[pfortuny]

So not so OBVIOUS, anyway. You need the notion of convexity (not so easy to give abstractly unless you already know the definition). Items 4 and 5 look clear but from there to obviousness...

Being visually intuitive is very different to being obvious.

[authoritarian]

This seems a bit pedantic. I'm certainly not a mathematician but it does seem obvious that you cannot cut a circle into any number of pieces and rearrange it to be a square, as a circle has curves which would prevent you from making the square a solid without gaps

[pfortuny]

No no; I’m trying to explain that “obviousness” is a bad idea to prove anything...

Like “an infinite te has an infinite branch”...