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Puzzles: Crazy curves

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Crazy curves 

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Except for the circle (which is shown for reference), on the other three curves, except where the curves cross an axis, all the points (x,y) have an interesting property. In fact this property holds for all the curves of this family for any power of x and y above 2. What is so special about the co-ordinates (x,y) of these points and why?
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Content Type: Discussion
Created at 10/01/2014 08:36 AM  by John Rowland 
Last modified at 13/01/2015 04:10 PM  by John Rowland