8,886 reputation
22042
bio website gottwurfelt.wordpress.com
location Atlanta, GA
age 30
visits member for 4 years, 3 months
seen 1 hour ago

Data scientist and math blogger.


Oct
15
answered Probability Question about Full Houses
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
13
answered For small $z, (1 + z)^{−2} \sim 1 − 2z$…
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
Oct
3
reviewed Approve suggested edit on The geometry of a spiral made of adjacent right triangles
Sep
30
awarded  Explainer
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
25
answered How find the positive numbers $n$ such that $n!=\overline{1999a_{1}a_{2}\cdots a_{k}\cdots}$
Sep
24
awarded  Nice Answer
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.
Sep
18
reviewed Approve suggested edit on Subgroup generated by a set
Sep
18
comment Proving $\frac{1}{\sin^{2}\frac{\pi}{14}} + \frac{1}{\sin^{2}\frac{3\pi}{14}} + \frac{1}{\sin^{2}\frac{5\pi}{14}} = 24$
If I'm not mistaken, this generalizes to give $\sum_{k=1}^n \csc^2 (k\pi/(2n+1)) = 2n(n+1)$, with $n = 3$ being the original question.
Sep
16
revised How many ways are there to write $675$ as a difference of two squares?
retagged
Sep
16
answered Finding a recursive formula for a number
Sep
15
comment Random walk on a finite square grid: probability of given position after 15 or 3600 moves
For a related blog post see John Cook's post.
Sep
12
awarded  Autobiographer
Sep
11
answered Odds for randomly assigning a men-only group in a team working assignment
Sep
5
awarded  Necromancer