Babylonian trigonometry "simpler, more accurate... has clear advantages over our own."

[muriel_volestrangler]

9. I want to know what they mean by 'simplified' values

This is by the paper's authors:

This precise arithmetic of the Babylonians also influenced their geometry, which they preferred to be exact. They were able to generate a wide variety of right-angled triangles within exact ratios b/l and d/l, where b, l and d are the short side, long side and diagonal of a rectangle.
...
Fundamentally a trigonometric table must describe three ratios of a right triangle. So we throw away sin and cos and instead start with the ratios b/l and d/l. The ratio which replaces tan would then be b/d or d/b, but neither can be expressed exactly in sexagesimal.

Instead, information about this ratio is split into three columns of exact numbers. A squared index and simplified values of b and d to help the scribe make their own approximation to b/d or d/b.

https://theconversation.com/written-in-stone-the-worlds-first-trigonometry-revealed-in-an-ancient-babylonian-tablet-81472

"The first five rows of Plimpton 322, with reconstructed columns and numbers written in decimal."

Now, of course, tan is not "b/d or d/b", since tan does not involve a diagonal. tan is b/l, or l/b (depending on whether you're looking at angles less than or greater than 45 degrees). So these guys are pretty awful at expressing whatever idea they think they have.

But what does "simplified values of b and d" mean? And how were the reconstruction columns and numbers actually written - as the precise fractions - eg for the 5th row (other value of the triplet not shown is 72), so b/l=65/72, d/l=97/72, (d/l) squared=9409/5184? If so, then I suggest a table with its 4th row as 12709/13500, 18541/13500 (or perhaps 1 and 5041/13500), and 343768681/182250000 is not that practical.