Adam Wilhelm Siegmund Günther (6 February 1848 – 3 February 1923) was a German geographer, mathematician, historian of mathematics and natural scientist.

Early life

Born in 1848 to a German businessman, Günther would go on to attend several German universities including

Erlangen Erlangen (; East Franconian: ''Erlang'', Bavarian: ''Erlanga'') is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative district Erlangen), and with 116,062 inhabi ...

Heidelberg Heidelberg (; Palatine German language, Palatine German: ''Heidlberg'') is a city in the States of Germany, German state of Baden-Württemberg, situated on the river Neckar in south-west Germany. As of the 2016 census, its population was 159,914 ...

Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as ...

Berlin Berlin is Capital of Germany, the capital and largest city of Germany, both by area and List of cities in Germany by population, by population. Its more than 3.85 million inhabitants make it the European Union's List of cities in the European U ...

, and

Göttingen Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...

Career

In 1872 he began teaching at a school in Weissenburg,

Bavaria Bavaria ( ; ), officially the Free State of Bavaria (german: Freistaat Bayern, link=no ), is a state in the south-east of Germany. With an area of , Bavaria is the largest German state by land area, comprising roughly a fifth of the total l ...

. He completed his

habilitation thesis Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including ...

continued fraction In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integ ...

s entitled ''Darstellung der Näherungswerte der Kettenbrüche in independenter Form'' in 1873. The next year he began teaching at

Munich Polytechnicum The Technical University of Munich (TUM or TU Munich; german: Technische Universität München) is a public research university in Munich, Germany. It specializes in engineering, technology, medicine, and applied and natural sciences. Establis ...

. In 1876, he began teaching at a university in

Ansbach Ansbach (; ; East Franconian: ''Anschba'') is a city in the German state of Bavaria. It is the capital of the administrative region of Middle Franconia. Ansbach is southwest of Nuremberg and north of Munich, on the river Fränkische Rez ...

where he stayed for several years before moving to Munich and becoming a professor of geography until he retired; he served as the university's rector from 1911 to 1913. For some years, Günther was a member of the federal parliament, the Reichstag, and later the Bavarian parliament, representing liberal parties. His mathematical work included works on the

determinant In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if ...

hyperbolic functions In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the ...

, and ''parabolic logarithms and trigonometry''.This is about connecting the ''rectified length'' of line segments along a parabola, giving logarithms for appropriate coordinates, and trigonometric values for suitable angles, in a similar way as the ''area'' under a hyperbola defines the ''

natural logarithm The natural logarithm of a number is its logarithm to the base of the mathematical constant , which is an irrational and transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, if ...

'', and a ''

hyperbolic angle In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of ''xy'' = 1 in Quadrant I of the Cartesian plane. The hyperbolic angle parametrises the unit hyperbola, which has hyperbolic functio ...

'' is defined via the area of a hyperbolically truncated triangle.

Publications (selection)

''Darstellung der Näherungswerthe der Kettenbrüche in independenter Form''
Eduard Besold, Erlangen, 1873
''Vermischte Untersuchungen zur Geschichte der mathematischen Wissenschaften''
Teubner, Leipzig, 1876
''Lehrbuch der Determinanten-Theorie für Studirende''
Eduard Besold, Erlangen, 1877
''Die Lehre von den gewöhnlichen und verallgemeinerten Hyperbelfunktionen''
Louis Nebert, Halle, 1881 *
''Parabolische Logarithmen und parabolische Trigonometrie''
Teubner, Leipzig, 1882

References

{{DEFAULTSORT:Guenther, Siegmund 1848 births 1923 deaths 20th-century German mathematicians 19th-century German mathematicians Technical University of Munich faculty Presidents of the Technical University of Munich Members of the Bavarian Chamber of Deputies

Early life

Career

Publications (selection)

Further reading

References