bio  website  math.ucla.edu/~pak 

location  Los Angeles, CA  
age  
visits  member for  5 years, 3 months 
seen  4 hours ago  
stats  profile views  8,853 
My work page. My personal blog.
5h

answered  Complexity of planar scissor congruence 
May 17 
awarded  Good Answer 
May 10 
revised 
Random Alternating Permutations
update 
May 2 
awarded  Autobiographer 
Apr 27 
awarded  Good Question 
Apr 21 
awarded  Promoter 
Apr 15 
awarded  Curious 
Apr 14 
comment 
3colorings of the unit distance graph of $\Bbb R^3$
@JMPerry  Yes. Every triangle in $\Gamma$ has all sides unit length. 
Apr 14 
comment 
3colorings of the unit distance graph of $\Bbb R^3$
@JMPerry. I don't understand your question/objection. Please write it in full if possible. 
Apr 14 
comment 
3colorings of the unit distance graph of $\Bbb R^3$
@JMPerry  No, since $2\beta \neq 1$. I meant to write "unit length triangle" in my comment above, which would mean it's a triangle in $\Gamma$. 
Apr 14 
revised 
3colorings of the unit distance graph of $\Bbb R^3$
added 12 characters in body 
Apr 14 
comment 
3colorings of the unit distance graph of $\Bbb R^3$
@TimChow. As I say in the note, this is not an important condition  we will be happy with any $\alpha$. However, we can rule out some values such as $\alpha = 1/\sqrt{2}$ when (ABCD) is a square  it's easy to see that such coloring does not extend from (ABCD) to $\Bbb R^3$. We cannot rule out any transcendental values. 
Apr 14 
comment 
3colorings of the unit distance graph of $\Bbb R^3$
@JMPerry  Not sure what you are asking. Main condition: every triangle must be nonrainbow, i.e. have at most 2 colors. Without (ABCD) one can just take a monochromatic coloring of the whole space. 
Apr 14 
awarded  Nice Question 
Apr 14 
revised 
3colorings of the unit distance graph of $\Bbb R^3$
clarification 
Apr 14 
revised 
3colorings of the unit distance graph of $\Bbb R^3$
note added 
Apr 14 
revised 
3colorings of the unit distance graph of $\Bbb R^3$
edited body 
Apr 14 
asked  3colorings of the unit distance graph of $\Bbb R^3$ 
Apr 14 
revised 
Fundamental Examples
Catalan numbers were introduced by Euler in the second half of 18th entury 
Mar 28 
revised 
Not especially famous, longopen problems which anyone can understand
reference to an article 