Editing Pi (section)

=== Motives for computing <span class="texhtml mvar" style="font-style:italic;">π</span> ===
[[File:Record pi approximations.svg|thumb|As mathematicians discovered new algorithms, and computers became available, the number of known decimal digits of {{pi}} increased dramatically. The vertical scale is [[logarithmic scale|logarithmic]].|upright=1.3]]
For most numerical calculations involving {{pi}}, a handful of digits provide sufficient precision. According to Jörg Arndt and Christoph Haenel, thirty-nine digits are sufficient to perform most [[cosmological]] calculations, because that is the accuracy necessary to calculate the circumference of the [[observable universe]] with a precision of one atom. Accounting for additional digits needed to compensate for computational [[round-off error]]s, Arndt concludes that a few hundred digits would suffice for any scientific application. Despite this, people have worked strenuously to compute {{pi}} to thousands and millions of digits.{{sfn|Arndt|Haenel|2006|pp=17–19}} This effort may be partly ascribed to the human compulsion to break records, and such achievements with {{pi}} often make headlines around the world.<ref>{{cite news |title=John W. Wrench, Jr.: Mathematician Had a Taste for Pi |first=Matt |last=Schudel |newspaper=The Washington Post |date=25 March 2009 |page=B5}} {{pb}} {{cite news |title=The Big Question: How close have we come to knowing the precise value of pi? |url=https://www.independent.co.uk/news/science/the-big-question-how-close-have-we-come-to-knowing-the-precise-value-of-pi-1861197.html |newspaper=The Independent |date=8 January 2010 |access-date=14 April 2012 |location=London |first=Steve |last=Connor |url-status=live |archive-url=https://web.archive.org/web/20120402220803/http://www.independent.co.uk/news/science/the-big-question-how-close-have-we-come-to-knowing-the-precise-value-of-pi-1861197.html |archive-date=2 April 2012}}</ref> They also have practical benefits, such as testing [[supercomputer]]s, testing numerical analysis algorithms (including [[Multiplication algorithm#Fast multiplication algorithms for large inputs|high-precision multiplication algorithms]]); and within pure mathematics itself, providing data for evaluating the randomness of the digits of {{pi}}.{{sfn|Arndt|Haenel|2006|pp=17-18}}<ref>{{cite journal |last1=Bailey |first1=David H. |author-link1=David H. Bailey (mathematician) |last2=Plouffe |first2=Simon M. |last3=Borwein |first3=Peter B. |last4=Borwein |first4=Jonathan M. |title=The quest for PI |journal=[[The Mathematical Intelligencer]] |volume=19 |issue=1 |year=1997 |pages=50–56 |issn=0343-6993 |doi=10.1007/BF03024340 |citeseerx=10.1.1.138.7085 |s2cid=14318695}}</ref>