55,201 reputation
6113434
bio website cs.smith.edu/~orourke
location Smith College, U.S.
age
visits member for 5 years
seen 4 hours ago

Professor of Computer Science; Professor of Mathematics; Associate Provost & Dean.


5h
answered Numerical equality testing
12h
comment Is every closed curve in 3D a geodesic on a genus-0 surface?
Your proof would make a nice paper for e.g., the American Mathematical Monthly or its equivalent, in case you are so inclined :-).
18h
accepted Is every closed curve in 3D a geodesic on a genus-0 surface?
1d
awarded  Good Question
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awarded  Nice Answer
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comment Is every closed curve in 3D a geodesic on a genus-0 surface?
Because (a) of the iterative nature of your answer, and (b) my lack of understanding of your linking-number obstruction (not your fault---my limitations), I am left unclear on the status of the answer. Is it the case that if $\gamma''$ never vanishes, it is a geodesic on a genus-zero surface? Has the (most generalized) question been answered completely? I.e., have you isolated necessary and sufficient conditions, or are there still pockets to explore?
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revised John Nash's Mathematical Legacy
Link to Deane's answer.
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answered John Nash's Mathematical Legacy
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comment How I can proof this conjecture if it's not open?
Despite your lack of interest in initial values, perhaps your conjecture is True for initial values of $1$.
1d
comment How I can proof this conjecture if it's not open?
Perhaps you intended some specific initial values, e.g., $z_0=z_1=z_2=1$...?
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awarded  Nice Question
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accepted The most number of points that realize only $k$ distinct distances
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comment The most number of points that realize only $k$ distinct distances
Excellent---Thanks!
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comment The most number of points that realize only $k$ distinct distances
Great, just what I need---Thanks! (I cannot access the handbook until next week.)
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comment The most number of points that realize only $k$ distinct distances
@SamHopkins: You are right, I need to study the Guth-Katz bound.
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comment The most number of points that realize only $k$ distinct distances
@AaronMeyerowitz: Hmm. For a pentagon inscribed in a unit-radius circle, I find $s \approx 1.176$ while the distance from each added above/below point to a pentagon point is $s' \approx 1.160$.
2d
comment The most number of points that realize only $k$ distinct distances
@SamHopkins: Yes, I think Gerhard's comment clarifies. The Erdős conjecture is that the min # of distances is $g_d(n)=\Theta(2^{n/d})$, which reverses to saying that my $f_d(k)$ grows like $d \log k$. This is already useful (Thanks!) but doesn't help me determine, e.g., $f_3(2)$...
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asked The most number of points that realize only $k$ distinct distances
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comment Is every closed curve in 3D a geodesic on a genus-0 surface?
:-) $\mbox{}\mbox{}$
2d
comment Euclidean Minimum Spanning Trees Restricted to One Vertex Per Grid Cell
"from the interior of each cell": Your drawings indicate: from the interior or boundary of each cell, i.e., the tree must touch each cell.