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Packing Ellipses Into a Circle - Preprint of WriteUp

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POSTED BY: Frank Kampas
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Todd, thanks for your comments. I'll forward them to my co-authors. My joking explanation of why I'm doing ellipse packing is that a sarcastic remark from Daniel Lichtbau caused me to realize I'd been stuck on packing circles for too long, so I decided to move on to something more complex. There's some truth to that statement. Also, I'm hoping that the approach used in the paper, using Lagrange multipliers to set up constraints for quantities that cannot be symbolically defined, has more general application. As to applications, some years ago a friend in the medical profession told me that it could be useful for radiation treatment of cancers to find ellipsoids that have small overlap except in the region of the cancer. I haven't yet looked into that. As to part 2 of your comments, I haven't yet been able to pack a large enough number of ellipses to look for patterns. Right now I've just started looking at packing ellipses into regular polygons, as that seems like a logical extension, although no applications come to mind.

POSTED BY: Frank Kampas
POSTED BY: Todd Rowland
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