How is the first column of plimpton 322 derived from the other columns?

Consider the first row of the tablet. The second, $b,$ and third, $ c,$ column are pythagorean triples $(a,b,c)= (120, 119, 169)$ that satisfy $a^2 + b^2 = c^2.$ We can derive, $a, $ by taking the root of $a^2= c^2 - b^2$ which give us $ 120 = \sqrt{169^2 -119^2}.$

Now the first column should be $b^2/a^2 = (119/120)^2 = 0.983403.$ But when I convert the $1:59:00:15 $ to a base $ 10$ notation then I get $428415. $ How are these supposed to be the same or where am I making an error ?

Reference: Wikipedia; ScienceDirect.


1 Answer 1


If I translated the notation correctly, the paper you link says that the first column is $c^2/a^2$, and in this example at least this seems correct (1;59,00,15 is in fact exactly $(169/120)^2$).


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