Editing Back-of-the-envelope calculation (section)

== History ==
In the natural sciences, ''back-of-the-envelope calculation'' is often associated with physicist [[Enrico Fermi]],<ref>[https://web.archive.org/web/20080219101037/http://www.encyclopedia.com/doc/1G1-78334537.html Where Fermi stood. - Bulletin of the Atomic Scientists | Encyclopedia.com (Archived)<!-- Bot generated title -->]</ref> who was well known for emphasizing ways that complex scientific equations could be approximated within an [[order of magnitude]] using simple calculations. He went on to develop a series of sample calculations, which are called "Fermi Questions" or "Back-of-the-Envelope Calculations" and used to solve [[Fermi problem]]s.<ref>[http://serc.carleton.edu/quantskills/teaching_methods/boe/index.html  Back of the Envelope Calculations<!-- Bot generated title -->]</ref><ref>[http://www.nap.edu/html/hs_math/be.html High School Mathematics at Work: Essays and Examples for the Education of All Students<!-- Bot generated title -->]</ref>

Fermi was known for getting quick and accurate answers to problems that would stump other people. The most famous instance came during the [[first atomic bomb]] test in [[New Mexico]] on 16 July 1945. As the blast wave reached him, Fermi dropped bits of paper. By measuring the distance they were blown, he could compare to a previously computed table and thus estimate the bomb energy yield. He estimated 10 kilotons of TNT; the measured result was 18.6.<ref name="Rhodes 1986 p. 674">{{cite book | last=Rhodes | first=Richard | title=The Making of the Atomic Bomb | publisher=Simon & Schuster | publication-place=New York | year=1986 | isbn=978-0-671-44133-3 | oclc=13793436 | page=674}}</ref><ref>{{Cite web |url=http://www.lanl.gov/science/weapons_journal/wj_pubs/11nwj2-05.pdf |title=Nuclear Weapons Journal, Los Alamos National Laboratory, Issue 2 2005. |access-date=2014-09-07 |archive-date=2018-12-29 |archive-url=https://web.archive.org/web/20181229223636/https://www.lanl.gov/science/weapons_journal/wj_pubs/11nwj2-05.pdf |url-status=dead }}</ref>

Perhaps the most influential example of such a calculation was carried out over a period of a few hours by [[Arnold Wilkins]] after being asked to consider a problem by [[Robert Watson Watt]]. Watt had learned that the Germans claimed to have invented a radio-based death ray, but Wilkins' one-page calculations demonstrated that such a thing was almost certainly impossible. When Watt asked what role radio might play, Wilkins replied that it might be useful for detection at long range, a suggestion that led to the rapid development of [[radar]] and the [[Chain Home]] system.<ref>{{cite journal |first=B.A. |last=Austin |title=Precursors To Radar — The Watson-Watt Memorandum And The Daventry Experiment |url=http://www.bawdseyradar.org.uk/wp-content/uploads/2012/12/Wilkins-Calculations.pdf |journal=International Journal of Electrical Engineering & Education |volume=36 |year=1999 |issue=4 |pages=365–372 |doi=10.7227/IJEEE.36.4.10 |s2cid=111153288 |access-date=2016-07-08 |archive-url=https://web.archive.org/web/20150525040134/http://www.bawdseyradar.org.uk/wp-content/uploads/2012/12/Wilkins-Calculations.pdf |archive-date=2015-05-25 |url-status=dead }}</ref>

Another example is [[Victor Weisskopf]]'s pamphlet ''Modern Physics from an Elementary Point of View''.<ref>[http://cdsweb.cern.ch/record/274976/ Lectures given in the 1969 Summer Lecture Programme, CERN (European Organization for  Nuclear Research), CERN 70-8, 17 March 1970.]</ref> In these notes Weisskopf used back-of-the-envelope calculations to calculate the size of a hydrogen atom, a star, and a mountain, all using elementary physics.