Obtaining a New Representation for the Golden Ratio by Solving a Biquadratic Equation

Affiliation(s)

^{1}
Department of Oncology, University of Alberta, Edmonton, Canada.

^{2}
Grupo de Física Teórica e Experimental, Departamento de Ciências Naturais, Universidade Federal do Estado do Rio de Janeiro, Rio de Janeiro, Brazil.

ABSTRACT

In the present work we show how different ways to solve biquadratic equations can lead us to different representations of its solutions. A particular equation which has the golden ratio and its reciprocal as solutions is shown as an example.

In the present work we show how different ways to solve biquadratic equations can lead us to different representations of its solutions. A particular equation which has the golden ratio and its reciprocal as solutions is shown as an example.

Cite this paper

Mondaini, L. (2014) Obtaining a New Representation for the Golden Ratio by Solving a Biquadratic Equation.*Journal of Applied Mathematics and Physics*, **2**, 1149-1152. doi: 10.4236/jamp.2014.213134.

Mondaini, L. (2014) Obtaining a New Representation for the Golden Ratio by Solving a Biquadratic Equation.

References

[1] Boyer, C.B. and Merzbach, U.C. (1991) A History of Mathematics. 2nd Edition, John Wiley & Sons, Inc., New York.

[2] Weisstein, E.W. Characteristic Equation. MathWorld—A Wolfram Web Resource.

http://mathworld.wolfram.com/CharacteristicEquation.html

[3] Lipschutz, S. and Lipson, M. (2013) Linear Algebra—Schaum’s Outlines. 5th Edition, The McGraw-Hill Companies, Inc., New York.

[4] Livio, M. (2002) The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. Broadway Books, New York.

[5] Cardano, G. (1993) Ars Magna or the Rules of Algebra. Dover Publications, Mineola.

[1] Boyer, C.B. and Merzbach, U.C. (1991) A History of Mathematics. 2nd Edition, John Wiley & Sons, Inc., New York.

[2] Weisstein, E.W. Characteristic Equation. MathWorld—A Wolfram Web Resource.

http://mathworld.wolfram.com/CharacteristicEquation.html

[3] Lipschutz, S. and Lipson, M. (2013) Linear Algebra—Schaum’s Outlines. 5th Edition, The McGraw-Hill Companies, Inc., New York.

[4] Livio, M. (2002) The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. Broadway Books, New York.

[5] Cardano, G. (1993) Ars Magna or the Rules of Algebra. Dover Publications, Mineola.