Yeah, and constructability is usually handled by proving that a length is constructable if it lives in an iterated quadratic extension of the rationals. Pi does not lie in such an extension, so is not a constructable length (and neither is its square root).
It's entertaining when reading is entertaining. This was a great "read while eating lunch at work" read because it was entertaining.
I didn't really care too much about rodent-repelling tape before reading and don't care much now. It was the entertaining writing that brought value for me.