x^a + y^a = 1 as a circle arc
- From: vreddyp@xxxxxxxxx
- Date: Sat, 01 Sep 2007 19:44:07 -0700
I was trying to find the equation for the mirror reflection of the
unit circle arc (x^2 + y^2 = 1) in the first quadrant (0<x<1, 0<y<1),
using x+y=1 as the mirror. The third quadrant of the circle (x-1)^2 +
(y-1)^2 = 1 would be the arc I'm looking for. However I need it in the
form of x^a + y^a = 1, where a < 1. I'm trying to find the value of a.
The value 0.5645... seems to be nearest one, but then this curve can
only touch the circle at three places tangentially. Can this be proven
that we can't find such value?
- venkat
.
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