**Karl Feuerbach** was a geometer who discovered the nine point circle of a triangle.

- The other boys were Joseph Anselm Feuerbach (1798-1851), philologist and archeologist, Eduard August Feuerbach (1803-1843), professor of law at the University of Erlangen, and Friedrich Heinrich Feuerbach (1806-1880), an orientalist.
- They were in Jena when Karl was born but soon moved to Kiel.
- Paul Feuerbach's fame had been recognised by King Maximilian Joseph who had ennobled him in 1808 and awarded him free university education for all his sons.
- In 1819 Paul Feuerbach was appointed as President of the Court of Appeals in Ansbach.
- After spending three years studying at the University of Erlangen, Karl Feuerbach moved to the University of Freiburg im Breisgau in 1820.
- This was a move designed to allow him to study under Karl Heribert Ignatius Buzengeiger (1771-1835) who had taught in Ansbach before been appointed to the University of Freiburg in the previous year; indeed this move was very fruitful as Feuerbach had hoped.
- These fears seemed groundless, however, when by the age of twenty-two, Karl Feuerbach had been awarded his doctorate, been appointed to a professorship in mathematics at the Gymnasium at Erlangen and had published an extremely important mathematical work Eigenschaft einiger merkwürdigen Punkte des geradlinigen Dreiecks und mehrerer durch sie bestimmten Linien und Figuren Ⓣ(Property of some strange points of the rectilinear triangle and its lines and figures).
- There seems little doubt that as a student Feuerbach had been, as many young men, somewhat rebellious.
- Feuerbach and the other nineteen were imprisoned in the New Tower in Munich.
- the weeks and months were allowed to drag on without action and that Karl was not allowed to receive letters or visitors.
- Karl became obsessed by the idea that only his death could free his 19 companions.
- This release allowed Feuerbach to await trial out of prison and indeed the trial eventually went ahead only to result in the release and total vindication of all concerned (one of the men had died in prison so there were only 19 to be declared 'not guilty').
- Part of the reason for choosing Erlangen was the knowledge that Feuerbach had been happy there.
- Feuerbach's fame is as a geometer who discovered the nine point circle of a triangle.
- Feuerbach also proved that the nine point circle touches the inscribed and three escribed circles of the triangle.
- These results appear in his 1822 paper, and it is on the strength of this one paper that Feuerbach's fame is based.
- The nine point circle which is described here had also been described in work of Brianchon and Poncelet the year before Feuerbach's paper appeared.
- Feuerbach did undertake further mathematical research.
- Ein Beytrag zu der analytischen Geometrie von Dr. Karl Wilhelm Feuerbach, Prof.
- A study in analytic geometry by Dr Karl Wilhelm Feuerbach, Professor of Mathematics).
- This is a second major work by Feuerbach and it has been studied carefully by Moritz Cantor who discovered that in it Feuerbach introduces homogeneous coordinates.

Born 30 May 1800, Jena, Germany. Died 12 March 1834, Erlangen, Germany.

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Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive