Farthest points in asymmetric 2D closed curve

Question

Is there a mathematically proper name for the two points that are located farther away from each other in a 2D asymmetric closed curve? See the image below to get an idea of what I mean.

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I am not familiar with an explicit name. Have you worked out the geometrical condition for this to happen? (It involves the normal lines.) Perhaps you could use that to invent a name. — Fly by Night, Nov 08 '13 at 16:51

score 1 · Accepted Answer · answered Dec 18 '13 at 06:16

1

A pair of points with this property ($d(a,b)=\operatorname{diam}C$) is called a diametral pair.

Every compact set has at least one diametral pair. It is not unique in general (e.g., for a circle).

answered Dec 18 '13 at 06:16

Post No Bulls

9,056

Great! Thank you very much for the answer! – Gabriel Dec 18 '13 at 12:32

Farthest points in asymmetric 2D closed curve

1 Answers1