As much as I love Mr Tompkins, I think there are some errors in the book.

I'm at the part where Mr Tompkins learns about curved space.
It's said in the book that positively curved area works like this:
>take the radius of the Earth. that radius corresponds to the area northern hemisphere
>now, add to it the area of the southern hemisphere
>you doubled the radius, and doubled the area
>thus area in positively curved space grows slower than in the case of a flat circle

This isn't true. The surface area of a sphere isn't directly proportionate to r, but r^2 just like a flat disk would.