180 Days of Ideas for Discussion in Math Class.
(as of 9July2014, we're in overtime!)
For the first figure:What is the sum of the areas of all the white triangles?What is the sum of the perimeters of all the white triangles?Why do the answers differ so much?
This reminds me of Cantor's Middle Third.Take a line segment. 0 to 1 will do.remove the middle third, from 1/3 to 2/3 but leave the end points.Do this to each of the remaining thirds.And again.And again.......The question is "What is left ?".