Multi Parameters Golden Ratio and Some Applications

References

[1] D. H. Fowler, “A Generalization of the Golden Section,” Fibonacci Quarterly, Vol. 20, 1982, pp. 146-158.

[2] A. P. Stakhov, “The Generalized Principle of the Golden Section and Its Applications in Mathematics, Science and Engineering,” Chaos, Solitons and Fractals, Vol. 26, No. 2, 2005, pp. 263-289. doi:10.1016/j.chaos.2005.01.038

[3] A. Stakhov, “Fundamentals of a New Kind of Mathematics Based on the Golden Section,” Chaos, Solitons and Fractals, Vol. 27, No. 5, 2006, pp. 1124-1146.
doi:10.1016/j.chaos.2005.05.008

[4] M. Basu and B. Prasad, “Coding Theory on the M-Extension of the Fibonacci P-Numbers,” Chaos, Solitons and Fractals, Vol. 42, No. 4, 2009, pp. 2522-2530.
doi:10.1016/j.chaos.2009.03.197

[5] M. Basu and B. Prasad, “The Generalized Relations among the Code Elements for Fibonacci Coding Theory,” Chaos, Solitons and Fractals, Vol. 41, No. 5, 2009, pp. 2517-2525.
doi:10.1016/j.chaos.2008.09.030

[6] E. G. Kocer, N. Tuglu and A. Stakhov, “On the M-Extension of the Fibonacci and Lucas P-Numbers, Chaos,” Chaos, Solitons and Fractals, Vol. 40, No. 4, 2009, pp. 1890-1906. doi:10.1016/j.chaos.2007.09.071

[7] J. Veladimirov, “Fundamental Physics,” Philosophy and Religion, Kostroma, 1996.

[8] E. Naschie, “On a Class of General Theories for High Energy Particle Physics,” Chaos, Solitons and Fractals, Vol. 14, No. 4, 2005, pp. 649-680.
doi:10.1016/S0960-0779(02)00033-4

[9] V. V. Petrunenko, “The Golden Section of Quantom States and Its Astronomical and Phisical Manifestations,” Pravo i economika, 2005.

[10] Y. S. Vladimirov, “Metaphysics,” Binom, Moscow, 2002.

[11] E. Kilic and A. P. Stakhov, “On the Fibonacci and Lucas p-numbers, Their Sums, Families of Bipartite Graphs and Permanents of Certain Matrices,” Chaos, Solitons and Fractals, Vol. 40, No. 5, 2009, pp. 2210-2221.
doi:10.1016/j.chaos.2007.10.007

[12] A. Stakhov and B. Rozin, “The Continuous Functions for the Fibonacci and Lucas P-Numbers,” Chaos, Solitons and Fractals, Vol. 28, No. 4 , 2006, pp. 1014-1025.
doi:10.1016/j.chaos.2005.08.158

[13] M. Akbulak and D. Bozkurt, “On the Order-M Generalized Fibonacci K-Numbers,” Chaos, Solitons and Fractals, Vol. 42, No. 3, 2009, pp. 1347-1355.
doi:10.1016/j.chaos.2009.03.019

[14] A. Stakhov and B. Rozin, “Theory of Binet for Fibonacci and Lucas p-Numbers,” Chaos, Solitons and Fractals, Vol. 27, No. 5, 2006, pp. 1162-1177.
doi:10.1016/j.chaos.2005.04.106

[15] A. Nalli and P. Haukkanen, “On Generalized Fibonacci and Lucas Polynomials,” Chaos, Solitons and Fractals, Vol. 42, No. 5, 2009, pp. 3179-3186.
doi:10.1016/j.chaos.2009.04.048

[16] F. Buyukkilic and D. Demirhan, “Cumulative Growth with Fibonacci Approach, Golden Section and Physics,” Chaos, Solitons and Fractals, Vol. 42, No. 1, 2009, pp. 24-32. doi:10.1016/j.chaos.2008.10.023

[17] A. Benavoli, L. Chisci and A. Farina, “Fibonacci Sequence, Golden Section, Kalman Filter and Optimal Control,” Signal Processing, Vol. 89, No. 8, 2009, pp. 1483-1488.
doi:10.1016/j.sigpro.2009.02.003

[18] E. Cureg and A. Mukherjea, “Numerical Results on Some Generalized Random Fibonacci Sequences,” Computer and Mathematics Application, Vol. 59, No. 1, 2010, pp. 233-246. doi:10.1016/j.camwa.2009.08.001

[19] E. M. Soroko, “Structural Harmony of System,” Nauka i Tekhnika, Russian, 1984.

[20] A. Stakhov and B. Rozin, “The Golden Shofar,” Chaos, Solitons and Fractals, Vol. 26, No. 3, 2005, pp. 677-684.
doi:10.1016/j.chaos.2005.01.057

[21] A. P. Stakhov, “Generalized Golden Section and a New Approach to Geometric Definition of a Number,” Ukrainian Mathematical Journal, Vol. 56, No. 8, 2004, pp. 1143-1150. doi:10.1007/s11253-005-0064-3

[22] O. Karpenkov, “On Examples of Two-Dimensinal Priodic Continued Fractions,” Academic Paper, Moscow State University, Moscow, 2004.

[23] M. Grundland, J. Patera, Z. Masakova and N. Dodgson, “Image Sampling with Quasicrystals,” Electrical and Electronic Engineering, Vol. 5, 2009, pp. 1-23.
doi: 10.3842/SIGMA.2009.075

[24] S. Dutch, “Why Trisecting of the Angle Is Impossible?” Natural and Applied Sciense, University of Wisconsin-Green Bay, Green Bay, 2009.

[25] J. B. Fraleigh, “A First Course in Abstract Algebra,” 7th Edition, Addison-Wesley, Boston, 1982.

[26] M. B. Farnworth, “Cubic Equations and Ideal Trisection of the Arbitrary Angle,” Theaching Mathematics and Its Applications, Vol. 25, No. 2, 2006.

[27] S. Falcon and A. Plaza, “On the Fibonacci K-Numbers,” Chaos, Solitons and Fractals, Vol. 32, No. 5, 2007, pp. 1615-1624. doi:10.1016/j.chaos.2006.09.022

[28] A. Stakhov, “The Golden Section, Secret of the Egyption Civilization and Harmony Mathematics,” Chaos, Solitons and Fractals, Vol. 30, No. 2, 2006, pp. 490-505.
doi:10.1016/j.chaos.2005.11.022