Properties of Abiyev’s Triangle

Abstract: The procedure for writing Abiyev’s triangle using symmetric graphs has been explained. The Fibonacci and Lucas sequences are formed, respectively, by adding the numbers from the lines of the triangles on the left and right sides of this triangle. Symmetrical diagonal elements of these triangles generate Pascal's and analogous triangles, and vice versa. The diagonal numbers of these triangles make up the elements of the left and right triangles of Abiyev’s triangle. The numbers in the lines of these ultimate triangles represent the coefficients of the polynomial terms corresponding to the binomial a n ±b n =f n [(a+b),ab]. Mathematical conversions are considerably simpler when polynomials are used in the calculations. Examples of this have been provided. Using this method, we obtain a simple solution to one of the Ramanujan’s problems.