Karl Georg Christian von Staudt Scientist
Karl Georg Christian von Staudt (January 24, 1798 – June 1, 1867) was a German mathematician born in the Free Imperial City of Rothenburg, which is now called Rothenburg ob der Tauber in Germany. From 1814 he studied in Gymnasium in Ausbach. He attended the University of Göttingen from 1818 to 1822 where he studied with Gauss who was director of the observatory. Staudt provided an ephemeris for the orbits of Mars and the asteroid Pallas. When in 1821 Comet Nicollet-Pons was observed, he provided the elements of its orbit. These accomplishments in astronomy earned him his doctorate from University of Erlangen in 1822.Staudt's professional career began as a secondary school instructor in Würzburg until 1827 and then Nuremberg until 1835. He married Jeanette Dreschler in 1832. They had a son Eduard and daughter Mathilda, but Jeanette died in 1848.The book Geometrie der Lage (1847) was a landmark in projective geometry. As Burau (1976) wrote:Staudt was the first to adopt a fully rigorous approach. Without exception his predecessors still spoke of distances, perpendiculars, angles and other entities that play no role in projective geometry.Furthermore, this book (page 43) uses the complete quadrangle to "construct the fourth harmonic associated with three points on a straight line", the projective harmonic conjugate.Hans Freudenthal (1974) has provided this picture of von Staudt's contribution to the foundations of projective geometry:To be able to consider von Staudt's approach as a rigorous foundation of projective geometry, one need only add explicitly the topological axioms which are tacitly used by von Staudt. ... how can one formulate the topology of projective space without the support of a metric? Von Staudt was still far from raising this question, which a quarter of a century later would become urgent. ... Felix Klein noticed the gap in von Staudt's approach; he was aware of the need to formulate the topology of projective space independently of Euclidean space.... the Italians were the first to find truly satisfactory solutions for the problem of a purely projective foundation of projective geometry, which von Staudt had tried to solve.Indeed, in 1889 Mario Pieri translated von Staudt, before writing his I Principii della Geometrie di Posizione Composti in un Systema Logico-deduttivo (1898). In 1900 Charlotte Scott of Bryn Mawr College paraphased much of von Staudt's work in English for The Mathematical Gazette.When Wilhelm Blaschke published his textbook Projective Geometry in 1948, a portrait of the young Karl was placed opposite the Vorwort.Staudt went beyond real projective geometry and into complex projective space in his three volumes of Beiträge zur Geometrie der Lage published from 1856 to 1860.The Von Staudt-Clausen theorem is partially named after him.In 1922 H. F. Baker wrote of von Staudt's work:It was von Staudt to whom the elimination of the ideas of distance and congruence was a conscious aim, if, also, the recognition of the importance of this might have been much delayed save for the work of Cayley and Klein upon the projective theory of distance. Generalised, and combined with the subsequent Dissertation of Riemann, v. Staudt's volumes must be held to be the foundation of what, on its geometrical side, the Theory of Relativity, in Physics, may yet become.Von Staudt is also remembered for his view of conic sections and the relation of pole and polar:Von Staudt made the important discovery that the relation which a conic establishes between poles and polars is really more fundamental than the conic itself, and can be set up independently. This "polarity" can then be used to define the conic, in a manner that is perfectly symmetrical and immediately self-dual: a conic is simply the locus of points which lie on their polars, or the envelope of lines which pass through their poles. Von Staudt’s treatment of quadrics is analogous, in three dimensions.↑ ↑ ↑ ↑ ↑
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