# Conformal mapping. From an ellipse to a rectangle

1. Jun 23, 2006

### traianus

Is it possible to transform an ellipse

x^2/a^2 + y^2/b^2 = 1 ("a" minor or major semiaxis)

Into a rectangle?
If so, how can I do it? I am not very familiar so please explain all the details. I know the transformation from a circle to an airfoil, but not this one.

2. Jun 23, 2006

### AKG

Conformally? I don't think so. Conformal mappings preserve angles.

3. Jun 23, 2006

### traianus

I know that there is a transformation from a rectangle to an ellipse (book advanced enginnering mathematics by Kreyszig) but it is not conformal somewhere

4. Jun 24, 2006

### AKG

Like I just said, conformal mappings preserve angles. There are at least four places where a rect-angle ('rect' means 'right', 'angle' means 'angle') cannot be mapped conformally to an ellipse. Are there any right angles on the boundary of an ellipse?

5. Jun 24, 2006

### traianus

AKG, what you are saying is obvious and I knew it. But, except these four points, is there a transformation?

6. Jun 24, 2006

### Hurkyl

Staff Emeritus
Are you really looking to turn an ellipse into a rectangle, or are you more interested in their interiors?

7. Jun 25, 2006

### traianus

I am trying to transform the ellipse into a rectangle

8. Aug 29, 2008

### afrdzak

Hi, I found your quote while doing a search for transforming a rectangle to an ellipse. I found the book you mentioned and could not find the information I am looking for.

Can anyone assist me in finding out how to transform a rectangle into an ellipse?

Thanks

9. Oct 22, 2010

### lvirany

What you can do is map the ellipse to the real axis and map the real axis to a regular 4-sided polygon using Schwartz-Christoffel.