Z. Nazari A. Delbaznasab Y. Bahrampour

Öz

In this paper, first, an induced algebra with respect to the polynomial P(x) is defined and then, an
induced Lie group with respect to P(x) is determined. Finally, Golden Algebras, Golden Lie groups, Golden
curves and Golden surfaces are introduced based on the definition of generalized Golden polynomials.

Anahtar Kelimeler

Polynomial, algebra, Lie group, generalized golden polynomial, golden algebra, golden Lie group, golden curve, golden surface

Kaynakça

• [1] M.S. El Nashie, Quantum Mechanics and the Possibility of a Cantorian Spacetime, Chaos, Solitons and Fractals, 1(5), (1992), 485-7.
• [2] M.S. El Naschie, The Concepts of E Infinity: An Elementary Introduction to the Cantorian-Fractal Theory of Quantum Physics, Chaos, Solitons and Fractals, 22(2), (2004), 495-511.
• [3] R. H. Fischler, The Shape of the Great Pyramid, Waterloo: Wilfrid Laurier University Press, (2000).
• [4] S. H. Hendi, M. Sharifzadeh, Special Relativity and the Golden Ratio, Journal of Theoretical Physics, 1, (2012), 37-45.
• [5] R. Heyrovska, The Golden Ratio Ionic and Atomic Radii and Bond Lengths, Molecular Physics, 103, (2005), 877-82.
• [6] W. Y. Hsiang, Lectures on Lie Groups, World Scientific, (2000).
• [7] A. W. Joshi, Elements of Group Theory for Physicists, New York: J. Wiley, (1982).
• [8] M. Livio, The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number Φ, Broadway Books, (2002).
• [9] E. Meinrenken, Lie Groups and Lie Algebra, Lecture Notes University of Toronto, (2010).
• [10] T. Needham, Visual Complex Analysis, Oxford University Press, (1997).
• [11] V.V. Trofimov, Introduction to Geometry of Manifolds with Symmetry, P. Kluwer Academic Publishers, (1994).