Euler's Formula
Pronunciation: /ˈɔɪ.lərz ˈfɔɹ.mjə.lə/ Explain
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Euler's formula is
.^{[1]}
It is remarkable in that it relates trigonometric function functions with complex
numbers. Euler's formula maps the natural constant
e
raised to the complex exponent
to the complex plane using the trigonometric expression
.
This equation is true only if the angle θ is measured
in radians.
Euler's formula is named after
Leonhard Euler
who published it in its present form in 1748. Leonard Euler was a very
prolific mathematician. Note that the phrase Euler's Formula is
used to indicate different formulas in different disciplines.

References
 McAdams, David E.. All Math Words Dictionary, euler's formula. 2nd Classroom edition 201501084799968. pg 73. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Paul J. Nahin. Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills. Princeton University Press. April 10, 2006. Last Accessed 7/9/2018. Buy the book
 Fine, Henry B., Ph. D.. NumberSystem of Algebra Treated Theoretically and Historically. 2nd edition. pg 30. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 7/9/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920pdf#page/n39/mode/1up. Buy the book
Cite this article as:
McAdams, David E. Euler's Formula. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/eulersformula.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
7/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (
McAdams, David E.)
1/29/2010: Added "References". (
McAdams, David E.)
12/23/2008: Initial version. (
McAdams, David E.)