depends on the method they used to come up with the formula. It's not obvious that the sum of a "more complicated than you can do in your head" series of fractions would be either the square root of two or the the diagonal of a square, let alone both. This is a fragment of a single clay tablet. If they had a systematic method of coming up with this convergent series, there might have been a stack of tablets showing square root of three, five, etc. It seems pretty highly suggestive to me.
I agree.Obtaining this formula by observing is more difficult than obtaining it by proving it. Besides, it is an issue that is already needed in field work. If you have pen, paper and a good number system, it shouldn't be too difficult to find the formula with shapes.
That entirely depends on how close you are to high-clay-content muddy bank with a growth of reeds vs. how close you are to the nearest convenience store/office supply store.
