Suppose S is a≤u≤b, A≤v≤B and let (u,v) → (r,θ) so then x=rcosθ, y=rsinθ … (i)
We need 1≤r≤√3, 0≤θ≤π/2 so suppose r=f(u), θ=g(v)
If f(a)=1 and f(b)=√3 we can set r=f(u)=3^{½(u−a)/(b−a)} so 1≤r≤√3
If g(A)=0 and g(B)=π/2 we can set θ=g(v)=(π/2)(v−A)/(B−A) so 0≤θ≤π/2
With (i) this r & θ define T
