9,961 reputation
22148
bio website gottwurfelt.wordpress.com
location Atlanta, GA
age 31
visits member for 4 years, 5 months
seen 3 hours ago

Data scientist and math blogger.


Oct
28
reviewed Reject Plot zeros of partial sum of zeta Riemann with Maple
Oct
28
answered Are there other accumulation functions that holds $a(n-t)={a(n) \over a(t)}$?
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
revised Differences of grade between this three books
changed tags
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
23
awarded  Enlightened
Oct
23
awarded  Nice Answer
Oct
21
reviewed Approve Simple real life problem
Oct
21
reviewed Approve Inverse Trigonometric Integrals
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 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 $n!=\overline{1999a_{1}a_{2}\cdots a_{k}\cdots}$