Misplaced Pages

Carl Anton Bretschneider

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
German mathematician
Bretschneider's formula allows for the calculation of the area of a general quadrilateral if the lengths of all sides are known.

Carl Anton Bretschneider (27 May 1808 – 6 November 1878) was a mathematician from Gotha, Germany. Bretschneider worked in geometry, number theory, and history of geometry. He also worked on logarithmic integrals and mathematical tables. He was one of the first mathematicians to use the symbol γ {\displaystyle \gamma } for Euler's constant when he published his 1837 paper. He is best known for his discovery of Bretschneider's formula for the area of a general quadrilateral on a plane,

A = ( s − a ) ( s − b ) ( s − c ) ( s − d ) − a b c d ⋅ cos 2 ⁡ ( α + γ 2 ) , {\displaystyle A={\sqrt {(s-a)(s-b)(s-c)(s-d)-abcd\cdot \cos ^{2}\left({\frac {\alpha +\gamma }{2}}\right)}},}

where, a , b , c , {\displaystyle a,b,c,} and d {\displaystyle d} are the sides of the quadrilateral, s = a + b + c + d 2 {\displaystyle s={\frac {a+b+c+d}{2}}} is the semiperimeter, and α {\displaystyle \alpha } and γ {\displaystyle \gamma } are two opposite angles.

He is the son of Karl Gottlieb Bretschneider, a theologian.

Publications

  • Carl Anton Bretschneider (1837). "Theoriae logarithmi integralis lineamenta nova". Crelle Journal, vol.17, p. 257-285 (submitted 1835)

See also

References

  • Leonard Eugene Dickson, Extensions of Waring's theorem on fourth powers, Bull. Amer. Math. Soc. vol. 33 (1927) pp. 319–327
  • Karl August Regel, Gedächtnissrede auf Carl Anton Bretschneider in der Aula des Gymnasium Ernestinum am 15. Januar 1879. In: Programm des Herzoglichen Gymnasium Ernestinum zu Gotha als Einladung zur Theilnahme an der am 31. März zu veranstaltenden Prüfung sämmtlicher Classen. Gotha, Engelhard-Reyer Hofbuchdruckerei, 1879, S. 1–10. (Mit Schriftenverzeichnis). JFM 11.0027.03
  • Alfred Bretschneider, Ein Gedenkblatt für seine Freunde und Schüler. Zeitschrift für Mathematik und Physik 24 – Historisch-literarische Abtheilung, 1879, S. 79–91. JFM 11.0027.04
  • Der Lehrsatz des Matthew Stewart, Grunert-Archiv 50, 1869, S. 11–17
  • Die harmonischen Polarcurven, Grunert-Archiv 50, 1869, S. 475–499
  • Die Geometrie und die Geometer vor Euklides: ein historischer Versuch, B. G. Teubner, Leipzig 1870
  • Zur Berechnung des Trapezes aus seinen Seiten, Grunert-Archiv 52, 1870, S. 24–25
  • Einfache Berechnung der Winkel eines ebenen oder sphärischen Dreiecks aus den Seiten der Figur, Grunert-Archiv 52, 1870, S. 371–374

External links

Categories: