In our weaving-pattern example, the number of stones (or thread crossings) of a square standing on the point is always odd and kan therefore never be a double square number that is always even.

This means that the doubling of the square will never work when the figure is made of countable or discreete elements arranged in a grid.

	Arithmetic and Weaving in Antiquity A pebble proof of the incommensurability in the square

	In our weaving-pattern example, the number of stones (or thread crossings) of a square standing on the point is always odd and kan therefore never be a double square number that is always even. This means that the doubling of the square will never work when the figure is made of countable or discreete elements arranged in a grid.