Talk:Three Cottages Problem
I appreciate the mouse overs a lot. The only thing that might be helpful is copying one of your earlier pictures and labeling a node, edge, and face.
I fixed a "teh" and made it "the." I'd also like to see you address my comments below.
Can you put mouse overs on "nodes" "edges" and most importantly "faces" to define them?
Also, is there any way to create a figure to go along with your second solution?
Also, link to the Torus page when you talk about it.
"The three cottage problem is an
elementary problem in graph theory." Hey, don't label like that! It's hard for some folks.
"and is the number of faces." I think we need an F in this Alternate Solution.
Ideas for future: "A interactive animation of the torus solution." But don't wait for that to go public!
The first proof is something that seems somewhat iffy to me. I'll do more modifications as needed.
The 2nd proof is somewhat long and tedious to read, any ideas for fixing that?
The pictures on this page on not very good since I used paint. I'll be collaborating with Brenden to use Mathematica to make better ones, so hold off judgment.
What if we had an applet where the three houses and three wells were already there and the user could draw lines trying to connect them but when two lines cross, those lines turn red and a message appears saying the solution won't work?
That sounds perfect. -Alan