Comment by lupire
What definition of area are you using in the first place, for non-swuare objects? Most people find area intuitive and informal, but if you describe area formally, it should be easy to use your definition to account for scaling.
What definition of area are you using in the first place, for non-swuare objects? Most people find area intuitive and informal, but if you describe area formally, it should be easy to use your definition to account for scaling.
I was saying two separate things. Thing 1, the non-square shapes are relevant to Einstein's nice proof. Thing 2, considering squares now if you like, pythagoras's theorem has a magical quality which proofs can't dispel.
If you travel some distance, square it, travel some other distance perpendicularly, square that too, and add the results, you get the square of the straight distance from start to finish. Every proof just seems like a reformulation of this freaky fact.