Do binômio de Newton ao polinômio de Leibniz, demonstrações e aplicações

Abstract

The purpose of this work is to present Newton’s Binomial (1643-1727) focusing on its generalization given by Leibniz’s Polynomial (1646-1716) and its utilities for calculating probabilities, establishing connections with real or non-real contexts. The idea of enabling applications of Newton’s Binomial and Leibniz’s Polynomial through practical examples such as coin toss, probability of defeat and their use in genetics, aimed to show the applicability and usability of these tools in events of any nature. In addition, we detail, in the algebraic and combinatorial scope, the demonstrations of all the properties and theorems existing in the work, with the aim of the reader to satisfactorily reach an understanding of the concepts presented. Finally, it is worth noting that in the body of the work the reader will be introduced to the history of the concepts that will be worked on and of the mathematicians present.