bridges of Konigsberg

[AntonioLao]

In 1736, Euler wrote a paper on the bridges of Konigsberg. This is now regarded as the earliest paper about the theory of graph. He presented his solution and present-day solution also existed. More about graph theory at the following site.

http://mathworld.wolfram.com/Graph.html

and

http://mathworld.wolfram.com/Koenigs...geProblem.html

Obviously, graph theory is based on two dimensions. But what is the 3D analogue of this theory?

[Guille]

I guess that at least the 3d analogy of this "graphs" would include faces. So it would have a big adjacent part to it.

[Guille]

I also think that graph theory in 3d would ahve different types of craphs.


But....wait.....These graphs already are 3 dimensional analizes. I say this because the edgs can cross, whiles in 2d that's important. I guess these graphs are 2d representations of 3d phenomena.

If you disagree, try this:

draw three circles and three triangles of the size you want and the positions you want on the same paper. You can't make any of the objects touch another object directly. Try to join each circle with each of the triangles. At the end, there is a minimum of one line that you can't do without crossing with another line. Thus, this exercise can't be done in 2d. It requiers 3d so that one line could go under another one.

[AntonioLao]

GUILLE,

What I'm trying to visualize are forbidden 3D regions, which can only be connected by 3D bridges. So, the bridges must exist in 4D! Maybe these are wormholes between different universes?

[Guille]

well,

wormholes haven't been proved and plus theoretically, they don't uccupy space: you can travell them in zero time, though they have legth they have no space. It's dificult to explain.

That's why I would be far from them. And you would have to say a way of proving the 4 dimension. I don't ahve problems with new dimensions, I just need strong proves.

[AntonioLao]

wormholes haven't been proved and plus theoretically, they don't uccupy space:

wormholes are 4D or higher dimensional bridges. connecting the future light cone to the past light cone centering on an event, which is called the present.

[Guille]

what is a light cone?

[Guille]

Antonio,

As an answer I must say that 3d objects can be conected via 3d objects. You can get two cars put thm one meter apart. You get a ruler. The ruler touches with each end a car. The cars are 3d obejcts conected via 3d object: ruler.

You don't need 4d at any time.

[AntonioLao]

As an answer I must say that 3d objects can be conected via 3d objects. You can get two cars put thm one meter apart. You get a ruler. The ruler touches with each end a car. The cars are 3d obejcts conected via 3d object: ruler.

If you happen to be in Texas, you will see many bridges and overpasses, which were built to solve traffic jams and rush hour congestions. These bridges and overpasses are analogous to the vacuum bridges to overcome the mass congestions found everywhere in the universe as galaxies and stars. All things moves along curvatures, which are geodesic bridges in 4 dimensional manifold. But these geodesic bridges do not cross the fifth dimension of spacetime.

[AntonioLao]

what is a light cone?

the following site contains information about light cone
http://en.wikipedia.org/wiki/Light_cone