Op 11 jun. 2018 om 09:18 heeft Jacco van Dorp <j.van.d...@deonet.nl> het volgende geschreven:
>> Remember, because π is irrational, we cannot actually call sin or cos on >> any rational multiple of π. We can only operate on multiples of pi, >> which is *close to* but not the same as π. That's why it is okay that >> tan(pi/2) returns a huge number instead of infinity or NAN. That's >> because the input is every so slightly smaller than π/2. That's exactly >> the behaviour you want when x is ever so slightly smaller than π/2. > > > This would basically be the reason for a PiMultiple class - you can > special case it. You'd know sin(PiMultiple(0.5)) == 0. You'd know > cos(PiMultiple(0.5)) == -1 and tan(PiMultiple(0.5)) == nan. This could > let you remember as much angles as possible into multiples of pi, and > as long as you're in multiples of pi, you're exact. > PiMultiple(Fraction(1, 6)) would be exact and could give the right > sin() and cos() behaviour. > > And because it'd be a numeric type, you could still use it with all > other numeric types and add/multiply etc it. When you add and subtract > it with another numeric type, it'd lose the special status, but even > with multiples and divisions you can preserve it's specialness. > > And if it gets weird values, you can always fall back on converting it > to a float, therefore never giving worse results. > > It also gives a reason -against- degrees. if you have PiMultiple or > TauMultiple, it's rather easy to give common angles, and students can > learn to properly learn radians for angles as they should.(because, > lets be honest, they're objectively better measures of angles than > degrees, or even *shiver* grads. ) > > We SHOULD make it easy to code exact and the right way, and I think a > PiMultiple class could help that a lot. That said, it does need a > better name. What is the real world advantage of such a class? So far I’ve only seen examples where the current behavior is said to be confusing for students. In most cases where I have used math.sin the angle wasn’t a constant and wasn’t an exact mulltiple of pi. Ronald > _______________________________________________ > Python-ideas mailing list > Python-ideas@python.org > https://mail.python.org/mailman/listinfo/python-ideas > Code of Conduct: http://python.org/psf/codeofconduct/ _______________________________________________ Python-ideas mailing list Python-ideas@python.org https://mail.python.org/mailman/listinfo/python-ideas Code of Conduct: http://python.org/psf/codeofconduct/
