## Mathematician of the Week: Karl Feuerbach

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Karl Feuerbach was born on May 30, 1800 in Jena, Germany, into an academic family. His father was a law professor, and five of the eight children earned doctorates, three going on to become professors (notably including Ludwig Feuerbach, whose writings had a significant influence on Karl Marx). Karl Feuerbach’s teaching career was cut short by failing health, and he died two months short of his 34th birthday.

Feuerbach’s most significant result concerned the 9 point circle associated with a triangle. Given any triangle, we can identify the following 9 points: the midpoints of the three sides of the triangle, the feet of the three altitudes of the triangle, and the three midpoints of the line segments connecting the orthocenter with each vertex. In any triangle, these 9 points lie on a circle (i.e. they are co-circular).

Feuerbach showed that this circle is tangent to the incircle of the triangle (the largest inscribed circle), as well as the three excircles (each excircle is tangent to one side of the triangle and the extensions of the other two sides). The point of intersection of the incircle and the 9 point circle is now known as the Feuerbach point of the triangle.

Other mathematicians with significant anniversaries for the week of May 25 through May 31:

May 25: Birthday of Karl Peterson [1828]; death of Johann Radon [1956]

May 26: Birthdays of Abraham de Moivre [1667], Yurii Sokolov [1896], and Otto Neugebauer [1899]

May 27: Death of Arthur Schönflies [1928]

May 28: Birthdays of Jacopo Riccati [1676], Johann Bernoulli (II) [1710]; death of Rolf Nevanlinna [1980]

May 29: Birthday of Finlay Freundlich [1885]; death of Frans van Schooten [1660]

May 30: Birthdays of Karl Feuerbach [1880] and Eugène Catalan [1814]; death of Vladimir Steklov [1926]

May 31: Deaths of Evariste Galois [1832] and George Green [1841]

Source:  MacTutor History of Mathematics Archive