# B Transforming a circle onto another plane

1. Apr 24, 2017

### guyburns

I am putting in a new flue for a Pot Belly stove. The ceiling through which the flue goes slopes at 12.5º. I want to cut a hole in a metal plate that will be fixed to the ceiling, and through which the flue passes.

So, a vertical circular flue, radius R, passing through a ceiling sloped at 12.5º to the horizontal.

How do I get the shape of the hole? I assume it is going to be an ellipse with short axis A, long axis B, where:
A = R
B = R/Cos (12.5º)

My thinking is to:

1. Generate a circle of Radius R in Photoshop.
2. Transform (stretch) the circle horizontally by 1/Cos(12.5º). It becomes an ellipse.
3. Print the result, lay it on top of the sheet metal, punch a few holes as markers, then cut it out.

Is the mathematical part of the above correct?

2. Apr 24, 2017

### PeroK

That looks right to me.

3. Apr 24, 2017

### guyburns

Thanks PeroK. I'm a bit long in the tooth to be sure of my maths anymore.

Next step: try it with a cardboard cutout.