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seen Sep 28 '10 at 22:16

Feb
25
answered Can t-test be used for non-inferiority hypothesis testing?
Feb
11
awarded  Teacher
Feb
11
answered Do you find your students are less competent in basic algebra and arithmetic, and, if so, do you believe that this is due to overuse of calculators at an early level?
Jan
11
comment Is the direction of the longest line of a polytope unique?
ok I understand. Thanks
Jan
11
comment Is the direction of the longest line of a polytope unique?
I edited the question to fix the terminology.
Jan
11
revised Is the direction of the longest line of a polytope unique?
Edited to fix terminology as per comment by Harald
Jan
9
comment Is the direction of the longest line of a polytope unique?
The way I have defined u_{max} above - it is a vector. However, all elements of u_{max} have the same value and hence we have a hypercube in p dimensions. X can have positive or negative values. The original context in which the above issue arises would constrain X to have only +1, 0 or -1 values but I did not mention this constraint as I felt that the general problem would have a positive answer.
Jan
9
awarded  Supporter
Jan
9
comment Is the direction of the longest line of a polytope unique?
Never mind my comment reg $P_v$. The argument does not work. However, I am confused about why you think a rectangle that is perpendicular to the top and the bottom faces of a cube becomes skinnier as $v$ increases. Such a plane will always have the same shape irrespective of the value of $v$. As $v$ increases, the plane shifts towards the origin but retains its orientation. (Note: The longest line is not unique as either diagonal is a longest line but that is a different issue.)
Jan
8
awarded  Student
Jan
8
comment Is the direction of the longest line of a polytope unique?
How about this: Define $S$ as the set of points where $L$ intersects the half-planes defined by $u'_i = 0$ and u'_j >= 0 for all $j$ not equal to $i$. I guess we are done if we can show that for some $v > v^*$ all the points in the set $S$ are less than $1$. The above would suggest that $P_v$ lies entirely in the hypercube and hence 'retains' its shape. Does that make sense? ps; I am unable to edit my comments after posting. I hope the above is clear.
Jan
8
comment Is the direction of the longest line of a polytope unique?
A clarification: Do you mean the transformation $u'\rightarrow u/v$ instead of $u \rightarrow vu$?
Jan
8
comment Is the direction of the longest line of a polytope unique?
@Qiaochu: I am afraid I do not understand your question. My knowledge of math is fairly limited.
Jan
8
awarded  Editor
Jan
8
comment Is the direction of the longest line of a polytope unique?
@Deane: Cleaned up notation to indicate that the question relates to real spaces.
Jan
8
revised Is the direction of the longest line of a polytope unique?
added 21 characters in body; added 10 characters in body
Jan
8
comment Is the direction of the longest line of a polytope unique?
Sorry for the confusion. I do not usually use LaTeX. I cleaned up the LaTeX glitches.
Jan
8
revised Is the direction of the longest line of a polytope unique?
deleted 9 characters in body; added 11 characters in body; added 2 characters in body
Jan
8
asked Is the direction of the longest line of a polytope unique?