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For a surface with boundary as a curve in $\mathbb{R^2}$ , the surface formed when blowing bubbles may looked like a sphere with a disc of area removed.

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I know that the surface tension forces on the sphere is completely controlled by the bubble blowing ring's radius, so by what theoretical reason was it concluded that a sphere be formed when blowing the bubble ring straight through the center?

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A sphere is the 3-D shape which encloses the maximum volume within the minimum surface area. Because of the elasticity of the bubble film, it strives to minimize its surface area, which naturally yields a spherical shape for the bubble at equilibrium.

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  • $\begingroup$ Hmm, but isn't surface tension controlled by the boundary? The boundary is fix so it seems to me whether it is sphere or paraboloid or whatelse, the force of surfacetension should be same $\endgroup$
    – Brian
    Commented Sep 24, 2021 at 5:15
  • $\begingroup$ Or, are there other reasons for it toenclose max volume with min surface area $\endgroup$
    – Brian
    Commented Sep 24, 2021 at 5:15
  • $\begingroup$ the maximum volume/minimum area fact can be derived mathematically. $\endgroup$
    – niels nielsen
    Commented Sep 24, 2021 at 5:25

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