UOBScholar Hubhttps://scholarhub.balamand.edu.lbThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 01 Feb 2023 12:45:59 GMT2023-02-01T12:45:59Z5031On the Egyptian method of decomposing 2/n into unit fractionshttps://scholarhub.balamand.edu.lb/handle/uob/2331Title: On the Egyptian method of decomposing 2/n into unit fractions
Authors: Abdulaziz, Abdulrahman Ali
Abstract: A fraction whose numerator is one is called a unit fraction. Unit fractions have been the source of one of the most intriguing mysteries about the mathematics of antiquity. Except for 2/3, the ancient Egyptians expressed all fractions as sums of unit fractions. In particular, The Rhind Mathematical Papyrus (RMP) contains the decomposition of 2/n as the sum of unit fractions for odd n ranging from 5 to 101. The way 2/n was decomposed has been widely debated and no general method that works for all n has ever been discovered. In this paper we provide an elementary procedure that reproduces the decompositions as found in the RMP.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/23312008-01-01T00:00:00ZInteger sequences of the form α^n±β^nhttps://scholarhub.balamand.edu.lb/handle/uob/113Title: Integer sequences of the form α^n±β^n
Authors: Abdulaziz, Abdulrahman Ali
Abstract: Suppose that we want to find all integer sequences of the form α^n + β^ n , where α and β are complex numbers and n is a nonnegative integer. Since α^0 + β ^0 is always an integer, our task is then equivalent to determining all complex pairs (α, β) such that α^n + β^n ∈ Z, n > 0.
Sun, 01 Jan 2012 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/1132012-01-01T00:00:00ZOn the contraction ratio of iterated function systems whose attractors are Sierpinski n-gonshttps://scholarhub.balamand.edu.lb/handle/uob/5152Title: On the contraction ratio of iterated function systems whose attractors are Sierpinski n-gons
Authors: Abdulaziz, Abdulrahman Ali; Judy Said
Abstract: In this paper we apply the chaos game to n-sided regular polygons to generate fractals that are similar to the Sierpinski gasket. We show that for each n-gon, there is an exact ratio that will yield a perfect gasket. We then find a formula for this ratio that depends only on the angle π/n.
Fri, 01 Jan 2021 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/51522021-01-01T00:00:00Z