n=500;
k=2;
x=rnorm(n);
y=rnorm(n);
u=x/sqrt(x^2+y^2);
v=y/sqrt(x^2+y^2);

r=runif(n);
s=r^(1/k);
uu=s*u;
vv=s*v;

t=seq(0,2*pi,.01);
#plot(x,y,xlab="x",ylab="y",main="N(0,I_2)",asp=1);
plot(uu,vv,xlim=c(-1,1),ylim=c(-1,1),xlab="x",ylab="y",main="unif(B^2) et unif(S^1)",col="blue",asp=1);
par(new=T)
plot(u,v,xlim=c(-1,1),ylim=c(-1,1),xlab="x",ylab="y",col="red",asp=1);
polygon(cos(t),sin(t));
abline(v=0,lwd=.5);abline(h=0,lwd=.5);
#points(0,0);

for (i in 1:n) {
#	abline(a=0,b=y[i]/x[i],lwd=.1)
	}