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Enhancing Computational Thinking with Spreadsheet and Fractal Geometry: Part 2 Root-finding using Newton Method and Creation of Newton Fractals
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 55 - Number 14 |
| Year of Publication: 2012 |
| Authors: K. P. Soman, Manu Unni V.g, Praveen Krishnan, V. Sowmya |
10.5120/8821-2742
|
K. P. Soman, Manu Unni V.g, Praveen Krishnan, V. Sowmya . Enhancing Computational Thinking with Spreadsheet and Fractal Geometry: Part 2 Root-finding using Newton Method and Creation of Newton Fractals. International Journal of Computer Applications. 55, 14 ( October 2012), 9-15. DOI=10.5120/8821-2742
Abstract
This article shows how Newton's iterative methods for finding root of a polynomial equation can be used to create fractals in spreadsheets. Newton's method has served as one of the most fruitful paradigms in the development of complex iteration theory. The process of iteration is impossible to carry out by hand but extremely easy to carry out with a computer. By doing such experiments students get a feeling that they have the power to explore the uncharted wilderness of the dynamics of Newton's method. It gives mathematics an experimental component. It also illustrates a symbiotic relationship between technology and mathematics [1]. Technology can be used to develop our intuition, and mathematics is used to prove that our intuition is correct. The article explores Innovative use of Microsoft Excel's What-if Analysis tool to do automation of repeated computation. The method employed can also be used for Neural Network training and data clustering [9] in Excel. A wide variety of fractals can be created by using different polynomial equations [2-7].
References
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- Barnsley,M. F. , Devaney,R. L. , Mandelbrot,B. B. , Peitgen,H. O. , Saupe,D. , Voss,R. F. , Heinz-Otto Peitgen, DietmarSaupe, "The science of Fractal Images", Springer-Verlag, 1988
- Barnsley,M. , "Fractals Everywhere", Academic Press Inc, 1988
- Falconer,K. , "Fractal Geometry: Mathematical Foundations and Applications",Wiley, 2003
- Peitgen,H. , Juergens,H. , and Saupe,D. , "Fractals for the Classroom",Springer-Verlag, New York, 1992
- Mumford,D. , Caroline Series David Wright , "Indra's Pearls: The Vision of Felix Klein" , Cambridge University Press, 2002
- Aravind, H. , Rajgopal, C. and Soman,K. P. , "A Simple Approach to Clustering in Excel", International Journal of Computer Applications 11(7):19–25, December 2010.
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