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bio website gottwurfelt.wordpress.com
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Quantitative analyst and math blogger.


Nov
7
comment Probability of cumulative dice rolls hitting a number
The related question mathoverflow.net/questions/18282/… at mathoverflow might be of interest. The consensus in that discussion was that there wasn't a "nice" explicit formula (although there is the partial-fraction formula that Moron gives below) but that these probabilities are easy to compute recursively.
Nov
3
comment Intuitive explanation of the difference between waves in odd and even dimensions
This is called Huygens' principle. See mathpages.com/home/kmath242/kmath242.htm although I wouldn't call the explanation there "intuitive".
Nov
2
answered Positive integers $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}} > 1$ satisfying $\sum_{i = 1}^{n} p_{i}^{-r_{i}} < 1$
Nov
1
comment Proof of $P(X < x) = F(x−)$
Hi, Josh! I have to keep saying hi so that this comment is long enough.
Oct
31
comment Asymptotic difference between a function and its binomial average
I agree that logarithmic growth is what you need. The "binomial average" of $f(n)$ should be about $f(n/2)$.
Oct
30
comment Does Stirling's formula give the correct number of digits for $n!\phantom{}$?
Portuguese is not that hard to read, at least if you know French and/or Spanish, which are languages more commonly known to speakers of English. That being said, the meta.mathoverflow discussion on posting in non-English posts: meta.mathoverflow.net/discussion/142/nonenglish-posts. (The consensus there was that posts in all languages should be allowed, but there would probably be few non-English posts.)
Oct
30
answered Generalization of cos: is this function known?
Oct
30
comment Does Stirling's formula give the correct number of digits for $n!\phantom{}$?
From Mathoverflow: mathoverflow.net/questions/19170/… and mathoverflow.net/questions/19086/number-of-digits-in-n
Oct
30
comment A good quick introduction to Knot Theory?
I've heard "The Knot Book", by Colin Adams, recommended for this purpose. (I'm leaving a comment instead of an answer because I haven't read the book myself.)
Oct
29
answered Five Fridays and Sundays on October
Oct
26
comment Evaluating limit of Summation
For what it's worth, the odd and even cases look to approach the same limit. (Evaluate numerically, for example, at $n = 99$ and $n = 100$.) Here's a hint for the solution: can you relate your sum to the sum $\sum_{k=1}^n cos(k\pi/n)$, which you know how to handle?
Oct
26
answered $n!+1$ being a perfect square
Oct
25
answered How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
Oct
24
answered Find an infinite set of positive integers such that the sum of any two distinct elements has an even number of distinct prime factors
Oct
21
comment What is the probability that every pair of students studies together at some point?
This feels like a generalization of the coupon collector problem to me, although this observation may not be helpful.
Oct
20
comment Why does this process, when iterated, tend towards a certain number? (the golden ratio?)
It's hard to test that $x = -(1+\sqrt{5})/2$ is a fixed point numerically, because it's a repelling fixed point.
Oct
19
answered Is it possible to get arbitrarily near any acute angle with Pythagorean triangles?
Oct
17
answered Prove that the sequence$ c_1 = 1$, $c_{n+1} = 4/(1 + 5c_n) $ , $ n \geq 1$ is convergent and find its limit
Oct
16
revised Finding $a,b$ such that $a^{n} + b^{n} $ is $(n+1)^{th}$ power
added 548 characters in body
Oct
15
answered Finding $a,b$ such that $a^{n} + b^{n} $ is $(n+1)^{th}$ power