Date of Award


Document Type


Degree Name

Master of Science

Degree Discipline



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


Prairie View A. & M. College


© 2021 Prairie View A & M University

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

Date of Digitization


Contributing Institution

John B Coleman Library

City of Publication

Prairie View





To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.