The Königsberg BridgeDate: 5/14/96 at 16:52:18 From: YA WANG/RAD. ONCOL. Subject: Königsberg's bridge Please send me information on Königsberg's bridge. Thanks from Suisui Song Date: 5/23/96 at 13:21:42 From: Doctor Betsy Subject: Re: Königsberg's bridge Hi Suisui, I searched for Königsberg in a Math history archive on the World Wide Web, and found information on a page at: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Topology_in_mathematics.html This is a Math history archive, and it has some information on the Königsberg bridge. Here is a little bit of what I found here in the history of Topology. I recommend you read it with a Web browser if you have World Wide Web access. There is a picture that you might find interesting. Topological ideas are present in almost all areas of today's mathematics. The subject of topology itself consists of several different branches, such as point set topology, algebraic topology and differential topology, which have relatively little in common. We shall trace the rise of topological concepts in a number of different situations. Perhaps the first work which deserves to be considered as the beginnings of topology is due to Euler. In 1736 Euler published a paper on the solution of the Königsberg bridge problem entitled Solutio problematis ad geometriam situs pertinentis which translates into English as The solution of a problem relating to the geometry of position. The title itself indicates that Euler was aware that he was dealing with a different type of geometry where distance was not relevant. The paper not only shows that the problem of crossing the seven bridges in a single journey is impossible, but generalises the problem to show that, in today's notation, a graph has a path traversing each edge exactly once if exactly two vertices have odd degree. I hope this information is helpful to you. Please write back if you have any more questions. -Doctor Betsy, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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