Jung's Theorem

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Royal
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Jung's Theorem

Post by Royal » Thu Mar 01, 2012 3:40 am

Imagine a finite set of scattered points, as you might see in a map of a constellation of stars or randomly placed drops of ink on a page. Draw a line between the two points that have the greatest separation. This largest possible distance d between two points that have the greatest separation. This largest possible distance d between two points is called the geometric span of the set of points. Jung's theorem says that no matter how scattered the points are, they are guaranteed to be enclosed by a circle with a radius no greater than d/[square root 3]

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Pigeon
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Re: Jung's Theorem

Post by Pigeon » Thu Mar 01, 2012 5:30 am

square root 3 = 1.7320508075689

Example of a distance of 10 units

10 / square root 3 = 5.7735026918963

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Royal
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Re: Jung's Theorem

Post by Royal » Thu Mar 01, 2012 5:41 am

Image

Yes

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