The Königsberg Bridge

Date: 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/