A Property of Pascal's Triangle that Helps to Simplify the Euler-Poisson Equation for a Class of Optimization Problems

Numbers in the Nth row of Pascal's triangle represent binomial coefficients C(N, k), k = 0, 1, ..., N. I describe a relationship between the numbers in rows and in “diagonals” of Pascal's triangle, provide an example and prove the formula. I show how this property appears useful for simplifying the Euler-Poisson equation for a class of optimization problems with constraints. A particular case of such optimization problems is finding geometric paths along which the maximally smooth trajectories have constant speed

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Year of publication:	2014
Authors:	Polyakov, Felix
Publisher:	[2014]: [S.l.] : SSRN
Subject:	Mathematische Optimierung \| Mathematical programming \| Theorie \| Theory

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