Minimal Oval

26/09/2007 - 13:48 von Narasimham | Report spam
Prove by variational calculus or otherwise that Ovals/ Jordan curves
of minimum perimeter through four given points in a plane are
ellipses. No given point falls inside a triangle with the other three
as vertices, avoiding a hyperbola.

Prove also that its area and eccentricity are minimums for this
solution.

Best Regards,
Narasimham
 

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#1 matt271829-news
26/09/2007 - 22:06 | Warnen spam
On Sep 26, 12:48 pm, Narasimham wrote:
Prove by variational calculus or otherwise that Ovals/ Jordan curves
of minimum perimeter through four given points in a plane are
ellipses.



What do you mean by "ovals"? AFAIK there is no mathematical definition
of an oval. To avoid the answer being four straight lines you are
obviously placing some restrictions on the type of curve allowed, but
it's not clear what those restrictions are. Not to me anyway.

No given point falls inside a triangle with the other three
as vertices, avoiding a hyperbola.

Prove also that its area and eccentricity are minimums for this
solution.

Best Regards,
Narasimham

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