Wonderful to read such an in-depth analysis of a true classic.

This part confused me:

Notice how the medium asteroid is twice the size of the small one, and the large is twice the size of the medium. If you think about it, this doesn't actually make much physical sense -- you can break a two-dimensional object into four pieces half its size, not two.

I'm looking at 2-dimensional objects on the table here, such as papers, and I just don't see how that is true. For instance split an A4 paper in half: you get two A5 papers, not four. By definition the size of an A5 is exactly half of an A4's size.

What am I missing?