bio  website  cs.smith.edu/~orourke 

location  Smith College, U.S.  
age  
visits  member for  5 years 
seen  4 hours ago  
stats  profile views  17,836 
Professor of Computer Science; Professor of Mathematics; Associate Provost & Dean.
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answered  Numerical equality testing 
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Is every closed curve in 3D a geodesic on a genus0 surface?
Your proof would make a nice paper for e.g., the American Mathematical Monthly or its equivalent, in case you are so inclined :). 
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accepted  Is every closed curve in 3D a geodesic on a genus0 surface? 
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awarded  Good Question 
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awarded  Nice Answer 
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Is every closed curve in 3D a geodesic on a genus0 surface?
Because (a) of the iterative nature of your answer, and (b) my lack of understanding of your linkingnumber obstruction (not your faultmy 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 genuszero 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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John Nash's Mathematical Legacy
Link to Deane's answer. 
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answered  John Nash's Mathematical Legacy 
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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 $1$. 
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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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The most number of points that realize only $k$ distinct distances
ExcellentThanks! 
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The most number of points that realize only $k$ distinct distances
Great, just what I needThanks! (I cannot access the handbook until next week.) 
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The most number of points that realize only $k$ distinct distances
@SamHopkins: You are right, I need to study the GuthKatz bound. 
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The most number of points that realize only $k$ distinct distances
@AaronMeyerowitz: Hmm. For a pentagon inscribed in a unitradius circle, I find $s \approx 1.176$ while the distance from each added above/below point to a pentagon point is $s' \approx 1.160$. 
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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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Is every closed curve in 3D a geodesic on a genus0 surface?
:) $\mbox{}\mbox{}$ 
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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. 