Origin of Irrational Numbers and Their Approximations

Computation

Hans Agarwal¹  RaviP. Agarwal² 

[1] 749 Wyeth Street, Melbourne, FL 32904, USA;Department of Mathematics, Texas A&M University-Kingsville, 700 University Blvd., Kingsville, TX 78363, USA;

关键词: irrational numbers;    transcendental numbers;    rational approximations;    history;   

DOI  :  10.3390/computation9030029

来源: DOAJ

【 摘 要 】

In this article a sincere effort has been made to address the origin of the incommensurability/irrationality of numbers. It is folklore that the starting point was several unsuccessful geometric attempts to compute the exact values of $\sqrt{2}$ and $\pi .$ Ancient records substantiate that more than 5000 years back Vedic Ascetics were successful in approximating these numbers in terms of rational numbers and used these approximations for ritual sacrifices, they also indicated clearly that these numbers are incommensurable. Since then research continues for the known as well as unknown/expected irrational numbers, and their computation to trillions of decimal places. For the advancement of this broad mathematical field we shall chronologically show that each continent of the world has contributed. We genuinely hope students and teachers of mathematics will also be benefited with this article.

【 授权许可】

Unknown