This is a follow up to a post entitled Radon related Problem. I hope to continue this series of posts.

Let me introduce Radon’s theorem: It is the following if there are more than d+2 points in a d dimensional space the points may be divided into two sets whose convex hulls intersect in at least one point. When the problem mentioned in the previous post is referred to as Radon related it is this theorem which is meant. Let me give a reference for this theorem:

http://en.wikipedia.org/wiki/Radon’s_theorem

If we try to go beyond a division into 2 sets of points to 3 and more there is a generalization called Tverberg’s theorem. I will talk about it in the next of these series of posts.

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This entry was posted on August 25, 2009 at 10:58 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
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August 27, 2009 at 5:01 pm |

Hi Kristal,

There is a small typo in your statement of Radon’s theorem; you forgot to mention the convex hulls, (and said “dimensiona” somewhere.)

August 27, 2009 at 5:47 pm |

Thank you for this I think I made the corrections.