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4h

comment 
Partial Sum of the Binomial Theorem
mathoverflow.net/questions/93744/… mathoverflow.net/questions/55585/… 
8h

awarded  Nice Answer 
10h

comment 
(Non)existence of mirrors with more than two foci
It is difficult to have a multipurpose boundary, although I did construct examples of that. Part of the idea here was to make sure each part of the boundary is visible from at most two points at a time. If you shine light from $x_1$ at something directing light from $x_2$ to $x_3$, you typically need another curve to refocus that. 
10h

revised 
(Non)existence of mirrors with more than two foci
Fixed picture. 
15h

revised 
(Non)existence of mirrors with more than two foci
Added picture. 
15h

answered  (Non)existence of mirrors with more than two foci 
1d

comment 
Is there a generalization of Polya urns to continuous outcome event?
N. Makarov talked about trying to formalize the following: Start with a compact subset of the plane, and let a small particle drift in from infinity under Brownian motion. Let it stick where it first hits, and add it to the set. Then release another particle, etc. Take a limit of this process as the size of the particle goes to 0. This is similar to a Pólya urn model because the harmonic measure may tend to expand where the particle hits. I believe he proposed it as a problem worthy of study. 
1d

comment 
Are numbers fundamental mathematical entities?
By the way, I have heard that the Ancient Greeks viewed geometry as more fundamental than arithmetic. To prove that two regions have the same area, we show that the areas are the same number, but they found geometric dissections from one region to the other, which is always possible for polygons of the same area. (See Hilbert's 3rd problem.) It's a good enough story that I pass it on without verifying it. 
2d

revised 
Thales' semicircle theorem in higher dimensions
Mainly fixed typos. 
2d

comment 
Thales' semicircle theorem in higher dimensions
When people ask how to visualize things in higher dimensions, I think it is good to mention problems like this showing that we struggle to visualize things in $3$ dimensions. 
2d

answered  Thales' semicircle theorem in higher dimensions 
Mar 27 
comment 
Solid angles of a tetrahedron
@Joseph O'Rourke: Thanks, I fixed them. 
Mar 27 
revised 
Solid angles of a tetrahedron
fixed expired picture links 
Mar 24 
revised 
Is there a natural bijection from $\mathbb{N}$ to $\mathbb{Q}$?
Added details 
Mar 18 
comment 
Expected value of the minimum with limited independence
Nice construction. Those should be $\frac{k+1}{k(k+1)}$ and $\frac{(k+1)^2}{k(k+1)}$ on the left hand sides. Also, in the middle, $\frac{1}{k+1}$ should be $\frac{1}{k}$. 
Mar 15 
comment 
Expected value of the minimum with limited independence
@Dorothy: I don't know. The argument that James Martin gave in the comments on his answer can be restated as that $E[X] =1+\sum_{k=1}^n P(N_k = 0) \le 1 + \sum_{k=1}^n \frac{1}{k}\frac{1}{n} = H_n \approx \log n + \gamma.$ The estimate $P(N_k =0 ) \le \frac{1}{k}  \frac{1}{n}$ can only be improved by a constant factor since if you define the partition $\mu_k = k+k+...+k$ then the distribution $\frac{k2}{k1} \mu_1 + \frac{1}{k1} \mu_k$ is pairwise independent and has $P(N_k = 0) \sim \frac{1}{ek}.$ I haven't found a distribution so that for many different $k$, $P(N_k=0)$ is large. 
Mar 14 
revised 
Expected value of the minimum with limited independence
added 32 characters in body 
Mar 14 
answered  Expected value of the minimum with limited independence 
Mar 12 
comment 
can you use Bayes' rule twice?
I don't think the naive Bayesian classifier assumes independence, only conditional independence. 
Mar 12 
comment 
can you use Bayes' rule twice?
Your assumption was not only that $X$ and $Y$ are independent, but also that they are conditionally independent given $C$. Those are very different and neither implies the other. 