# Andreas von Ettingshausen

Andreas von Ettingshausen
Andreas Freiherr von Ettingshausen (1796–1878)
Born 25 November 1796
Died 25 May 1878 (aged 81)
Residence Austria
Nationality Austrian
Alma mater University of Vienna
Known for Electric machines
Scientific career
Fields Physicist and mathematician
Institutions University of Innsbruck
University of Vienna
Vienna Polytechnic Institute
Doctoral students Ernst Mach
Jožef Stefan
Viktor von Lang

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

## 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 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 ${\displaystyle {\tbinom {n}{k}}}$ for the binomial coefficient, which is the coefficient of xk in the expansion of the binomial (x+1)n and, more generally, the number of k-element subsets of an n-element set.[2][3]

## References

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. Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics. p. 25. ISBN 0-89871-420-6.