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> They then proved that a Gömböc's flatness and thinness both have to be equal to 1, that is, both values have to be as small as is possible.

I don’t get this. The shape in the video looks neither flat nor thin.



It's the other way round. Flatness and thinness are values greater than or equal to 1, so a shape with a flatness of 1 is minimally flat.




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