全学共通科目講義(1回生~4回生対象)
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現代の数学と数理解析 |
―― 基礎概念とその諸科学への広がり |
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日時: | 2013年6月14日(金) 16:30-18:00 |
場所: | 数理解析研究所 420号室 |
講師: | HELMKE, Stefan 助教 |
題目: | On Cramer's Paradox |
要約: |
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.
References: 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. |
"http://www.kurims.kyoto-u.ac.jp/ja/special-02.html" |