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Re: Sine and Cosine Accuracy
Marc Espie wrote:
Sorry for chiming in after all this time, but I can't let this pass.
Scott, where on earth did you pick up your trig books ?
Sorry, too, but why one earth do modern time mathematics scholars
think that sine and cosine are bound to have to do with an equally
modern notion of real numbers that clearly exceed what a circle
has to offer? What is a plain unit circle of a circumference that
exceeds 2Ï?
How can a real mathematical circle of the normal kind have
more than 360 non-fractional sections?
By "real circle" I mean a thing that is not obfuscated by the useful
but strange ways in which things are redefined by mathematicians;
cf. Halmos for some humor.
And yes, I know that all the other stuff mentioned in this thread
explains very well that there exist useful definitions of sine for real
numbers outside "(co)sine related ranges", and that these definitions
are frequently used. Still, at what longitude does your your trip around
the world start in Paris, at 2Â20' or at 362Â20', if you tell the story
to a seaman? Cutting a pizza at 2.0^90. Huh?!
Have a look into e.g. "Mathematics for the Million" by Lancelot
Hogben for an impression of how astounding works of architecture
have been done without those weird ways of extending angle related
computations into arbitrarily inflated numbers of which no one knows
how to distinguish one from the other in sine (what you have dared to call
"obvious", when it is just one useful convention. Apparently some
applications derive from different conventions if I understand Scott's
remarks correctly).
Sure this might have little to do with ANSI C99 requirements of fpt
computations, but then this thread teaches me that -ansi C should be given
up in favor of -pedantic Autoconf...
-- Georg