><snip> which we neglected in this approximation <snip>
>That statement takes me back to High School physics where we neglected a lot of things to make it easier to calculate (like friction, wind resistance, gravity) and there was also naver any measurement errors even when measuring with a old wooden ruler :) Life sure was simple in High School physics

...which continued into college physics, in my case. I had one extended course in physics (it was something like a minor to us mathematicians), but we had the course together with chemists, and guess what - almost all the approximations we scoffed at in high school were still there. In case of pendulum, I couldn't ever understand how could they replace the sin(phi) with phi, just like that? It's sufficiently different for any decent swing. But then, even such a simplification was too much for the poor chemists :).

The main reason I never liked physics was this lack of precision... at least they could have said "here we discard the members of degree higher than 1 because we don't know how to calculate them" :).

I can't imagine what sort of jokes were the physicists telling about us :).