9,381 reputation
22146
bio website gottwurfelt.wordpress.com
location Atlanta, GA
age 30
visits member for 4 years, 4 months
seen yesterday

Data scientist and math blogger.


2d
comment Will it become impossible to learn math?
I don't know this book, but I am intrigued. I think this may shed some light on the original question: there could be an upper limit on the depth of possible research imposed by the human lifespan.
Nov
19
comment Numerical value of $\sum_{p \in \mathcal P} \frac1{p\ln p}$
Your difference should be $1/(2 \log 2)$, not $1/2$.
Nov
19
comment How to draw greek letters on paper / blackboard?
I have seen $\phi$ and $\varphi$ used by the same lecturer in the same lecture (in physical chemistry). One was pronounced "fee" and the other "fie". I found this lecture essentially impossible to follow because I thought of those two glyphs as interchangeable.
Nov
19
comment Prove that $\sum_{n=0}^{\infty }\frac{(2n+1)!!}{(n+1)!}2^{-(2n+4)}=\frac{3-2\sqrt{2}}{4}$
Yes - that numerical value corresponds to your analytical value.
Nov
19
comment Prove that $\sum_{n=0}^{\infty }\frac{(2n+1)!!}{(n+1)!}2^{-(2n+4)}=\frac{3-2\sqrt{2}}{4}$
As a check on this value, when the sum is computed numerically one gets 0.1035533906.
Nov
17
comment Characteristics of odd parts in a partion
Guessing this is a homework question, so I'll give a hint. Have you seen a proof that the number of partitions with only odd parts is the same as the number of distinct parts, using generating functions? You can adapt that proof to this problem.
Nov
1
comment How do calculators evaluate inverse trig functions?
I do like it. The question to me seems to be whether one wants the more conceptual (yours) or calculational approach; yesterday calculation felt worthwhile to me, but in the light of morning I can see how the more conceptual approach is superior.
Oct
31
comment How do calculators evaluate inverse trig functions?
God plays dice is my blog. The commenter "logosintegralis" there took a stab at using Pade approximants to derive that approximation.
Oct
29
comment Expected number of turns for a rook to move to top right-most corner?
The fact that the move is to move to a random square in the same column or row - i. e. change one coordinate uniformly at random - explains why G7 is no closer to H8 than A1 is.
Oct
29
comment Calculate limit $\lim_{n\rightarrow\infty}\dfrac{(4n-100)^{4n-100}n^n}{(3n)^{3n}(2n)^{2n}}?$
You're right. That'll teach me to do tricky limits in my head.
Oct
29
comment Are there other accumulation functions that holds $a(n-t)={a(n) \over a(t)}$?
Yes, if you assume that the function $a$ is continuous.
Oct
27
comment Calculate limit $\lim_{n\rightarrow\infty}\dfrac{(4n-100)^{4n-100}n^n}{(3n)^{3n}(2n)^{2n}}?$
It's not true that $\lim_{n \to \infty} (4n-100)^{4n-100} / (4n)^{4n} = 1$. This limit is $4^{-100}$. That being said, a constant factor won't have an effect on the limit going to infinity.
Oct
26
comment Mathematician vs. Computer: A Game
Let's let the largest number that can be picked be $n$ (so in the problem $n = 1000$.) If the mathematician picks a prime $p$, then they lose if a multiple of $p$ or a number less than $p$ is picked. There are $n/p + p$ such numbers (approximately), and this is minimized when $p = \sqrt{n}$.
Oct
24
comment $f\left(x + \frac1x\right)= x^3+x^{-3},$ find $f(x)$
If you do the algebra, it turns out that this gives $f(y) = y^3 - 3y$, agreeing with the answer many others have given.
Oct
15
comment Betting system for coin toss game?
This is in fact a martingale. You can win this way if you have unlimited money and can place arbitrarily large bets - but if you have unlimited money, why are you gambling?
Oct
3
comment The geometry of a spiral made of adjacent right triangles
This is related to the "spiral of Theodorus": en.wikipedia.org/wiki/Spiral_of_Theodorus
Sep
29
comment Trig sum: $\tan ^21^\circ+\tan ^22^\circ+…+\tan^2 89^\circ = ?$
Also, possibly relevant SE links: math.stackexchange.com/questions/217240/…, math.stackexchange.com/questions/2339/… , although I'm not sure if any of the proofs here satisfy your requirements - this problem seems very naturally to live in the complex numbers.
Sep
29
comment Trig sum: $\tan ^21^\circ+\tan ^22^\circ+…+\tan^2 89^\circ = ?$
One thing to try: instead of doing the "special" case where you're looking at degrees, can you find a formula for $\sum_{k=1}^{n-1} \tan^2 {k \pi \over 2n}$, where the angles are in radians? Your question is the $n = 90$ case of this. If you try small integer values of $n$ it's not terribly hard to conjecture a formula.
Sep
27
comment How many non-collinear points determine an $n$-ellipse?
I don't know, but see this presentation by Sturmfels: math.berkeley.edu/~bernd/feb19.pdf or this paper: math.ucsd.edu/~njw/PUBLICPAPERS/kellipse_imaproc_toappear.pdf
Sep
23
comment How do I show that the series: $\sin(m) + \sin(\sin(m)) + \sin(\sin(\sin(m))) + \cdots$ converges for all real numbers $m$?
I don't have my copy at hand, but I believe that $a_k \sim \alpha \sqrt{3/k}$ is shown in de Bruijn's Asymptotic Methods in Analysis.