2018-06-11 19:33 GMT+02:00 Michael Selik <m...@selik.org>: > Whoops, it turns out Euler's formula does work! I expected imprecision, > but at least one test matched. > > x = 42 > cos(x) + 1j * sin(x) == e ** (1j * x) >
I think you will find it holds for any x (except inf, -inf and nan). The boat is less leaky than you think; IEEE floating-point arithmetic goes out of its way to produce exact answers whenever possible. (To great consternation of hardware designers who felt that requiring 1.0*x == x was too expensive.) > I suppose that's because it's radians. > Well, the formula obviously only holds in exact arithmetic if cos and sin are the versions taking radians. Stephan > > > On Mon, Jun 11, 2018, 10:24 AM Michael Selik <m...@selik.org> wrote: > >> Would sind and cosd make Euler's formula work correctly? >> >> sind(x) + i * sind(x) == math.e ** (i * x) >> >> I suspect that adding these functions is kind of like those cartoons >> where the boat is springing leaks and the character tried to plug them with >> their fingers. Floating point is a leaky abstraction. >> >> Perhaps you'd prefer an enhancement to the fractions module that provides >> real (not float) math? >> > > _______________________________________________ > Python-ideas mailing list > Python-ideas@python.org > https://mail.python.org/mailman/listinfo/python-ideas > Code of Conduct: http://python.org/psf/codeofconduct/ > >
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