# Smooth Mapping of Unit Circle

Pip021
Hi, I have been told that in R^2 the unit circle {(x,y) | x^2 + y^2 = 1} is smoothly mappable to the curve {(x,y) | x^4 + y^2 = 1}.

Can someone please tell me what this smooth map is between them? I can only think of using the map (x,y) --> (sqrt(x), y) if x is non-negative and (sqrt(-x), y) if x is negative. Thanks for any help.

Homework Helper
Both $x^2+ y^2= 1$ and $x^4+ y^2= 1$ loop around the origin. Draw the line from the origin through a point on the circle. Where that ray crosses the second graph is s(x,y).

Homework Helper
is there a smoothness problem at x=0? (in answer #1)