International Journal of Engineering Science Invention (IJESI) ISSN (Online): 2319 – 6734, ISSN (Print): 2319 – 6726 www.ijesi.org ||Volume 7 Issue 6 Ver V || June 2018 || PP 28-34 www.ijesi.org 28 | Page A Brief Historical Overview Of the Gaussian Curve: From Abraham De Moivre to Johann Carl Friedrich Gauss Edel Alexandre Silva Pontes 1 1 Department of Mathematics, Federal Institute of Alagoas, Brazil Abstract : If there were only one law of probability to be known, this would be the Gaussian distribution. Faced with this uneasiness, this article intends to discuss about this distribution associated with its graph called the Gaussian curve. Due to the scarcity of texts in the area and the great demand of students and researchers for more information about this distribution, this article aimed to present a material on the history of the Gaussian curve and its relations. In the eighteenth and nineteenth centuries, there were several mathematicians who developed research on the curve, including Abraham de Moivre, Pierre Simon Laplace, Adrien-Marie Legendre, Francis Galton and Johann Carl Friedrich Gauss. Some researchers refer to the Gaussian curve as the "curve of nature itself" because of its versatility and inherent nature in almost everything we find. Virtually all probability distributions were somehow part or originated from the Gaussian distribution. We believe that the work described, the study of the Gaussian curve, its history and applications, is a valuable contribution to the students and researchers of the different areas of science, due to the lack of more detailed research on the subject. Keywords - History of Mathematics, Distribution of Probabilities, Gaussian Curve. -------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 09-06-2018 Date of acceptance: 25-06-2018 --------------------------------------------------------------------------------------------------------------------------------------- I. INTRODUCTION If there were only one law of probability to be known, this would be the Normal distribution or Gaussian distribution or Laplace-Gauss distribution. After all, who is the creator of this major distribution of probabilities? Faced with this uneasiness, this article intends to discuss about this distribution associated with its graph called the normal curve or Gaussian curve or Laplace-Gauss curve. For reasons of didactic and nomenclature of the text we will adopt Gaussian distribution associated with its Gaussian curve graph. The history of the Gaussian curve is related to the discovery of probability theory. In the eighteenth and nineteenth centuries, there were several mathematicians who developed research on the curve, including Abraham de Moivre, Pierre Simon Laplace, Adrien-Marie Legendre, Francis Galton and Johann Carl Friedrich Gauss. The Gaussian curve is the most important distribution of probabilities [2] [3] and physical, biological, psychological, social and financial phenomena can be adequately modeled by it. In the early nineteenth century, mathematicians Laplace and Gauss have two primary tools in Statistics: (a) The Use of Gaussian Distribution, not only as an approximation of the Binomial Distribution, to describe errors. (b) For large samples, the use of the Gaussian Distribution as an approximate distribution of the mean - Central Limit Theorem or Laplace Theorem. . In this way, this article aimed to present a material on the history of the Gaussian curve and its relations, due to the scarcity of texts in the area and the great demand of students and researchers for more information about this distribution. II. CONTRIBUTIONS OF MAJOR MATHEMATICIANS OF THE 17TH AND 14TH CENTURIES [5] Abraham de Moivre (Figure 1) was born in France, May 26, 1667. French mathematician exiled in England, several were his contributions to science, among them, the Formula de De Moivre, which relates the complex numbers with trigonometry and , especially the Normal Curve in probability theory. In 1711 he published Philosophical Transactions a work on the laws of chance. In 1725, he used scientific bases and actuarial methods for calculating life insurance.