5 ms·
> Obviously 4 is possible due to the 4 colour theorem... Unless your bathroom includes a loop, such as all four walls (even with holes for windows and doors) o
by rlpb 11y ago
> Obviously 4 is possible due to the 4 colour theorem...
Unless your bathroom includes a loop, such as all four walls (even with holes for windows and doors) or over the ceiling. Then the coloured area is no longer a plane, and so the 4 colour theorem does not apply.
- T-hawk 11y agoWouldn't all four walls still function as a plane, topologically? Think about looking into a cube (box) with one side open, so that you see five faces. The projection of those faces onto your retina or a photograph is a direct mapping to a plane. Four walls plus the ceiling are equivalent to that open box. Four walls minus the ceiling are equivalent to a plane with a hole. You have to include both the ceiling and the floor to break out of plane topology. And what you get is a sphere.
- Chinjut 11y agoA sphere is also four-colorable, functioning equivalently to a plane for such purposes; consider stereographically projecting the sphere (minus a point) onto a plane.