Jordan's theorem
How to prove that the problem of the three houses has no solution on the plane. We should add three more paths to the hexagon that join every vertex with its opposite, but every path can pass either though the interior or the exterior of the region.
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")
Jordan's theorem and the three houses problem (Topology)
Images from the topology section (From the exhibitions of matematita)
