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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 

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