Franz Taurinus

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Franz Adolph Taurinus (born November 15, 1794 in Bad König , † February 13, 1874 in Cologne ) was a German mathematician who did preparatory work on non-Euclidean geometry .

Live and act

Franz Taurinus was the son of a court official of the Counts of Erbach-Schöneberg. He studied law in Heidelberg , Giessen and Göttingen , but was able to lead the life of a private scholar thanks to an inheritance in Cologne. With his uncle Ferdinand Karl Schweikart (1780-1859), who was a law professor in Königsberg , he corresponded, among other things, on mathematics. So he began to be interested in Euclid's postulate of parallels , which has always been felt to be exceptional among Euclid's axioms. Giovanni Girolamo Saccheri and Johann Heinrich Lambert already examined models of geometry in which it is not necessary to find contradictions, and Schweikart also examined these new geometries (he called them "astral theory of size", published in 1807). Taurinus examined the model of geometry suggested by Lambert on a "sphere" of imaginary radius, which he called "logarithmic-spherical" (today called hyperbolic geometry ). Finally he was convinced that no contradictions could be found and published his theory of parallel lines in Cologne in 1825 and Geometriae prima elementa in 1826 . He finally distinguished three types of geometries, the Euclidean, the spherical (for which he saw the great circles on the spherical surface as a model) and the hyperbolic. But he remained convinced of the special role of Euclidean geometry. According to Zacharias he is the founder of non-Euclidean trigonometry, but not to be counted among the actual founders of non-Euclidean geometry like Nikolai Lobatschewski or János Bolyai .

About his ideas he corresponded with Carl Friedrich Gauß (as well as Schweikart before) in 1824. Gauß encouraged Taurinus and commented extensively on his own attempts, but also warned him not to quote him publicly. When Taurinus later sent his works to Gauss, the latter did not answer. According to Stäckel, he was probably annoyed that Taurinus was quoting him in the prefaces of his books.

literature

  • F. Engel, P. Stäckel: The theory of parallel lines from Euclid to Gauss. Leipzig, Teubner 1895.
  • Stäckel: Franz Adolph Taurinus. Journal for Mathematics and Physics, Vol. 44, 1899, Supplement, Treatises on the History of Mathematics, Issue 9, pp. 401–427. ( Digitized version of Heidelberg University )
  • Roberto Bonola: The non-Euclidean geometry. Leipzig, Teubner 1908.

Web links

Remarks

  1. ↑ Astral should mean that deviations from Euclidean geometry would only be recognizable on astronomical dimensions.
  2. ↑ Zacharias: Elementary Geometry. Encyclopedia of Mathematical Sciences 1913. Following pages  ( page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice.@1@ 2Template: Toter Link / gdz.sub.uni-goettingen.de  
  3. ^ Stäckel: Gauss as a geometer. In: Gauss, Collected Works. Volume 10, Department 2. On page 34  ( page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice.@1@ 2Template: Toter Link / gdz.sub.uni-goettingen.de  
personal data
SURNAME Taurinus, Franz
ALTERNATIVE NAMES Taurinus, Franz Adolph (full name)
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH November 15, 1794
PLACE OF BIRTH Bad King
DATE OF DEATH February 13, 1874
Place of death Cologne