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Person: Von Nagel, Christian Heinrich

Christian Heinrich von Nagel was a German geometer. The "Nagel point" of a triangle is named after him.

Mathematical Profile (Excerpt):

• However, two people helped Christian Heinrich to receive an education.
• The only route to an education was through the church and this is the route Christian Heinrich took.
• Nagel attended classes at the Gymnasium in Stuttgart and then after taking the county examinations in 1817 he was accepted into the Evangelical Seminaries of Maulbronn and Blaubeuren in Baden-Württemburg.
• Nagel studied in these Gymnasiums for four years and, although the aim was an education based on theology, he also studied science and mathematics at Blaubeuren.
• However he also attended lectures on mathematics and physics at the university given by the astronomer Johann Gottlieb Friedrich von Bohnenberger (1765-1831), who was the professor of mathematics and astronomy at the University of Tübingen, and Friedrich Joseph Pythagoras Riecke (1794-1876) who was a lecturer in Tübingen until 1823 when he left to become Professor of Mathematics and Physics in Hohenheim.
• Nagel had hoped to study under Christoph Friedrich von Pfleiderer, professor of mathematics at Tübingen, but Pfleiderer died in September 1821 just when Nagel was starting his studies.
• Nagel completed his studies in 1825 and, having qualified as a clergyman, entered the Church.
• When Nagel realised that his chances of becoming a professor at Tübingen were very slight, he decided to accept the offer of an appointment as Professor of Mathematics and Natural Science at the Gymnasium in Ulm.
• Nagel published six mathematical articles, the most important of which is Untersuchungen über die Eigenschaften der wichtigsten mit dem Dreieck in Verbindung stehenden Kreise Ⓣ(Studies on the properties of the key associated with the triangular circles) (1835) and Untersuchungen über die wichtigsten zum Dreiecke gehörigen Kreise.
• He is most famous for one of these points of intersection that is today called the Nagel point.
• Then the lines Aa,Bb,CcAa, Bb, CcAa,Bb,Cc are concurrent at NNN, the Nagel point.
• Particularly interesting is Nagel's idiosyncratic, purely elementary geometrical method of proof.
• In his papers he proved the existence of the Nagel point and other points such at the Gergonne point and the Middle point.
• Other interesting properties of the Nagel point is that it, the centroid and the incentre of a triangle are collinear.
• Other mathematical publications by Nagel include Theorie der periodischen Decimalbrüche nebst Tabellen zur leichteren Verwandlung gewöhnlicher Brüche in Decimalbrüche Ⓣ(The theory of periodic decimal expansions along with tables to facilitate transformation of ordinary fractions in decimals) (1845).
• Nagel made other contributions to Ulm in addition to serving as a teacher and rector there.
• In particular he acted as an advisor to the city magistrates and it was Nagel who was instrumental in setting up gas lighting in Ulm.

Born 28 February 1803, Stuttgart, Germany. Died 27 October 1882, Ulm, Germany.

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References

Adapted from other CC BY-SA 4.0 Sources:

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