LUCAS NUMBERS TRIANGLE
| Autor: | Dr. R. Sivaraman |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| DOI: | 10.5281/zenodo.5758677 |
| Popis: | Among several number triangles that exist in mathematics, Pascal���s triangle is well known for its extra-ordinary combinatorial properties and applications. It is well known that stacking entries of Pascal���s triangle in a particular fashion and adding them in North ��� East diagonal direction, we can generate Fibonacci numbers. In this paper, I will introduce a number triangle constructed similar to Pascal���s triangle through which I have proved eight interestingand new mathematical properties and also have generated Lucas numbers which is connected with Golden Ratio. {"references":["1.\tR. Sivaraman, Number Triangles and Metallic Ratios, International Journal of Engineering and Computer Science, Volume 10, Issue 8, pp. 25365 – 25369. 2.\tR. Sivaraman, Generalized Pascal's Triangle and Metallic Ratios, International Journal of Research, Volume 9, Issue 7, pp. 179 – 184. 3.\tR. Sivaraman, Summing Through Pascal and Power Matrices, Bulletin of Mathematics and Statistics Research, Vol. 9, Issue 2, 2021, pp. 1 – 8. 4.\tKrcadinac V., A new generalization of the golden ratio. Fibonacci Quarterly, 2006;44(4):335–340. 5.\tK. Hare, H. Prodinger, and J. Shallit, Three series for the generalized golden mean, Fibonacci Quart. 52(2014), no. 4, 307–313. 6.\tJuan B. Gil and Aaron Worley, Generalized Metallic Means, Fibonacci Quarterly, Volume 57 (2019), Issue. 1, 45-50. 7.\tR. Sivaraman, Generalized Lucas, Fibonacci Sequences and Matrices, Purakala, Volume 31, Issue 18, April 2020, pp. 509 – 515. 8.\tR. Sivaraman, Exploring Metallic Ratios, Mathematics and Statistics, Horizon Research Publications, Volume 8, Issue 4, (2020), pp. 388 – 391."]} |
| Databáze: | OpenAIRE |
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