Fractal Folds Lab Answers

Here are schematics (left) and photos (right) of the first four steps in forming a back fold.

By superimposing the schematics, it is easy to see that in the limit the back folds converge to the line of length sqrt(2).

This is clear, but on closer inspection leads to an observation that may seem paradoxical:

step	number of segments	length/segment	back fold length
1	2	1	2
2	4	1/2	2
3	8	1/4	2
4	16	1/8	2
		...
n	2n	1/2n-1	2

We have a sequence of broken lines, each having length 2, converging to a line of length sqrt(2). What does this suggest to you?

Return to Length of the Cuts.