Avoiding Trigonometry (2013)

Post by the__alchemist » Sat, Mar 14, 2026, 12:00 PM UTC

adrian_b wrote: post #82

the__alchemist wrote: post #81

Earlier quoted context omitted.

Holy shit I have to try this.

Unfortunately, IEEE Std 754 contains a huge mistake, which has been followed by some standard libraries for programming languages. As an alternative to the trigonometric functions with arguments measured in radians, it recommends a set of functions with arguments measured in half-cycles: sinPi, cosPi, atanPi, atan2Pi and so on. I do not who is guilty for this, because I have never ever encountered a case when you wan…

Great's great info on curvature! Also don't see the use of the half cycle, although obviously see use of cycle. (As was thinking in terms of them anyway, just with a tau term to convert to radians.)

Post by ajkjk » Sat, Mar 14, 2026, 5:02 PM UTC

donkeybeer wrote: post #90

ajkjk wrote: post #88

Earlier quoted context omitted.

I think it's just a perspective shift. The main idea is that you can't ever measure a real number, only an approximation to one, so if two values differ by less than the resolution of your measurement they are effectively the same. For example consider the derivative f(x+dx) = f(x) + f'(x) dx + O(dx^2). The analysis version of the derivative says that in the limit dx -> 0 the O(dx^2) part vanishes and so the limit [f…

Yes but like I was thinking more how you'd do any kind of "and it vanishes" or even "becomes sufficiently small" with a gappy number system as it would have to pass through gaps where "undefined" non-rationals exist.

I guess my stance (which is not very well-developed or anything) is that you try to learn to live with the gaps: define everything in terms of only what you can measure and it no longer matters whether a number is rational or irrational, or infinitesimal vs small-but-finite, because you can't tell. Instead of saying "it vanishes" as an absolute statement you say "it appears to vanish from my perspective".

Re: Avoiding Trigonometry (2013)

Re: Avoiding Trigonometry (2013)