Hints for reading Euler's "Konigsberg" article

Euler's article is short and is mostly text, but it is nevertheless trying to construct a precise mathematical argument. As you read it, keep the following questions in mind.

  1. What is the question Euler is trying to answer? Is it the same question throughout, or does he address more than one issue?

  2. How does Euler represent a path through the sequence of bridges? Is this representation clear? Is it unambiguous?

  3. Read paragraph 8 carefully--it is a crucial one. Do you understand it? Has Euler convinced you that his rule is correct?

  4. In paragraphs 8-14, Euler makes an argument that leads to a specific method to determine whether the desired path exists. The goal, then, is to prove that the method which appears in paragraph 14 does answer the question.

  5. What happens after paragraph 14. Hasn't he already answered the question? What is he up to now?

  6. What do you make of paragraph 21?

Fernando Q. Gouvêa ---- fqgouvea@colby.edu
Last modified: Tue Sep 16 09:21:15 1997