- #1
mnb96
- 715
- 5
Hi,
I have a doubt about parabolic coordinates in 2D.
if u,v are the parabolic coordinates in a plane, and we keep v=v0 constant, we have a parabola. Analogously keeping u=u0 we have another parabola which intersect the previous one in two points.
My question is, how there can be a 1-1 mapping between parabolic and cartesian coordinates without introducing a third coordinate?
What confused me is that Mathworld defines parabolic coordinates using 3 coordinates, while in wikipedia you can find a definition which uses only two coordinates and an elegant form using complex numbers: [tex]f(z)=z^{2}[/tex]. What's the difference?
I have a doubt about parabolic coordinates in 2D.
if u,v are the parabolic coordinates in a plane, and we keep v=v0 constant, we have a parabola. Analogously keeping u=u0 we have another parabola which intersect the previous one in two points.
My question is, how there can be a 1-1 mapping between parabolic and cartesian coordinates without introducing a third coordinate?
What confused me is that Mathworld defines parabolic coordinates using 3 coordinates, while in wikipedia you can find a definition which uses only two coordinates and an elegant form using complex numbers: [tex]f(z)=z^{2}[/tex]. What's the difference?