4 ms·

Where is the proof?

• aneesh 18y ago
  I don't think there is one. At least from what I can gather, this isn't quite a proof that the diagonal of a unit square has length √2. The tablet tells us that the Babylonians knew the length was √2, but it doesn't tell us how they knew, or how they could prove they were right.
• deleted 18y ago
  [deleted]
• Avshalom 18y ago
  There is no proof specifically this is really annoying about most of the Babylonian Texts, they never go into method very much. However from the numbers they got (30, 1;24,51,10, and 30*1;24,51,10=42;25,35) it looks less like they used a proof as they did use an iterative approximation method as follows: let a be some number let a1 be an approximation of sqrt(a) such that a1 > sqrt(a) then B1 = a/a1 is also an approximation of sqrt(a) but deviates in the other direction s B1 < sqrt(a). we have now bracketed sqrt(a) so a new better bracketing can now be made by a2 = (a1 +B1)/2 and B2 = a/a2 and then a3 = (a2 + B2)/2, B3 = a/a3 etc. the answer for sqrt(2) of 1;24,51,10 happens to equal a3 in this case. note that the above is only speculation, but the method DOES produce the Babylonian numbers so and it uses only arithmetic that we know they had, so it seems pretty likely (All this information and more can be found in Mathematical Cuneiform Texts by Otto Neugebauer)