Irrationality and Some Historical Remarks on Euler’s Number e
Abstract
One of the most important constants of mathematics is the Euler’s number e. Many world mathematicians have studied the properties of number e and this number has an irreplaceable place not only in mathematics but also in other scientific disciplines. In the first part of the article we will focus on the introduction of the number e from a historical view and we will show some of its important features. The irrationality of the number e was first proven by Leonhard Euler in 1737. We present one of the possible proofs in the second part of this article.
- Keywords
- Leonhard Euler, number e, irrational, proof, historical remarks
- Classification
- 11A99, 01A99
References
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[2] Hablik M. (2011). 5 Million Digits of Euler's Constant ??. Amazon Digital Services LLC, e-book.
[3] Šalát T. (1977). e. In: Matematické obzory 10/1976. Bratislava: JSMF, p. 43-56.
[4] Allendoerfer O. (1969). Principles of Mathematics. US: McGraw-Hill, Inc. ISBN: 9780070013902.
[5] Keng H. L. (1982). Introduction to Number Theory. New York: Springer-Verlag, ISBN 3-540-10818-1.
[6] Vít P. (1982): Řetězové zlomky. Prague: Mladá fronta.
[2] Hablik M. (2011). 5 Million Digits of Euler's Constant ??. Amazon Digital Services LLC, e-book.
[3] Šalát T. (1977). e. In: Matematické obzory 10/1976. Bratislava: JSMF, p. 43-56.
[4] Allendoerfer O. (1969). Principles of Mathematics. US: McGraw-Hill, Inc. ISBN: 9780070013902.
[5] Keng H. L. (1982). Introduction to Number Theory. New York: Springer-Verlag, ISBN 3-540-10818-1.
[6] Vít P. (1982): Řetězové zlomky. Prague: Mladá fronta.