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I was wondering is it possible to try and do optimisation of an ellipsoid given the formulae for its volume and surface area? I would be trying to keep the volume constant whilst minimising SA.

This is for one of my maths investigations, basically trying to minimise packaging of a kinder egg, so if this is somewhat of a dead end, what are some alternative approaches I can take forwards?

Any help would be really appreciated!

Update: Ive derived the equations for the SA and Volumes of an egg shape

Would the Lagrangian Multiplier Method work here enter image description here

enter image description here

Ray Yao
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  • If you do not the formulae, they are given in https://www.had2know.org/academics/egg-surface-area-volume-calculator.html I do no think that it is a dead end but you have three parameters. So, may be, fixing a ratio between two of them .... ? – Claude Leibovici Jul 18 '23 at 02:35
  • my intuition tells me it would be a sphere, as minimizing a rectangle's perimeter for a fixed area is a square. – Set Jul 18 '23 at 03:18
  • @ClaudeLeibovici I've gotten the formulae, do you think setting them as a ratio would work for this – Ray Yao Jul 18 '23 at 07:04
  • Suppose that you make $c=k, b$ and you fix $k >1$. It could me an interesting numerical problem. – Claude Leibovici Jul 18 '23 at 07:17
  • Hmm. Is there any software that I can use to compute this minimum that uses Lagrangian Multipliers? – Ray Yao Jul 18 '23 at 16:10

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