Obtaining a New Representation for the Golden Ratio by Solving a Biquadratic Equation ()
Leonardo Mondaini1,2*
1Department of Oncology, University of Alberta, Edmonton, Canada.
2Grupo de Física Teórica e Experimental, Departamento de Ciências Naturais, Universidade Federal do Estado do Rio de Janeiro, Rio de Janeiro, Brazil.
DOI: 10.4236/jamp.2014.213134
PDF HTML XML
3,969
Downloads
4,670
Views
Citations
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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
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.
|