A related puzzle is: why is sin(333) + sin(355) = sin(22) [angles in radians] good to 1e-9? It's easy to say why it's good to 1e-3, a bit more work to s

A related puzzle is: why is sin(333) + sin(355) = sin(22) [angles in radians] good to 1e-9? It's easy to say why it's good to 1e-3, a bit more work to show it's 1e-6, and just a little bit more to say why it's 1e-9. If you know 22/7 and 355/113 then you just subtract them to get another continued fraction for π: (355 - 22)/(113 - 7) = 333/106 ~ pi; that's a bit of a hint. https://recursed.blogspot.com/2014/01/math-challenge-1.html https://recursed.blogspot.com/2014/01/math-challenge-1.html