# Euler's Number

Pronunciation: /ˈɔɪ.lərz ˈnʌm.bər/ Explain

In mathematics, e represents a constant, sometimes called Euler's number after Leonhard Euler (1707-1783). The importance of this constant comes from its use for:

• The base of natural logarithms: • The base of growth functions: • Euler's equation that relates exponents and trigonometric functions: The value of e is approximately 2.71828. A more exact value of e can be calculated by one of several methods:

• • n 1/n! Sum (approx) This calculation uses the infinite sum 0 1/0! = 1/1 = 1 1 1 1/1! = 1/1 = 1 2 2 1/2! = 1/2 = 0.5 2.5 3 1/3! = 1/6 ≈ 0.16666667 2.66666667 4 1/4! = 1/24 ≈ 0.04166667 2.70833333 5 1/5! = 1/120 ≈ 0.00833333 2.71666667 6 1/6! = 1/720 ≈ 0.00138889 2.71805556 7 1/7! = 1/5040 ≈ 0.00019841 2.71825397 8 1/8! = 1/40320 ≈ 0.00002480 2.71827877 9 1/9! = 1/362880 ≈ 0.00000275 2.71828152 10 1/10! = 1/3628800 ≈ 0.00000027 2.71828179 11 1/11! = 1/39916800 ≈ 0.00000003 2.71828181 ... Table 1
1. McAdams, David E.. All Math Words Dictionary, euler's number. 2nd Classroom edition 20150108-4799968. pg 73. Life is a Story Problem LLC. January 8, 2015. Buy the book

McAdams, David E. Euler's Number. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/e.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)