Auguste Miquel

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Auguste Miquel (* around 1816 in Albi , † 1851) was a French mathematician, known for his contributions to geometry.

Life

Little known about Auguste Miquel. In 1835/36 he received the Baccalauréat in literature and then in science and then studied mathematics in Paris for a year. While still a student at the local institution Barbet, a preparatory school for the Grande école , in 1836 he published a mathematical essay in the journal Le Géomètre, which existed for a short time , in which he proved theorems of Jakob Steiner for which no evidence had previously been published.

After his studies he taught in Nantua (as Régent ), in Castres (southern France) and other places, in the department of Gard at the Collège in Bagnols-sur-Cèze and Le Vigan . He published various articles on geometry in the Journal de mathématiques pures et appliquées founded by Joseph Liouville in 1836 (called "Journal de Liouville").

Theorems about the intersections of circles

Miquel's theorem; M = Miquel point

Auguste Miquel is particularly known for the sentences about the intersection of circles, which he published in 1838.

  • Miquel's theorem , also Miquel's triangle theorem : About the intersection points of a chain of three circles (Miquel circles), each of which goes through one of the corners of a triangle and where the intersection points of neighboring circles are on the sides of the triangle: at the second intersection point (Miquel Point) all three circles intersect.
    There is a generalized version (also Miquel's Rectangle theorem ), which was already known to William Wallace and Jakob Steiner : consider four straight lines, three of which form four triangles. The circles around the triangles intersect at a point (Miquel point).
  • Miquel's Five Circle Theorem or Miquel's Pentagram Theorem (also Miquel's Pentagon Theorem): Look at a convex pentagon and extend the sides to a pentagram and form the circles of the five triangles that protrude in the pentagram over the pentagon. The second points of intersection of neighboring perimeters lie on a circle.
  • Theorem of six circles: Four circles form a chain, with neighboring circles each intersecting at two points. If four of the intersection points are on a circle, the others are also on a circle.

Fonts

In the Journal de mathématiques pures et appliquées , Paris (Journal de Liouville):

  • Sur quelques questions relatives à la théorie des Courbes , Volume 3, 1838, pp. 202-208, Gallica
  • Théorèmes de Géométrie , Volume 3, 1838, pp. 485-487 (theorem of Miquel), Gallica
  • Théorèmes sur les intersections des cercles et des spheres , Volume 3, 1838, pp. 517-522, Gallica
  • Mémoire de Géométrie , three parts, Volume 9, 1844, pp. 20-27, Volume 10, 1845, pp. 347-350, Volume 11, 1846, pp. 65-75, Part 1, Gallica , Part 2, Gallica , Part 3, Gallica

Otherwise:

  • Problème d'Optique , Nouvelles Annales de Mathématiques, Volume 5, 1846, pp. 235-238, online

Web links

Individual evidence

  1. ↑ ChronoMath website, see web links
  2. ^ Barbet Institution
  3. ↑ Jean-Louis Ayme Feuerbach's theorem. A new purely synthetic proof , pdf
  4. ^ Evidenced by his publications in the Journal de Liouville, Nantua is given for 1838
  5. ^ The Régent was assistant to the Rector (Principal) of the high school
  6. ↑ Proven for 1844 from the Journal de Liouville, p. 20: Professor of Mathematics in Castres
  7. ↑ Gazette spéciale de l'instruction publique, October 8, 1842 after he was provisionally appointed Regent of mathematics at the Collège de Bagnols, having previously held the same position at the College of Castres
  8. ^ Weisstein, Mathworld
  9. ^ Ostermann / Wanner Geometry by its history , Springer Verlag 2012
  10. ^ Theorem of Miquel
  11. ^ Weisstein, Mathworld
  12. ^ Math World
  13. ↑ Alexander Ostermann, Gerhard Wanner Geometry by its history , Springer Verlag 2012, chapter 4.8. Miquel's theorems
personal data
SURNAME Miquel, Auguste
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH around 1816
PLACE OF BIRTH Albi
DATE OF DEATH 19th century or 20th century