#### Date of Award

5-1971

#### Document Type

Thesis

#### Degree Name

Master of Science

#### Department

Master of Mathematics

#### Abstract

This paper is centered around proving the irrationality of some common known real numbers. For several centuries man has been fascinated by irrational numbers such as 2 II, and e. Euclid gave an early proof of the irrationality of t2. Of course we now that It is irrational, and this fact shall be proved in this paper. Through the years mathematicians have developed various expressions that approximate the value of ll. Archimedes, a great mathematician of the ancient world, about 24.0 B. C. was able to establish that IX is between the numbers 22 and 22. In the Middle Ages1/l0 was often used as the value of IT in Europe and throughout the East. Now with our high-speed computers and mathematical knowledge of decimal expansions, H has been determined to many thousands of decimal places. Johann Heinrich Lambert (1728-1777), a Swiss-German mathematician, was the first to prove rigorously that the number I? is irrational. He showed that if X is rational, but not zero, then tan X cannot be rational: since tan IT = 1, it follows U that II , and also IT cannot be rational.

In this paper, the author shall also investigate whether roots of some real numbers are irrational in addition to proving that IT, e, and the common logarithm and trigonometric functions of certain real numbers are irrational.

#### Committee Chair/Advisor

Frederick R. Gray

#### Committee Member

Frank Hawkins

#### Committee Member

S.M. Lloyd

#### Publisher

Prairie View A. & M. College

#### Rights

© 2021 Prairie View A & M University

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

#### Date of Digitization

3/22/2022

#### Contributing Institution

John B Coleman Library

#### City of Publication

Prairie View

#### MIME Type

Application/PDF

#### Recommended Citation

Franklin, R. T. (1971). Elementary Proofs Of The Irrationality Of Some Real Numbers. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1374