GENERALIZED PASCAL’S TRIANGLE AND METALLIC RATIOS

Authors

  • Dr. R. Sivaraman Independent Research Scholar, California Public University, USA

DOI:

https://doi.org/10.29121/granthaalayah.v9.i7.2021.4109

Keywords:

Generalized Pascal’s Triangle, Metallic Ratio Of Order K, Binomial Coefficient, Hockey Stick Property, Binet’s Formula Respresentation

Abstract

In this paper, I had demonstrated the way to determine the sequence of metallic ratios by generalizing the usual Pascal’s triangle. In doing so, I found several interesting properties that had been discussed in detail in this paper. I had proved four new results upon generalizing Pascal’s triangle. Thus, the primary aim of this paper is to connect the idea of Generalized Pascal’s triangle with that to the sequence of metallic ratios.

Downloads

Download data is not yet available.

References

And, J. B. G. & Worley, A. (2019). Generalized Metallic Means, Fibonacci Quarterly. 57(1), 45–50.

Hare, K., Prodinger, H. & Shallit, A. J. (2014). Three Series For The Generalized Golden Mean, Fibonacci Quart. 52(4), 307–313.

Krcadinac, V. (2006). A New Generalization Of The Golden Ratio. Fibonacci Quarterly. 44(4), 335–340.

Passoja, D. (2015). Reflections On The Gold, Silver And Metallic Ratios. .

Sivaraman, Dr. R. (2021). Expressing Numbers in terms of Golden, Silver and Bronze Ratios. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12(2), 2876–2880. Retrieved from https://dx.doi.org/10.17762/turcomat.v12i2.2321 10.17762/turcomat.v12i2.2321 DOI: https://doi.org/10.17762/turcomat.v12i2.2321

Sivaraman, R. (2020). Exploring Metallic Ratios. Mathematics and Statistics 8(4), 388–391. Retrieved from https://dx.doi.org/10.13189/ms.2020.080403 10.13189/ms.2020.080403 DOI: https://doi.org/10.13189/ms.2020.080403

Sivaraman, R. (2021). Relation Between Terms Of Sequences And Integral Powers Of Metallic Ratios. Turkish Journal Of Physiotherapy And Rehabilitation 32(2), 1308–1311.

Published

2021-08-02

How to Cite

Sivaraman, R. (2021). GENERALIZED PASCAL’S TRIANGLE AND METALLIC RATIOS. International Journal of Research -GRANTHAALAYAH, 9(7), 164–169. https://doi.org/10.29121/granthaalayah.v9.i7.2021.4109