Carl Anton Bretschneider (27 May 1808 – 6 November 1878) was a mathematician from

Gotha Gotha () is the fifth-largest city in Thuringia, Germany, west of Erfurt and east of Eisenach with a population of 44,000. The city is the capital of the district of Gotha and was also a residence of the Ernestine Wettins from 1640 until the ...

, Germany. Bretschneider worked in

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

, and

history of geometry Geometry (from the ; '' geo-'' "earth", '' -metron'' "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmeti ...

. He also worked on

logarithmic integral In mathematics, the logarithmic integral function or integral logarithm li(''x'') is a special function. It is relevant in problems of physics and has number theoretic significance. In particular, according to the prime number theorem, it is a ...

s and

mathematical table Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely u ...

s. He was one of the first mathematicians to use the symbol

\gamma

for Euler's constant when he published his 1837 paper. He is best known for his discovery of

Bretschneider's formula In geometry, Bretschneider's formula is a mathematical expression for the area of a general quadrilateral. It works on both convex and concave quadrilaterals, whether it is cyclic or not. The formula also works on crossed quadrilaterals provided ...

for the area of a general quadrilateral on a plane,

A = \sqrt ,

where,

a, b, c,

and

d

are the sides of the quadrilateral,

s = \frac

is the

semiperimeter In geometry, the semiperimeter of a polygon is half its perimeter. Although it has such a simple derivation from the perimeter, the semiperimeter appears frequently enough in formulas for triangles and other figures that it is given a separate name ...

, and

\alpha

and

\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)

References

Leonard Eugene Dickson Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also rem ...

, 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). *Alfred Bretschneider, ''Ein Gedenkblatt für seine Freunde und Schüler''. Zeitschrift für Mathematik und Physik 24 – Historisch-literarische Abtheilung, 1879, S. 79–91. * ''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

*
Beiträge zur sphärischen Trigonometrie
', Crelles Journal 13, 1835, S. 85–92 *
Beiträge zur sphärischen Trigonometrie. (Schluß)
', Crelles Journal 13, 1835, S. 145–158 *
Theoriae logarithmi integralis lineamenta nova
', Crelles Journal 17, 1837, S. 257–285 *
Untersuchung der trigonometrischen Relationen des geradlinigen Viereckes
', Grunert-Archiv 2, 1842, S. 225–261 *
Tafeln für die Zerlegung der Zahlen bis 4100 in Biquadrate
', Crelles Journal 46, 1853, S. 1–23 {{DEFAULTSORT:Bretschneider, Carl Anton 19th-century German mathematicians 1808 births 1878 deaths German geometers

Publications

See also

References

External links