#### Re: Trigonometry is not about triangles...

The Coward is right - and the diagrams show it.

The authors seem a little confused...

"it does not use angles and it does not use approximation": " A squared index and simplified values of b and d to help the scribe make their own approximation to b/d or d/b" - so did they approximate or not?

As has been pointed out, the examples are just special cases of right angle triangle ratios, only relevant when processing those triangles, or the "half a rectangle", whereas the sine/cosine/tan ratio mechanism is not restricted to right-angled triangles, just to angles. Even better if you further generalize to the circle view and bring in radians...

Then they say "The Babylonian approach is also much simpler because it only uses exact ratios. There are no irrational numbers and no angles, and this means that there is also no sin, cos or tan or approximation."

Well a 30 degree angle, which has a lovely sine value of 0.5, would have an inconvenient "ratio" expression that is irrational in any base. So much for exact calculation.

The only reason those examples are exact and don't involve irrationals is because they cannot handle the cases where irrationals are needed and so restrict themselves to a few special cases.

There's a reason why we don't do things their way, and haven't for a long time. And it isn't because the ancients had a deeper understanding of trigonometry than we do... two thousand years ago the Greeks knew you can't square the circle.