00:01
So if we start here with a square that has sides x0, x0, x0, x0, and i make a new square going from midpoint to midpoint to midpoint to midpoint, then x0 is 8, x1 according to the pythagorean theorem is going to be the square root of 1 half x0 squared plus 1 half x0 quantity squared.
00:40
So that then is the square root of 2 times x0 squared over 4, which is x0 over 2 times the square root of 2.
01:11
X2, if we do this again, midpoint to midpoint to midpoint to midpoint.
01:22
Now these are length x1, x1, x1, x1.
01:28
These are going to be length x2, x2, x2, and x2.
01:36
So x2 here, according to the pythagorean theorem, is the square root of 1 half x1 squared plus 1 half x1 squared.
01:50
Which is x1 over 2 times the square root of 2.
02:04
So xn is going to be xn minus 1 over 2 times the square root of 2, or xn minus 1 times the square root of 2 over 2...