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I'm trying to understand Menger curvature in terms of shape determination in isolated cases of 3 well-distributed (defining) coordinate points that could form part of a shape that may be either a circle or an oval.

It seems that the menger curvature will generate a smaller number for bigger circles (inverse R), but can this be used to determine the simple geometrical shape of three points, i.e, whether in the plane, they are a circle or oval (oblong)?

ina
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    Three points are not enough to distinguish a circle from any other shape, because there is always a circle passing through three points. This is like trying to tell if a shape is a straight line given only two points. –  Mar 26 '18 at 04:28
  • @Rahul : Under the circumstances (i.e. nobody has posted an answer and it does not appear that more can be said than what is in your comment), maybe you should make your comment an answer. – Michael Hardy Apr 20 '18 at 15:50

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