Editing Blaise Pascal (section)

===Cycloid===
[[File:Pascal Pajou Louvre RF2981.jpg|thumb|upright|Pascal studying the [[cycloid]], by [[Augustin Pajou]], 1785, [[Louvre]]|alt=]]

In 1658, Pascal, while suffering from a toothache, began considering several problems concerning the cycloid. His toothache disappeared, and he took this as a heavenly sign to proceed with his research. Eight days later he had completed his essay<ref name="Ball_1960">{{cite book |last=Ball |first= W. W. Rouse |date=2010-09-16 |title=A Short Account of the History of Mathematics |url=https://www.gutenberg.org/files/31246/31246-pdf.pdf |location=New York, NY, USA |publisher=Dover Publications, Inc |page=234 |isbn=978-0486206301}}</ref> and, to publicize the results, proposed a contest.<ref name="Ferroli_1935">{{cite journal |last1=Ferroli |first1=D. |date=April 1935 |title=A Note on Blaise Pascal (1623-1662). A Forerunner of Leibnitz and Newton in the Discovery of the Calculus |url=https://www.jstor.org/stable/24221628 |journal=Current Science |volume=3 |issue=10 |pages=459–461 |jstor=24221628 |access-date=2024-03-02}}</ref>

Pascal proposed three questions relating to the [[Center of mass|center of gravity]], area and volume of the cycloid, with the winner or winners to receive prizes of 20 and 40 Spanish [[doubloon]]s. Pascal, [[Gilles de Roberval]] and [[Pierre de Carcavi]] were the judges, and neither of the two submissions (by [[John Wallis]] and [[Antoine de Lalouvère]]) were judged to be adequate.<ref>{{citation
| last=Conner
| first=James A.
| title=Pascal's Wager: The Man Who Played Dice with God
| pages=[https://archive.org/details/pascalswagermanw00conn/page/224 224]
| isbn=9780060766917
| edition=1st
| year=2006
| publisher=HarperCollins
| url-access=registration
| url=https://archive.org/details/pascalswagermanw00conn/page/224
}}</ref> While the contest was ongoing, [[Christopher Wren]] sent Pascal a proposal for a proof of the [[arc length|rectification]] of the cycloid; Roberval claimed promptly that he had known of the proof for years. Wallis published Wren's proof (crediting Wren) in Wallis's ''Tractus Duo'', giving Wren priority for the first published proof.
{{Clear}}