Ques: Extreme configuration of vectors on a set of planes

Dr. Sumanta Guha guha at blatz.cs.uwm.edu
Sat Sep 14 08:06:41 PDT 2002

Any light on the following problem will be much appreciated.

Let P be a set of n planes in R^3. A configuration C of
vectors on P is a set of n vectors, one each lying on
a plane of P. Define max(C) to be the maximum of
angles between pairs of vectors from C. The question
is: determine min {max(C): C is a configuration
on P}. Equivalently, what is the largest angle X s.t.
given any configuration C on P there will be at least
one pair from C making an angle at least X?

Eg., if P is the set of 3 co-ordinate planes the
answer is 60deg. In other words, if we place 3 vectors, 
one each on a co-ord. plane, at least two will have an 
angle of 60 between them. An extreme configuration of 
vectors in this case is easily seen to be with
the vectors at 45 to the axes.

A cc of your response to guha at uwm.edu will be appreciated.
Thanks in advance,
Sumanta Guha

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