YBC 8633 Babylonian Partitioned Triangle Problem

  The Old Babylonians did partitioned triangle problems. An example is YBC 8633.

The cuneiform tablet is somewhat damaged but according to Neugebauer the data for the triangle in the upper left corner can be read as follows.

The calculation of the areas is somewhat off since the base of the inner triangle is 20/60=1/3 and the side, taken to be 1+1/3, is used as the altitude of the triangle. The calculations are as follows with a decimal translation which multiplies the sexagesimal fractions by 60 for convenience.

The tablet would make more sense if 1;12 was used instead of 1;20 for the inner side and 1;11 was used as the altitude.

Perhaps the length of the inner side was misread and the problem then recalculated incorrectly. The Pythagorean theorem would have allowed the scribe to solve for the altitude correctly. The writing is rather cramped and a copyist may have had the same problem working with damaged tablets.

This problem shows how the Old Babylonians might have used steps and a common distance of a line from a point to record changes in direction.