| 词条 | Moritz Pasch |
| 释义 |
Moritz Pasch (8 November 1843, Breslau, Prussia (now Wrocław, Poland) – 20 September 1930, Bad Homburg, Germany) was a German mathematician of Jewish ancestry[1] specializing in the foundations of geometry. He completed his Ph.D. at the University of Breslau at only 22 years of age. He taught at the University of Giessen, where he is known to have supervised 30 doctorates. In 1882, Pasch published a book, Vorlesungen über neuere Geometrie, calling for the grounding of Euclidean geometry in more precise primitive notions and axioms, and for greater care in the deductive methods employed to develop the subject. He drew attention to a number of heretofore unnoted tacit assumptions in Euclid's Elements. He then argued that mathematical reasoning should not invoke the physical interpretation of the primitive terms, but should instead rely solely on formal manipulations justified by axioms. This book is the point of departure for:
Pasch is perhaps best remembered for Pasch's axiom: Given three noncollinear points a, b, c and a line X not containing any of these points, if X includes a point between a and b, then X also includes one and only one of the following: a point between a and c, or a point between b and c. In other words, if a line crosses one side of a triangle, that line must also cross one of the two remaining sides of the same triangle. Selected publications
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References1. ^Dirk Schlimm, "The correspondence between Moritz Pasch and Felix Klein" in Historia Mathematica Volume 40, Issue 2, May 2013, Page 186 2. ^{{cite journal|title=Review: Vorlesungen über neuere Geometrie by Moritz Pasch, Second edition. With an appendix: Die Grundlegung der Geometrie in historischer Entwicklung by Max Dehn.|author=Hollcroft, T. R.|authorlink=Temple Rice Hollcroft|journal=Bull. Amer. Math. Soc.|volume=33|year=1927|pages=785–786|doi=10.1090/S0002-9904-1927-04481-0}} 3. ^{{cite journal|title=Review: Grundlagen der Analysis von Moritz Pasch|author=Owens, F. W.|journal=Bull. Amer. Math. Soc.|volume=16|year=1910|pages=213–214|doi=10.1090/S0002-9904-1910-01893-0}} External links
5 : 1843 births|1930 deaths|German Jews|German mathematicians|Geometers |
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