Please Email comments or suggestions to:curtin@nku.edu or to:otero@xavier.xu.edu
The Second Meeting of the ORESME Reading Group September 18-19, 1998 Northern Kentucky University In attendance: Chris Christensen, Northern Kentucky University Dan Curtin, Northern Kentucky University, host Dick Davitt, University of Louisville Chuck Groetsch, University of Cincinnati David Kullman, Miami University Danny Otero, Xavier University Steve Pelikan, University of Cincinnati Dick Pulskamp, Xavier University Fred Rickey, Bowling Green State University Linda Saliga, University of Akron We met for dinner Friday evening at Sloppy Joe's on the Kentucky side of the river--indeed, in the river--for Carribean fare. Afterwards, we reconvened at NKU at the Hermann Center, a most comfortable facility, to read the paper "On a continuous curve without tangents constructible from elementary geometry" by Helge von Koch (an English translation by Ilan Vardi from the French original Sur une courbe continue sans tangente obtenue pare une construction geometrique elementaire, Archive for Matematik, Astronomi och Fysik, 1 (1904), 681-702. which appears in Classics on Fractals, Gerald Edgar (ed.), Addison-Wesley, 1993, 25-45.) We also worked closely with a later and expanded version of the same paper, also in French: Une methode geometrique elementaire pour l'etude de certaines questiones de la theorie des courves planes, Acta Mathematica 30 (1906), 145-174. After spending some time reviewing basic historical data on von Koch and his career (b. 1870, Ph.D. at U. Uppsala in 1892 with a dissertation under Mittag- Leffler, asst. prof. at U. Stockholm in 1893, prof. at the Swedish Royal Inst. of Tech. in 1905, member of the Royal Acad. of Arts & Sci. in 1910, prof. at U. Stockholm in 1911, d. 1924), we considered some interesting questions brought up by our individual readings of the paper. Errata in Vardi's translation were shared. The question of what von Koch meant by "a continuous uniform function" arose. We also discussed the motivation that compelled von Koch to present this example as a response to a "question [which] is of importance also as a didactic point in analysis and geometry--whether one could find a curve without tangents for which the geometrical aspect is in agreement with the facts", unlike the example of Weierstrass which "is defined by an analytic expression that hides the geometrical nature of the corresponding curve". A more detailed review of the paper and its arguments followed and was continued on Saturday morning. Among the important points noted was that alongside a synthetic description of the curve, von Koch also presents an analytic description, and at key points in the proof of its properties, he leans rather heavily on the analytic properties of the parametrization function! Finally, the membership considered suggestions for the next meeting of ORESME, scheduled for January 29-30, 1999, at Xavier University, and decided to devote not one but *two* meetings to a study of the Erlangerprogramm of Felix Klein. Respectfully submitted, Danny Otero