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| '''Giulio Carlo''', '''Count Fagnano''', and '''Marquis de Toschi''' (December 6, 1682 – September 26, 1766) was an [[Italy|Italian]] [[mathematician]]. He was probably the first to direct attention to the theory of [[elliptic integral]]s. Fagnano was born in [[Senigallia]]. | | The writer is known as Irwin Wunder but it's not the most masucline name out there. Playing baseball is the hobby he will by no means stop performing. For a while she's been in South Dakota. My day job is a meter reader.<br><br>Check out my website: [http://kpchurch.org/?document_srl=1359143 http://kpchurch.org] |
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| ==Work==
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| Fagnano is best known for investigations on the length and division of arcs of certain curves, especially the [[Lemniscate of Bernoulli|lemniscate]]; this seems also to have been in his own estimation his most important work, since he had the figure of the lemniscate with the inscription: "Multifariam divisa atque dimensa Deo veritatis gloria", engraved on the title-page of his ''Produzioni Matematiche'', which he published in two volumes (Pesaro, 1750), and dedicated to [[Pope Benedict XIV]]. The same figure and words "Deo veritatis gloria" also appear on his tomb.
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| Failing to [[arc length|rectify]] the [[ellipse]] or [[hyperbola]], Fagnano attempted to determine [[Arc (geometry)|arc]]s whose difference should be [[rectifiable curve|rectifiable]]. He also pointed out the remarkable analogy existing between the [[integral]]s which represent the arc of a [[circle]] and the arc of a lemniscate. Finally he proved the formula
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| :<math>\pi = 2i\log{1 - i \over 1 +i}</math>
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| where ''i'' stands for <math>\sqrt{-1}</math>.
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| His works were collected and published in two volumes at [[Pesaro]] in 1750.
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| Some mathematicians objected to his methods of analysis founded on the [[infinitesimal calculus]]. The most prominent of these were [[Vincenzo Viviani|Viviani]], [[Philippe de La Hire|De la Hire]] and [[Michel Rolle|Rolle]].
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| ==Life==
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| He made his higher studies at the [[Collegio Clementino]] in [[Rome]] and there won great distinction, except in mathematics, to which his aversion was extreme. Only after his college course he took up the study of mathematics. Later, without help from any teacher, he mastered mathematics from its foundations. His most important research was published in the ''Giornale de' Letterati d'Italia''.
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| ==References==
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| {{Rouse History of Mathematics}}
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| {{catholic}}
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| ==External links==
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| * {{MacTutor Biography|id=Fagnano_Giulio}}
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| {{Authority control|VIAF=27850041}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Fagnano, Giulio Carlo
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Italian mathematician
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| | DATE OF BIRTH = December 6, 1682
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| | PLACE OF BIRTH =
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| | DATE OF DEATH = September 26, 1766
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Fagnano, Giulio Carlo}}
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| [[Category:1682 births]]
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| [[Category:1766 deaths]]
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| [[Category:People from Senigallia]]
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| [[Category:18th-century Italian mathematicians]]
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| [[Category:17th-century Italian mathematicians]]
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| [[Category:Fellows of the Royal Society]]
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| {{Italy-mathematician-stub}}
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The writer is known as Irwin Wunder but it's not the most masucline name out there. Playing baseball is the hobby he will by no means stop performing. For a while she's been in South Dakota. My day job is a meter reader.
Check out my website: http://kpchurch.org