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'''Introduction'''<br /> | '''Introduction'''<br /> | ||
| − | Euler's Number, written as <math>e</math>, | + | Euler's Number, written as <math>e</math>, has become one of the most important constants used in numerous different fields of mathematics. Its value is approximately 2.718; however, it is an irrational number, so its exact decimal representation is infinite. |
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| + | Jacob Bernoulli originally discovered an approximation for the constant in 1683 while doing work related to compounding interest. He discovered a limit for calculating compound interest which will be discussed later, but he could not determine the value of this limit. The only property he could determine about this constant was that it had to lie between 2 and 3. It was the first time a number was defined by taking the limit of a formula (O'Connor, Robertson, 2001). | ||
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| + | It would not be until Swiss mathematician Leonhard Euler studied the number in 1731 that the constant would be given the widely used symbol <math>e</math> and a value. He would also come up with a number of formulas to describe this new constant. | ||
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| + | Euler was born the son of an Evangelical-Reformed minister in Basel, Switzerland, on April 15, 1707, and 17 years later, Euler graduated from the University of Basel (1). After this, he was invited to join the Academy of Sciences in St. Petersburg, Russia where he became a professor of physics in 1730 and later a professor of matheamtics in 1733. In 1941, Euler, after being called to Berlin, became director of mathematics in the Academy of Sciences (Berlin) until 1766 when Euler decided that he would return to St. Petersburg to assume the position of director of the Academy of Sciences (St. Petersburg). Shortly after Euler returned, he became blind. Nonetheless, he continued to create books and papers. He died in St. Petersburg on September 7, 1783. (1) | ||
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| + | [[File:Leonhard-euler.jpg|framed|right|Leonhard Euler (1707 - 1883)]]<br /> | ||
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| + | Since the time it was discovered by Euler, the number has played important roles in a number of fields including but not limited to: finance, calculus, engineering, and physics. In the following sections, we discuss more about <math>e</math> and the unique ways in which it is used and makes appearances. | ||
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| + | <big>References</big><br> | ||
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| + | (1) Bradley, R., & Sandifer, C. (2007). Leonhard Euler life, work and legacy (Studies in the history and philosophy of mathematics; v. 5). Amsterdam; Oxford: Elsevier. <br /> | ||
| + | Leonard Euler. (1998). In Encyclopedia of World Biography. Detroit, MI: Gale. Retrieved from http://link.galegroup.com/apps/doc/K1631002086/BIC?u=purdue_main&sid=BIC&xid=f53da831<br /> | ||
| + | O'Connor, J. J., & Robertson, E. F. (2001, September). The number e. Retrieved from http://www-history.mcs.st-and.ac.uk/HistTopics/e.html <br /> | ||
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| + | [[Walther_MA279_Fall2018_topic3|Back to Mysteries of the Number e]] | ||
[[Category:MA279Fall2018Walther]] | [[Category:MA279Fall2018Walther]] | ||
Latest revision as of 00:01, 3 December 2018
Introduction
Euler's Number, written as $ e $, has become one of the most important constants used in numerous different fields of mathematics. Its value is approximately 2.718; however, it is an irrational number, so its exact decimal representation is infinite.
Jacob Bernoulli originally discovered an approximation for the constant in 1683 while doing work related to compounding interest. He discovered a limit for calculating compound interest which will be discussed later, but he could not determine the value of this limit. The only property he could determine about this constant was that it had to lie between 2 and 3. It was the first time a number was defined by taking the limit of a formula (O'Connor, Robertson, 2001).
It would not be until Swiss mathematician Leonhard Euler studied the number in 1731 that the constant would be given the widely used symbol $ e $ and a value. He would also come up with a number of formulas to describe this new constant.
Euler was born the son of an Evangelical-Reformed minister in Basel, Switzerland, on April 15, 1707, and 17 years later, Euler graduated from the University of Basel (1). After this, he was invited to join the Academy of Sciences in St. Petersburg, Russia where he became a professor of physics in 1730 and later a professor of matheamtics in 1733. In 1941, Euler, after being called to Berlin, became director of mathematics in the Academy of Sciences (Berlin) until 1766 when Euler decided that he would return to St. Petersburg to assume the position of director of the Academy of Sciences (St. Petersburg). Shortly after Euler returned, he became blind. Nonetheless, he continued to create books and papers. He died in St. Petersburg on September 7, 1783. (1)
Since the time it was discovered by Euler, the number has played important roles in a number of fields including but not limited to: finance, calculus, engineering, and physics. In the following sections, we discuss more about $ e $ and the unique ways in which it is used and makes appearances.
References
(1) Bradley, R., & Sandifer, C. (2007). Leonhard Euler life, work and legacy (Studies in the history and philosophy of mathematics; v. 5). Amsterdam; Oxford: Elsevier.
Leonard Euler. (1998). In Encyclopedia of World Biography. Detroit, MI: Gale. Retrieved from http://link.galegroup.com/apps/doc/K1631002086/BIC?u=purdue_main&sid=BIC&xid=f53da831
O'Connor, J. J., & Robertson, E. F. (2001, September). The number e. Retrieved from http://www-history.mcs.st-and.ac.uk/HistTopics/e.html
