Jakob Steiner

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Jakob Steiner

Jakob Steiner (born March 18, 1796 in Utzenstorf ; †  April 1, 1863 in Bern ) was a Swiss mathematician . He is considered one of the main representatives of synthetic geometry .

Live and act

Steiner was the son of a small farmer, attended the local village school, where he did not learn to write until he was fourteen, and at the age of seventeen went to Johann Heinrich Pestalozzi in Yverdon , at whose institution he later worked as an assistant teacher for some time. When this was closed, he moved to Heidelberg in 1818 to study mathematics with Ferdinand Schweins (1780–1856) , among others , but was almost entirely dependent on self-study due to the poor quality of the lectures there. He financed his living through private lessons. The lectures on algebra and on the differential and integral calculus stimulated investigations into mechanics , which he recorded in his compendia in 1821, 1824 and 1825.

He lived in Berlin from the winter of 1820/21, initially as a private mathematics teacher, and was soon considered the best private teacher in the city. Among other things, he taught the son of the former Minister Wilhelm von Humboldt , which promoted his rise. Even Felix Eberty received in his schooling from him private lessons. During this time Steiner published some work on geometric problems in Crelle's Journal for Pure and Applied Mathematics . Then he was a teacher at the Plamann School , which was influenced by Pestalozzi's pedagogy. From 1827 Steiner worked at the trade academy (senior teacher, from 1833 with the title of professor), from 1834 as an associate professor at the university and as a full member of the Prussian Academy of Sciences . In 1854 he was accepted as a corresponding member of the Académie des sciences . He spent the last years of his life in Switzerland, tormented by severe physical ailments.

Steiner mainly worked in geometry . The Steiner set in mechanics, the Steiner tree problem , the set of Steiner on the production of conic sections, the Poncelet-Steiner's theorem (stating that that geometric design tasks ruler and compass with the ruler alone and a predetermined circuit can be executed), the Steiner-Tripel systems , the Steiner Roman surface , the Steiner chain and over a dozen other mathematical terms are named after him. His geometrical solution to the isoperimetric problem is well known (to show that the circle is the curve that encloses the greatest content for a given circumference).

In his lectures, Steiner attached great importance to the development of geometrical intuition, which was also an important topic in Pestalozzi pedagogy. In order to promote intuition, Steiner refrained from using geometric figures in his lectures. Another characteristic that came from the Pestalozzi school was the responding to the needs of the students, who were supposed to discover mathematical knowledge for themselves as far as possible, with the teacher only indicating the direction, similar to the Socratic method or the later influential Moore in the USA -Method. Steiner asked a lot of his students, the tone was often harsh, and he was not easy to satisfy, but nevertheless he was able to gather a circle of loyal students around him.

In 1832 he was awarded an honorary doctorate from the Albertus University in Königsberg . This happened on the initiative of Carl Gustav Jacob Jacobi , who sponsored Steiner and, together with the Humboldt brothers, was responsible for setting up a chair for geometry for Steiner at the Berlin University. Steiner also socialized with Niels Henrik Abel and Dirichlet in Berlin. Steiner, in turn, promoted the Swiss autodidact and geometer Ludwig Schläfli , whom he met in Bern in 1843 and invited to Rome a year later, where he taught him. He was in correspondence with him.

Felix Klein suspects that Steiner did not receive a full professorship in Berlin because he lacked social etiquette - he also suggests that Steiner was arguable and isolated in later years, disintegrated with God and the world and his arguments in conversation often through one used to emphasize unsurpassed primeval rudeness . In later years he fell out with his friend Jacobi (they both spoke on two) as well as with Schläfli and others. The decisive factor, however, must have been that he had not received any higher education, spoke no foreign languages ​​and did not speak Latin, at that time something like the official language at Berlin University, in which dissertations were written. Even in the field of mathematics outside of geometry (for example in analysis, algebra and number theory) he had only very limited knowledge and freely admitted this. But he insisted that his students train in it - students who wanted to do the same and only practice geometry, he threw down with the words: Not everyone who says Lord, Lord to me will come to the kingdom of heaven . Klein also suggests that from around 1845 (when he was concerned with algebraic structures of a higher than second order) Steiner slackened his creativity and used the writings of English algebraic surveyors willingly or unwillingly without citing them. According to his student Lampe, on the other hand, it was Steiner's typical way of working not to study any literature except to determine whether a sentence he had found was already known (and even then he often left the literature research to his friend Jacobi) - he even often mocked learned things Knowledge. One of the reasons for the decline in productivity was his constant illness. In Berlin he was a frequent theater-goer and associated with the actor Ludwig Devrient , among others . As a member of the Academy, although he was not a full professor, he was on an equal footing with it, and he earned well. On his death he left his relatives 60,000 francs and donated a third of this sum as prize money for the Steiner Prize of the Berlin Academy, which is named after him. Steiner Prize winners included Rudolf Sturm , Luigi Cremona (1866), Henry John Stephen Smith , Hermann Kortum , Georges Henri Halphen (1880), Wilhelm Fiedler and Sigmund Gundelfinger .

The writer Theodor Fontane was one of Steiner's students at the trade school .



  • Systematic development of the interdependence of geometric shapes, taking into account the work of old and new geometries on porisms, projection methods, geometry of position, transversals, duality and reciprocity, etc. , G. Fincke, Berlin 1832 (as the first part of the planned five Share, but no further volume was published; on Google Books: [1] , [2] )
  • The geometric constructions, carried out by means of the straight line and a solid circle, as a subject of instruction in higher educational institutions and for practical use , Ferdinand Dümmler, Berlin 1833 (at Google Books: [3] , [4] )
  • Jacob Steiner's lectures on synthetic geometry , BG Teubner, Leipzig 1867 (on Google Books: [5] )
    • Carl Friedrich Geiser (Ed.): First part: The theory of conic sections in elementary representation (on Google Books: [6] , [7] )
    • Heinrich Schröter (Ed.): Second part: The theory of conic sections, based on projective properties (on Google Books: [8] , [9] )
  • Karl Weierstraß (Ed.): Jacob Steiner's Gesammelte Werke , G. Reimer, Berlin, 1881/82, online
    • First volume , 1881 (in the internet archive, digitization heavily flawed: [10] , [11] , [12] )
    • Second volume , 1882 (in the Internet archive: [13] , [14] )



See also

Web links

Commons : Jakob Steiner  - Collection of images, videos and audio files
Wikisource: Jakob Steiner  - Sources and full texts

Individual evidence

  1. Geiser: In memory of Jakob Steiner , 1874
  2. Burckhardt: Jakob Steiner , 1976
  3. Felix Klein: Lectures on the development of mathematics in the 19th century . Springer Verlag, 1926, p. 127. After Klein he was drawn to Berlin because there was an interest in Pestalozzi's methods in ministerial circles.
  4. ^ Felix Eberty: Memories of the youth of an old Berliner. Based on the handwritten notes of the author by J. von Bülow, supplemented and newly published edition of the youth memories of 1878 . Verlag für Kulturpolitik, Berlin 1925, p. 238
  5. ^ List of members since 1666: Letter S. Académie des sciences, accessed on March 5, 2020 (French).
  6. Felix Klein: Lectures on the development of mathematics in the 19th century. Parts 1 and 2. Springer, 1926, p. 128. According to Klein, the darkening of the lecture hall to enhance the view was not done by Steiner, but by Wilhelm Adolf Diesterweg in his teachers' seminars in Moers.
  7. ^ Emil Lampe: On the biography of Jacob Steiner In: Bibliotheca mathematica, 3rd part, Volume 1, 1900, p. 133
  8. The correspondence was published in 1896 by JH Graf, The correspondence between Jakob Steiner and Ludwig Schläfli , Bern: KJ Wyss
  9. Felix Klein: Lectures on the development of mathematics in the 19th century. Parts 1 and 2. Springer, 1926, p. 127
  10. ^ Emil Lampe: On the biography of Jacob Steiner . In: Bibliotheca mathematica, 3rd episode, Volume 1, 1900, p. 138. He even challenged Jacobi to a duel, which Jacobi refused with the words that if he wanted to commit suicide, he should buy pistols and do it himself if he didn't need him (Jacobi).
  11. ^ Emil Lampe: On the biography of Jacob Steiner In: Bibliotheca mathematica, 3rd part, Volume 1, 1900, p. 134
  12. Felix Klein: Lectures on the development of mathematics in the 19th century. Parts 1 and 2. Springer, 1926, pp. 128f
  13. ^ Emil Lampe: On the biography of Jacob Steiner In: Bibliotheca mathematica, 3rd part, Volume 1, 1900, p. 138
  14. ^ Emil Lampe: On the biography of Jacob Steiner In: Bibliotheca mathematica, 3rd part, Volume 1, 1900, p. 132
  15. Martin Lowsky Unforgettable Soul Kinship. Theodor Fontane learns mathematics with Jacob Steiner , in Katja Legnink, Susanne Prediger, Franziska Siebel Mathematik und Mensch , Mühltal: Verlag Allgemeine Wissenschaft, Darmstädter Schriften zur Allgemeine Wissenschaft, Volume 2, 2001