how was solved by Euler the Königsberg bridges problem ?

Question

jhonyy9 · Answer

@ganeshie8 anything about this please ? ty.

zzr0ck3r · Answer

graph theory was created :)

zzr0ck3r · Answer

That problem literally started graph theory. It was posted in a newspaper back when people cared about cool things. They actually used to post monthly problems on the front page! It was very hip!!

zzr0ck3r · Answer

Do you know what a Eulerian circuit is?

welshfella · Answer

the type of graph he created became to be known as a Eulerian grpah.

welshfella · Answer

- or a Eulerian trail.

zzr0ck3r · Answer

Next, Euler observed that (except at the endpoints of the walk), whenever one enters a vertex by a bridge, one leaves the vertex by a bridge. In other words, during any walk in the graph, the number of times one enters a non-terminal vertex equals the number of times one leaves it. Now, if every bridge has been traversed exactly once, it follows that, for each land mass (except for the ones chosen for the start and finish), the number of bridges touching that land mass must be even (half of them, in the particular traversal, will be traversed "toward" the landmass; the other half, "away" from it). However, all four of the land masses in the original problem are touched by an odd number of bridges (one is touched by 5 bridges, and each of the other three is touched by 3). Since, at most, two land masses can serve as the endpoints of a walk, the proposition of a walk traversing each bridge once leads to a contradiction.

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jhonyy9 · Answer

ty. @zzr0ck3r