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Here's a bit of a math stump I've been trying to work out. If you have a quarter unit circle, without using sqrt or trig funcs, given x can you find y for the line of the circle? Maybe helpful: the triangle (x,y), (x,0), (1,0) is similar (0,0), (x,0), (x,y).pic.twitter.com/triNFFcOVX
Additional thought on the similar smaller triangle. Because we know 1-x, we know the length of all three sides, just not all in the right "scale" at the same time. If one more side could be determined on the smaller triangle, I think we could determine the difference in scale.
Hm. Observation that the other triangle is similar may not be true in all cases. But maybe in all cases above 0.5? Need to think more...
Yeah congruent triangle thing was wrong. I was thinking of a half circle. *shrug*
Why do you not want a sqrt? Is it because of performance or lack of instruction? 1 - x^4 is the cheapest approximation but quite off with an RMS error of 5% over the [0, 1] Otherwise you can just do taylor expansions around x=0 or x=1/sqrt(2) or x=1 depending on what you need
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