Location of Points on Plane and the Order of Disposition of Sum of Powers of Cardinal Coordinates
Article Abstract
This article exposed the structure of all orders of the sum of powers of cardinal coordinates with the explicitly determined computational disposition of similarity, between the coefficient of binomial expansion and the sum of powers of pairs of cardinal points on the plane. The proofs were achieved by a logical deployment of combinatorial techniques, laws of indices on powers of cardinal bases, and a comparison of corresponding results. The results proved conclusively that the sum of the powers of cardinal points is equal to the coefficients of the Binomial expansion with respect to the Pascal triangle pattern and entries. Theorem, the sum of powers of cardinal coordinate equals the corresponding elements of Binomial coefficient at every stage on a plane ʃn (x + y) = nCr : n ≥ 0, r ≤ n, r n ≥ 0.
Indexed Terms
sum power place of indices combination Pascal Bernoulli
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Ladan Umaru Ibrahim, Aliyu Nuhu Shuaibu, Tanko Ishaya1, Ahmed Tijjani Salawudeen, Kabiru Ahmed. "Location of Points on Plane and the Order of Disposition of Sum of Powers of Cardinal Coordinates." KIU Journal of Science, Engineering and Technology , vol. 1 , no. 2 , 2022 , pp. 1-8