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Jacob Steiner and Synthetic Geometry

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Abstract

Jacob Steiner (18.3.1796-1.4.1863) was born in Utzendorf near Bern in Switzerland on March 18, 1796, as son of a farmer. Growing up on a farm, he did not learn to write until his 14th year (see appendix in [5]). He then entered Pestalozzi’s pedagogical institute at Iferten (Yverdon), at first as a student, then as a teacher. Here he learned to combine numbers with spatial illustrations. In 1818 Steiner moved to Heidelberg where he lived as a private teacher. There he acquired knowledge of contemporary French geometry. In Heidelberg he received his PhD.

Keywords

  • Steiner Tree
  • Triple System
  • Steiner Point
  • Steiner Triple System
  • Steiner System

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Steiner, J., Gesammelte Werke I, II, ed. Karl Weierstrass, Georg Reimer, Berlin, 1881, 1882.

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  2. Steiner, J., Allgemeine Theorie über das Berühren und Schneiden der Kreise und Kugeln, Posthumous Edition by K. Fueter and F. Gonseth, Orell Füssli Verlag, Zürich und Leipzig, 1931.

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  3. Steiner, J., Systematische Entwicklung der Abhängigkeit geometrischer Gestalten voneinander mit Berücksichtigung der Arbeiten alter und neuer Geometer über Porismen, Projektionsmethoden, Geometrie der Lage, Transversalen, Dualität und Reziprozität, etc., Fircke, Berlin, 1832 (see also [1], vol. I, 229-460, or Ostwalds Klassiker der exakten Naturwissenschaften 82, 83, Engelmann, Leipzig, 1896).

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  4. Steiner, J., Vorlesungen über synthetische Geometrie I, II, Teubner, Leipzig und Berlin, 1867.

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  5. Steiner, J., Die geometrischen Konstruktionen, ausgeführt mittels der geraden Linie und eines festen Kreises, Dammler, Berlin, 1833 (see also [1], vol. I, 461-522, or Ostwalds Klassiker der exakten Naturwissenschaften 60, Engelmann, Leipzig, 1895).

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  6. Steiner, J., Einige geometrische Betrachtungen, J. Reine Angew. Math. 1 (1826), 161–184, 252-288 (see also Ostwalds Klassiker der exakten Naturwissenschaften 123, Engelmann, Leipzig, 1901).

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  7. Steiner, J., Über Maximum und Minimum bei den Figuren, in der Ebene, auf der Kugelfläche und im Räume überhaupt, J. Reine Angew. Math. 24 (1842), 93–162, 189-250 (see also [1], vol. II, 177-242, 245-308, or J. Math. Pures Appl. Ser. 1, 6 (1841), 105-170).

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  8. Steiner, J., Einfache Beweise der isoperimetrischen Hauptsätze, J. Reine Angew. Math. 18 (1838), 281–296 (see also [1], vol. II, 77-91).

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  9. Biermann, K.-R., Die Mathematik und ihre Dozenten an der Berliner Universität 1810-1933, Akademie Verlag, Berlin, 1988.

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  10. Klein, F., Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, 2 vols., Springer-Verlag, Berlin, 1926-1927.

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Begehr, H., Lenz, H. (1998). Jacob Steiner and Synthetic Geometry. In: Begehr, H., Koch, H., Kramer, J., Schappacher, N., Thiele, EJ. (eds) Mathematics in Berlin. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8787-8_6

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  • DOI: https://doi.org/10.1007/978-3-0348-8787-8_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-5943-0

  • Online ISBN: 978-3-0348-8787-8

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