Talk:Group of rational points on the unit circle
Latest comment: 12 years ago by Richard L. Peterson in topic Error in first paragraph
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Why not a^2 + b^2 =p^2?
editHi, thanks for spotting the error a^2 + b^2 = p. That's terrific! But offhand, is it necessary to change it to, essentially, an a' and a b' that are equal to a^2-b^2 and 2ab, respectively?24.7.28.186 (talk) 02:23, 23 August 2011 (UTC)
- And, supposing you wanted to choose the generating points so that they were all in the first octant(First quadrant, x>y)? Then the numerator of the y coordinate must be allowed to sometimes be odd, and vice versa for x coordinate. So (a/p, b/p) is more flexible.24.7.28.186 (talk) 05:43, 24 August 2011 (UTC)
Error in first paragraph
editThe third sentence states:
"if (x, y) is a rational point on the unit circle, then there exists a primitive right triangle with sides xc, yc, c."
If c and xc are sides of a triangle, then they are both > 0. But there are rational points (x,y) on the circle with x < 0, forcing c < 0 also -- contradiction.Daqu (talk) 04:03, 8 March 2012 (UTC)
- you're right, thanks.Rich (talk) 04:55, 3 August 2012 (UTC)