|講師：||HELMKE, Stefan 助教|
|題目：||On Cramer's Paradox|
In a letter from September 30, 1744, G. Cramer asked L. Euler the
following question. On the one hand, two plane curves of degree 3
can meet in 9 points. On the other hand, a plane curve of degree 3
is determined by 9 points. This seems to be a contradiction, since
there are then at least two curves of degree 3 passing through those
9 intersection points while there should be only one. In my lecture,
I will discuss the historic background of this problem, Euler's
detailed answer to Cramer's question and some of the later
developments related to Cramer's Paradox.
L. Euler, Sur une contradiction apparente dans la doctrine des lignes courbes, Mémoires de l'Academie des Sciences de Berlin 4, 219-233, 1750.
This paper is available at
And an English translation of this paper by W. Marshall:
E. Sandifer, How Euler Did It -- Cramer's Paradox, 2004.