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{{Short description|Austrian mathematician and physicist}}
{{Use dmy dates|date=February 2021}}
{{Infobox scientist
{{Infobox scientist
|name = Andreas von Ettingshausen
| name = Andreas von Ettingshausen
|image = Andreas von Ettingshausen.jpg
| image = Andreas von Ettingshausen.jpg
|image_size = 220px
| image_size =
|caption = Andreas Freiherr von Ettingshausen (1796–1878)
| caption =
|birth_date = 25 November 1796
| birth_date = 25 November 1796
|birth_place = [[Heidelberg]], [[Electorate of the Palatinate]]
| birth_place = [[Heidelberg]], [[Electorate of the Palatinate]]
|death_date = {{death-date and age|25 May 1878|25 November 1796}}
| death_date = {{death-date and age|25 May 1878|25 November 1796}}
|death_place = [[Vienna]], [[Austria-Hungary]]
| death_place = [[Vienna]], [[Austria-Hungary]]
| children = Carolina Augusta von Ettingshausen, grandmother of [[Rudolf Allers]]
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|residence = Austria
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| fields = [[Physicist]] and [[mathematician]]
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|citizenship =
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| workplaces = [[University of Innsbruck]]<br/>[[University of Vienna]]<br/>[[Vienna University of Technology|Vienna Polytechnic Institute]]
|nationality = Austrian
|ethnicity =
| alma_mater = [[University of Vienna]]
| doctoral_advisor =
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|fields = [[Physicist]] and [[mathematician]]
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| academic_advisors = Ignaz Lindner<ref>Andreas von Ettingshausen, ''Vorlesungen über die höhere Mathematik: Vorlesungen über die Analysis'', Volume 1, Gerold, 1827, p. v.</ref>
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|workplaces = [[University of Innsbruck]]<br>[[University of Vienna]]<br>[[Vienna University of Technology|Vienna Polytechnic Institute]]
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| doctoral_students = [[Ernst Mach]]<br/>[[Francesco Rossetti]]<br/>[[Jožef Stefan]]<br/>[[Viktor von Lang]]
|alma_mater = [[University of Vienna]]
|doctoral_advisor =
| notable_students =
| known_for = [[Electric machine]]s
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|academic_advisors = [[Ignaz Lindner]]<ref>Andreas von Ettingshausen, ''Vorlesungen über die höhere Mathematik: Vorlesungen über die Analysis'', Volume 1, Gerold, 1827, p. v.</ref>
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| author_abbrev_bot =
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|doctoral_students = [[Ernst Mach]]<br>[[Jožef Stefan]]<br>[[Viktor von Lang]]
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| author_abbrev_zoo =
|notable_students =
|known_for = [[Electric machine]]s
| influences =
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| influenced =
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|author_abbrev_bot =
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| awards =
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|author_abbrev_zoo =
|influences =
| religion =
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| signature = <!--(filename only)-->
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}}
}}


'''Andreas Freiherr von Ettingshausen''' (25 November 1796 – 25 May 1878) was a [[Austrians|Austrian]] [[mathematician]] and [[physicist]].
'''Andreas Freiherr von Ettingshausen''' (25 November 1796 – 25 May 1878) was an Austrian [[mathematician]] and [[physicist]].


⚫
Ettingshausen studied [[philosophy]] and [[jurisprudence]] at the [[University of Vienna]]. In 1817, he joined the University of Vienna and taught mathematics and physics as an [[adjunct professor]]. In 1819, he became professor of physics at the [[University of Innsbruck]] and 1821 professor of higher mathematics at the [[University of Vienna]]. His lectures of that time marked a new era for the [[University of Vienna]], and they were published in 1827 in two volumes. In 1834 Ettingshausen became the chair of physics.
==Biography==
⚫
Ettingshausen studied [[philosophy]] and [[jurisprudence]] at the [[University of Vienna]]. In 1817, he joined the University of Vienna and taught mathematics and physics as an [[adjunct professor]]. In 1819 he became professor of physics at the [[University of Innsbruck]] and 1821 professor of higher mathematics at the [[University of Vienna]]. His lectures of that time marked a new era for the [[University of Vienna]], and they were published in 1827 in 2 volumes. In 1834 Ettingshausen became the chair of physics.


Ettingshausen was the first to design an [[Electric machine|electromagnetic machine]], which used the electrical induction for power generation. He promoted [[optics]] and wrote a textbook of physics. His method of lecturing was widely influential. In addition he wrote a book on [[combinatorial analysis]] (Vienna 1826). In 1866, he retired.
Ettingshausen was the first to design an [[Electric machine|electromagnetic machine]], which used the electrical induction for power generation. He promoted [[optics]] and wrote a textbook of physics. His method of lecturing was widely influential. In addition he wrote a book on [[combinatorial analysis]] (Vienna 1826). In 1866, he retired.


Among his lasting impacts in mathematics is the introduction of the notation <math> \tbinom nk </math> for the [[binomial coefficient]], which is the [[coefficient]] of ''x<sup>k</sup>'' in the expansion of the [[binomial (polynomial)|binomial]] (''x''+1)<sup>''n''</sup> and, more generally, the number of ''k''-[[element (set theory)|element]] [[subsets]] of an ''n''-element [[set (mathematics)|set]].<ref>{{cite book|last1=Ettingshausen|first1=Andreas von|title=Die combinatorische Analysis als Vorbereitungslehre zum Studium der theoretischen höhern Mathematik|trans-title=Combinatorial analysis as preparatory instruction for the study of theoretical higher mathematics|date=1826|publisher=J.B. Wallishauffer|location=Vienna, Austria|pages=30, 31|url=https://archive.org/stream/diecombinatoris00ettigoog#page/n71/mode/2up|language=German}} From p. 30: ''"Da wir im Folgenden sehr häufig Gelegenheit haben werden, von dem numerischen Ausdrucke dieser Menge Gebrauch zu machen, so wollen wir dafür das Zeichen (n k) wählen, und es mit dem Worten n über k ausprechen, wobei die obere Zahl stets die Anzahl der combinirten Elemente, die untere aber den Rang der Combinationsklasse angibt."'' (Since we will very frequently have occasion in the following to make use of numerical expressions of these quantities, then we will choose for that purpose the symbol (n k) and will express it with the words "n over k", whereby the upper number always specifies the number of combined elements whereas the lower [number] specifies the rank of the classes of combinations.)
Among his lasting impacts in mathematics is the introduction of the notation <math>\binom{n}{k}</math> for the [[binomial coefficient]], which is the [[coefficient]] of <math>x^k</math> in the expansion of the [[binomial (polynomial)|binomial]] <math>(1+x)^k</math> and, more generally, the number of <math>k</math>-[[element (set theory)|element]] [[subsets]] of an <math>n</math>-element [[set (mathematics)|set]].<ref>{{cite book|last1=Ettingshausen|first1=Andreas von|title=Die combinatorische Analysis als Vorbereitungslehre zum Studium der theoretischen höhern Mathematik|trans-title=Combinatorial analysis as preparatory instruction for the study of theoretical higher mathematics|date=1826|publisher=J.B. Wallishauffer|location=Vienna, Austria|pages=30, 31|url=https://archive.org/stream/diecombinatoris00ettigoog#page/n71/mode/2up|language=German}} From p. 30: ''"Da wir im Folgenden sehr häufig Gelegenheit haben werden, von dem numerischen Ausdrucke dieser Menge Gebrauch zu machen, so wollen wir dafür das Zeichen (n k) wählen, und es mit dem Worten n über k ausprechen, wobei die obere Zahl stets die Anzahl der combinirten Elemente, die untere aber den Rang der Combinationsklasse angibt."'' (Since we will very frequently have occasion in the following to make use of numerical expressions of these quantities, then we will choose for that purpose the symbol (n k) and will express it with the words "n over k", whereby the upper number always specifies the number of combined elements whereas the lower [number] specifies the rank of the classes of combinations.)
Page 31 shows that (n k) = n! / k! (n-k)! .</ref><ref>{{cite book |author=[[Nicholas J. Higham]] |title=Handbook of Writing for the Mathematical Sciences |publisher=[[Society for Industrial and Applied Mathematics]] |isbn=0-89871-420-6 |page=25}}</ref>
Page 31 shows that (n k) = n! / k! (n-k)! .</ref><ref>{{cite book |author=Nicholas J. Higham |title=Handbook of Writing for the Mathematical Sciences |url=https://archive.org/details/handbookofwritin0000high |url-access=registration |publisher=[[Society for Industrial and Applied Mathematics]] |isbn=0-89871-420-6 |page=[https://archive.org/details/handbookofwritin0000high/page/25 25]|author-link=Nicholas Higham |year=1998 }}</ref>

His daughter Carolina Augusta von Ettingshausen was the grandmother of [[Rudolf Allers]].


== References ==
== References ==
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[[Category:19th-century Austrian people]]
[[Category:Austrian scientists]]
[[Category:Austrian physicists]]
[[Category:German scientists]]
[[Category:German physicists]]
[[Category:Austrian mathematicians]]
[[Category:German mathematicians]]
[[Category:University of Vienna alumni]]
[[Category:University of Vienna alumni]]
[[Category:University of Vienna faculty]]
[[Category:Academic staff of the University of Vienna]]
[[Category:University of Innsbruck faculty]]
[[Category:Academic staff of the University of Innsbruck]]
[[Category:German untitled nobility]]
[[Category:German untitled nobility]]
[[Category:Austrian people of German descent]]
[[Category:Scientists from Heidelberg]]
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[[Category:People from Heidelberg]]
[[Category:1796 births]]
[[Category:1796 births]]
[[Category:1878 deaths]]
[[Category:1878 deaths]]
[[Category:Austro-Hungarian mathematicians]]
[[Category:Mathematicians from Austria-Hungary]]
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[[Category:Mathematicians from the Austrian Empire]]
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[[Category:Physicists from Austria-Hungary]]

Latest revision as of 01:38, 24 May 2024

Andreas von Ettingshausen
Born25 November 1796
Heidelberg, Electorate of the Palatinate
Died25 May 1878 (1878-05-26) (aged 81)
Vienna, Austria-Hungary
Alma materUniversity of Vienna
Known forElectric machines
ChildrenCarolina Augusta von Ettingshausen, grandmother of Rudolf Allers
Scientific career
FieldsPhysicist and mathematician
InstitutionsUniversity of Innsbruck
University of Vienna
Vienna Polytechnic Institute
Academic advisorsIgnaz Lindner[1]
Doctoral studentsErnst Mach
Francesco Rossetti
Jožef Stefan
Viktor von Lang

Andreas Freiherr von Ettingshausen (25 November 1796 – 25 May 1878) was an Austrian mathematician and physicist.

Ettingshausen studied philosophy and jurisprudence at the University of Vienna. In 1817, he joined the University of Vienna and taught mathematics and physics as an adjunct professor. In 1819, he became professor of physics at the University of Innsbruck and 1821 professor of higher mathematics at the University of Vienna. His lectures of that time marked a new era for the University of Vienna, and they were published in 1827 in two volumes. In 1834 Ettingshausen became the chair of physics.

Ettingshausen was the first to design an electromagnetic machine, which used the electrical induction for power generation. He promoted optics and wrote a textbook of physics. His method of lecturing was widely influential. In addition he wrote a book on combinatorial analysis (Vienna 1826). In 1866, he retired.

Among his lasting impacts in mathematics is the introduction of the notation for the binomial coefficient, which is the coefficient of in the expansion of the binomial and, more generally, the number of -element subsets of an -element set.[2][3]

His daughter Carolina Augusta von Ettingshausen was the grandmother of Rudolf Allers.

References

[edit]
  1. ^ Andreas von Ettingshausen, Vorlesungen über die höhere Mathematik: Vorlesungen über die Analysis, Volume 1, Gerold, 1827, p. v.
  2. ^ Ettingshausen, Andreas von (1826). Die combinatorische Analysis als Vorbereitungslehre zum Studium der theoretischen höhern Mathematik [Combinatorial analysis as preparatory instruction for the study of theoretical higher mathematics] (in German). Vienna, Austria: J.B. Wallishauffer. pp. 30, 31. From p. 30: "Da wir im Folgenden sehr häufig Gelegenheit haben werden, von dem numerischen Ausdrucke dieser Menge Gebrauch zu machen, so wollen wir dafür das Zeichen (n k) wählen, und es mit dem Worten n über k ausprechen, wobei die obere Zahl stets die Anzahl der combinirten Elemente, die untere aber den Rang der Combinationsklasse angibt." (Since we will very frequently have occasion in the following to make use of numerical expressions of these quantities, then we will choose for that purpose the symbol (n k) and will express it with the words "n over k", whereby the upper number always specifies the number of combined elements whereas the lower [number] specifies the rank of the classes of combinations.) Page 31 shows that (n k) = n! / k! (n-k)! .
  3. ^ Nicholas J. Higham (1998). Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics. p. 25. ISBN 0-89871-420-6.
[edit]
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