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I guess the answer is 2, but I cannot prove it.

I mean supermum of the minimum B/A among all A.

Notice:

Central convex curve means the convex curve is symmetric about a point in it, that is, when you rotate the curve 180 degrees about the point, it comes back to the original curve.

For triangle, which is considered the most asymmetric, 2 is a lower bound. That is why I think 2 is a lower bound for all other convex curves

I need to calculate a minimum r=B/A such that for all of the colsed convex curves，their always exists a central convex curve (with area A*r) circumscribe it. Please help me, a lot of thanks.

Nan Zhang
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    Suppose we have two circles, one inside the other with the same center. In terms of theory, `B/A` can go to `1` in limit. – OmG Nov 09 '20 at 12:38
  • If the first curve is "central convex", the ratio is obviously 1. If not, the problem seems terrible. – Yves Daoust Nov 09 '20 at 13:00
  • I know this, but I do not mean a certain case. I need to calculate the lower bounds for all of the convex curves – Nan Zhang Nov 09 '20 at 13:01
  • **I need to calculate a minimum r=B/A such that for all of the colsed convex curves，their always exists a central convex curve (with area A*r) circumscribe it. Please help me, a lot of thanks.** – Nan Zhang Nov 09 '20 at 13:15
  • Please don't shout. We understood that you want this question answered. – Yves Daoust Nov 09 '20 at 13:17
  • Question answered: https://math.stackexchange.com/questions/3900257/for-all-closed-convex-curves-let-central-convex-curves-circumscribe-them-what – Serge de Gosson de Varennes Nov 10 '20 at 18:47

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