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Majoring in Mathematics (view source)
Revision as of 05:20, February 9, 2012
, 05:20, February 9, 2012→The Bridges of Konigsberg: graph theory isn't a subset of topology
=== Topology ===
=== Topology ===
==== The Bridges of Konigsberg ====
==== The Bridges of Konigsberg ====
The earliest roots of the modern study of topology (and [[graph theory]] in particular) lie in [[Leonhard Euler]]'s investigations of a famous puzzle from the 1730s. The town of Konigsberg (now [[Kaliningrad]]) was bisected by a river, which contained two large islands. There were seven bridges connecting the islands, as indicated in the accompanying image. The problem asked for a walk through the town which would cross each bridge exactly once: every bridge must be crossed once, and none more than once.
The earliest roots of the modern study of topology (and [[graph theory]]) lie in [[Leonhard Euler]]'s investigations of a famous puzzle from the 1730s. The town of Konigsberg (now [[Kaliningrad]]) was bisected by a river, which contained two large islands. There were seven bridges connecting the islands, as indicated in the accompanying image. The problem asked for a walk through the town which would cross each bridge exactly once: every bridge must be crossed once, and none more than once.
[[Image:Konigsberg.jpg|center|alt=Layout of Konigsberg|Layout of Euler's Konigsberg]]
[[Image:Konigsberg.jpg|center|alt=Layout of Konigsberg|Layout of Euler's Konigsberg]]