The problem of the three houses
How to prove that the problem of the three houses on the plane has no solution: in the figure we see that the first six paths are bouded to create a simple, closed curve (the boudary of the yellow region). We should add three more paths to the closed line which is the boundary of the yellow region and these paths should join every vertex with its opposite (D and G, L and N, S and C); but every path can go through the interior of the exterior of the region, so....
You can also try to solve this problem online with the interactive animation Paths without crossings.
© matematita
The image belongs to the sections...:
From "fragments of topology" (From "XlaTangente")
From the exhibition matemilano (Topology)
Jordan's theorem and the three houses problem (Topology)
Images from the topology section (From the exhibitions of matematita)
Further information:
http://matemilano.mat.unimi.it
