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| {{for|the Italian physiologist|Giovanni Vacca (doctor)}}
| | Alyson is the name people use to contact me and I believe it seems quite good when you say it. As a lady what she really likes is fashion and she's been performing it for fairly a whilst. My spouse and I live in Kentucky. For years she's been working as a travel agent.<br><br>my web page; online psychic readings ([http://Www.khuplaza.com/dent/14869889 khuplaza.com]) |
| {{Infobox scientist
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| |name = Giovanni Vacca
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| |box_width =
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| |image = Giovanni Vacca.jpg
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| |image_size = 180px
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| |caption =
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| |birth_date = {{Birth date|df=yes|1872|11|18}}
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| |death_date = {{Death date and age|df=yes|1953|1|6|1872|11|18}}
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| |birth_place = [[Genoa]], [[Italy]]
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| |death_place =[[Rome]], Italy
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| |nationality = Italian
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| |field = Mathematics
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| |known_for =
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| | notable_students =
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| |prizes =
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| }}
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| '''Giovanni Enrico Eugenio Vacca''' (18 November 1872 – 6 January 1953) was an [[Italian language|Italian]] [[mathematician]], [[Sinologist]] and historian of science.
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| Vacca studied mathematics and graduated from the [[University of Genoa]] in 1897 under the guidance of G. B. Negri. He was a politically active student and was banished for that from Genoa in 1897. He moved to [[Turin]] and became an assistant to [[Giuseppe Peano]]. In 1899 he studied, at [[Hanover]], unpublished manuscripts of [[Gottfried Wilhelm Leibniz]], which he published in 1903. Around 1898 Vacca became interested in Chinese language and culture after attending a Chinese exhibition in [[Turin]]. He took private lessons of Chinese and continued to study it at the [[University of Florence]]. Vacca then traveled to China in 1907–8 and defended a PhD in Chinese studies in 1910. In 1911, he became a lecturer in Chinese literature at the [[Sapienza University of Rome|University of Rome]]. In 1922, he moved to Florence and taught Chinese literature and language at university until 1947. <ref>{{MacTutor Biography|id=Vacca}}</ref>
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| The interests of Vacca were almost equally split between mathematics, Sinology and history of science, with a corresponding number of papers being 38, 47 and 45. In 1910, Vacca developed a [[complex number]] iteration for [[pi]]:<ref>G. Vacca. ''A new analytical expression for the number π and some historical considerations'', Bulletin of the American Mathematical Society (Ser. 2), 1910, vol.16, pp. 368–369</ref>
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| :<math>x_0 = i,\quad x_{n+1} = \frac{x_n + |x_n|}2,\qquad\lim_{n\to\infty} x_n = \frac2\pi.</math>
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| The calculation efficiency of these formulas is significantly worse than of the modern [[Borwein's algorithm]] – they converge by only about half a decimal point with each iteration.
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| Vacca published his two major contributions to mathematics in 1910 and 1926, on [[series expansion]] (later named Vacca series) of the [[Euler constant]]. They are, respectively
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| :<math>
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| \begin{align}
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| \gamma &= \sum_{k=2}^\infty (-1)^k \frac{ \left \lfloor \log_2 k \right \rfloor}{k}
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| = \tfrac12-\tfrac13
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| + 2\left(\tfrac14 - \tfrac15 + \tfrac16 - \tfrac17\right)
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| + 3\left(\tfrac18 - \cdots - \tfrac1{15}\right) + \cdots\\
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| \zeta(2) + \gamma &= \sum_{k=2}^\infty\left(\frac1{\lfloor \sqrt{k} \rfloor^2} - \frac1{k}\right)
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| = \sum_{k=2}^{\infty} \frac{k - \lfloor\sqrt{k}\rfloor^2}{k\lfloor\sqrt{k}\rfloor^2}
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| = \tfrac12 + \tfrac23 + \tfrac1{2^2}\left(\tfrac15 + \tfrac26 + \tfrac37 + \tfrac48\right)
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| + \tfrac1{3^2}\left(\tfrac1{10} + \cdots + \tfrac6{15}\right) + \cdots
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| \end{align}
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| </math><BR> | |
| Vacca noted in 1910 that:<ref>{{cite book|author1=[[James Joseph Sylvester]]|author2=[[James Whitbread Lee Glaisher]]|title=The Quarterly journal of pure and applied mathematics|url=http://books.google.com/books?id=Q4qXAAAAMAAJ|accessdate=16 August 2011|year=1910|publisher=J.W. Parker|page=364}}</ref>
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| :''There is some hope that this series can be of some use in the proof of the irrationality of <math>\gamma</math>, a very difficult problem, proposed, but not resolved, in the Correspondence, recently published, between [[Charles Hermite|Hermite]] und [[Thomas Joannes Stieltjes|Stieltjes]].''
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| ==References==
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| {{reflist}}
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| {{Authority control|VIAF=90248804}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Vacca, Giovanni Enrico Eugenio
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Italian mathematician
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| | DATE OF BIRTH = 18 November 1872
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| | PLACE OF BIRTH = [[Genoa]], [[Italy]]
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| | DATE OF DEATH = 6 January 1953
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| | PLACE OF DEATH = [[Rome]], Italy
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| }}
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| {{DEFAULTSORT:Vacca, Giovanni Enrico Eugenio}}
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| [[Category:1872 births]]
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| [[Category:1953 deaths]]
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| [[Category:19th-century Italian mathematicians]]
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| [[Category:20th-century Italian mathematicians]]
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| [[Category:Historians of science]]
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| [[Category:Historians of mathematics]]
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Alyson is the name people use to contact me and I believe it seems quite good when you say it. As a lady what she really likes is fashion and she's been performing it for fairly a whilst. My spouse and I live in Kentucky. For years she's been working as a travel agent.
my web page; online psychic readings (khuplaza.com)