Abstract / Excerpt:

Abstract: This study explores methods to derive one of the most popular and highly applicable formula to compute the binomial coefficients, the binomial formula. Principles and ideas in the field of numerical analysis were utilized to derive the formula. The Pascal triangle and its transformation through translation were analyzed and utilized to determine the interpolating polynomials which passes through all the points of the Pascal Triangle by columns. Using the Newton's Divided Difference formula, the sets of interpolating polynomials were computed. These sets of interpolating polynomials were proved to work for any size of the parameter r and n by mathematical induction. These two sets of formulas conform with the binomial formulas. In this study, there were two approaches used to derive the formula for C (n,r). Using Pascal triangle, sets of interpolating polynomials, Pn(X), is derived. Another approach is through the use of the modified Pascal triangle, a second set of interpolating polynomial Pn(x) is derived. It is recommended to explore other types of transformation of Pascal triangle other than translation to derive the formula for C9n,r). in addition, further study may be done by finding the bivariate interpolating polynomial or function or functions to compute or approximate C9n,r) when n and r are non-integral values.

Info

Source Institution	Ateneo de Davao University
Unit	Natural Science
Authors	Opol, Rito C.
Page Count	1
Place of Publication	Davao City
Original Publication Date	March 4, 2002
Tags	Dissertations, Mathematics, Study and Teaching

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