Not long ago I found an animated gif on the web that showed a carpenter's square placed on an ellipse such that both arm's of the square remained in contact with the ellipse at all times. The gif traced out the loci formed by the intersection of the square's arms, and that was a circle! Now, I thought, how cool is that? So I took the challenge and proved this result analytically.
I worded the theorem as follows:
The loci of the vertices of all rectangular bounding boxes of an ellipse with semi major and semi minor axes $a$ and $b$ respectively form an ellipse centered circle of radius $c=\sqrt{a^2 + b^2}$, independent of the angle between the ellipse axes and bounding box edges.
(I tried to upload an image, but SE wouldn't let me!)
I have two (related) questions about this 'theorem':
- What's this theorem called?
- Who is credited for 'discovering' it?
The result is perhaps called the Director Circle. Is it like this? A special case shown..
Director Circle Ellipse