Keywords:-
Article Content:-
Abstract
Among several interesting number triangles that exist in mathematics, Pascal’s triangle is one of the best triangle possessing rich mathematical properties. In this paper, I will introduce a number triangle containing triangular numbers arranged in particular fashion. Using this number triangle, I had proved five interesting theorems which help us to generate Pythagorean triples as well as establish bijection between whole numbers and set of all integers.
References:-
References
Thomas Koshy, Triangular Arrays with Applications. Oxford University Press, New York, 2011.
R.P. Stanley, Enumerative Combinatorics, Volume 1, Cambridge University Press, 1997.
T. Mansour, Combinatorics of Set Partitions, CRC Press, 2013.
D. I.A. Cohen, Basic Techniques of Combinatorial Theory, John Wiley & Sons, 1978.
R. Sivaraman, Polygonal Properties of Number Triangle, German International Journal of Modern Science, 17, 2021, pp. 10 – 14.
R. Sivaraman, Fraction Tree, Fibonacci Sequence and Continued Fractions, International Conference on Recent Trends in Computing (ICRTCE – 2021), Journal of Physics: Conference Series, IOP Publishing, 1979 (2021) 012039, 1 – 10.
Krcadinac V., A new generalization of the golden ratio. Fibonacci Quarterly, 2006;44(4):335–340.
R. Sivaraman, Number Triangles and Metallic Ratios, International Journal of Engineering and Computer Science, Volume 10, Issue 8, 2021, pp. 25365 – 25369.