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post #8 of Old 09-20-2012 Thread Starter
Classic30
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Re: Moment curves

Quote:
Originally Posted by SloopJonB View Post
Add me and we have "dimmest". Unless it's Steven Hawking speaking I can usually grasp the concept but that link was totally ununderstandable.
At least now I know I'm not the only one!

From Wikipedia: "The convex hull of any finite set of points on the moment curve is a cyclic polytope.[3] Cyclic polytopes have the largest possible number of faces for a given number of vertices, and in dimensions four or more have the property that their edges form a complete graph. More strongly, they are neighborly polytopes, meaning that each set of at most d/2 vertices of the polytope forms one of its faces. Sets of points on the moment curve also realize the maximum possible number of simplices, among all possible Delaunay triangulations of sets of n points in d dimensions.[4]"

Repeat that quickly at your next dinner party and your 'neighbourly polytopes' will tie you up in white canvas and pack you off to the local looney bin!!


(..so I'm secretly hoping one of the Design Gurus around here can teach us something before we all go barmy. )

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"Honestly, I don't know why seamen persist in getting wrecked in some of the outlandish places they do, when they can do it in a nice place like Fiji." -- John Caldwell, "Desperate Voyage"

Last edited by Classic30; 09-20-2012 at 03:28 AM.
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