bio | website | jamespropp.org |
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location | ||
age | ||
visits | member for | 4 years, 10 months |
seen | Nov 21 at 20:49 | |
stats | profile views | 2,009 |
I am interested in combinatorics, probability, dynamical systems, and various other topics.
Nov 14 |
accepted | Origin of the numbers game |
Nov 14 |
comment |
Origin of the numbers game
I hear that Knuth studied it as well; can anyone provide a pointer to Knuth's article? |
Nov 13 |
asked | Origin of the numbers game |
Nov 12 |
comment |
Isotropy of Apollonian disk-packing
You are completely right! My bad for assuming Hee was a he. |
Nov 12 |
revised |
Isotropy of Apollonian disk-packing
I corrected a few typos |
Nov 11 |
answered | Isotropy of Apollonian disk-packing |
Nov 11 |
comment |
Isotropy of Apollonian disk-packing
@Hao Chen: The work of Hee Oh is very relevant; thanks for the suggestion! I recommend the slides at gauss.math.yale.edu/~ho2/extendedICM.pdf ; they are well-written and the pictures are both pleasurable and informative. |
Nov 11 |
awarded | Socratic |
Nov 10 |
revised |
Spirals in Apollonian circle-packings
Added forward pointer to follow-up question |
Nov 10 |
asked | Three-dimensional Apollonian spirals |
Nov 8 |
awarded | Good Question |
Nov 5 |
comment |
Spirals in Apollonian circle-packings
I like Noam's argument. Can anyone complete the proof by showing that the angle in question is irrational? |
Nov 5 |
comment |
Spirals in Apollonian circle-packings
I should point out a subtlety that some readers may have missed: conformal maps are only locally angle-preserving, so the angular distribution of the unit vectors in the general case cannot be obtained by applying a rotation or other simple map to the unit vectors in the special case that Noam proposes. However, since the points $P_n$ and $Q_n$ all approach $P_{\infty}$, and since the inversive map preserves angles in the vicinity of $P_{\infty}$, we can ignore this distortion for purposes of the asymptotic angular distribution of the vectors. |
Nov 4 |
accepted | Bijective proof of an Abel-Hurwitz-type identity |
Nov 4 |
comment |
Bijective proof of an Abel-Hurwitz-type identity
That's a nice style of argument (and it helps me get a better feel for Postnikov's point of view). Thanks for explaining it to me. (By the way, I think Sunday's meeting was officially reckoned as the 60th meeting of the Cambridge Combinatorics and Coffee Club, not the 61st; not that it matters.) |
Nov 4 |
comment |
Bijective proof of an Abel-Hurwitz-type identity
Yes, it's $n^{n-2}$. |
Nov 4 |
asked | Bijective proof of an Abel-Hurwitz-type identity |
Nov 3 |
asked | Spirals in Apollonian circle-packings |
Oct 15 |
asked | Isotropy of Apollonian disk-packing |
Oct 14 |
awarded | Nice Question |