One proof I found compelling was a proof of the inability to trisect an angle given a compass & straightedge. http://web.maths.unsw.edu.au/~norman/papers/Trisection.pdf At 02:04 PM 4/17/2011, Fred lunnon wrote:
On 4/16/11, Henry Baker <hbaker1@pipeline.com> wrote:
Has anyone here dealt with Rational Trigonometry?
I found it as a link through Chebyshev polynomials ?!? http://web.maths.unsw.edu.au/~norman/Rational1.htm http://en.wikipedia.org/wiki/Chebyshev_polynomial
I came across Wildberger's material a few years ago, but haven't pursued it. It is noteworthy that he treats only 2-space in his book, and mentions how much more difficult 3-space would be. His "quadrance" (length squared) and "spread" (sine squared --- would cosine not be a better choice?) hardly seem an earth-shaking improvement on traditional trigonometry ... Squares of length and cosine also turn up as magnitudes in the Euclidean geometric algebra which I've been buttonholing everybody about for the last ten years or so. See â¹TTT_EGA.txt⺠for n-space, and â¹teabag.pdf⺠for 3-space, at
https://docs.google.com/leaf?id=0B6QR93hqu1AhZTcyM2EzNzItYWYwNi00NDU3LTk3NzQ...
The difference is that the GA approach is to a considerable extent independent of the dimension (stand up the man who muttered "just as incomprehensible in two dimensions as ten!"). Admittedly, applying it to plane geometry does look such a pushover that I have never even bothered to try ...
Fred Lunnon