Author(s)

Balasubramani Prema Rangasamy

Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India.

Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.

Fibonacci Series, Lucas Series, Golden Ratio, Various Type of Fibonacci Series Generated by Matrices, Matrix Operations on Pascal’s Elements and Hex Numbers

Rangasamy, B. (2020) Non Degeneration of Fibonacci Series, Pascal’s Elements and Hex Series. Advances in Pure Mathematics, 10, 393-404. doi: 10.4236/apm.2020.107024.