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Data scientist and math blogger.


1d
revised Differences of grade between this three books
changed tags
1d
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.
2d
awarded  Enlightened
2d
awarded  Nice Answer
Oct
21
comment True or False: Basis in the space of polynomials of degree less or equal to 2014 should contain polynomial of degree 2013.
Not sure if this question will stay alive. In case it does, here's a hint: there's nothing special about 2014. Can you construct a basis in the space of polynomials of degree less than or equal to 2 that does not contain a polynomial of degree 1?
Oct
21
reviewed Approve suggested edit on Simple real life problem
Oct
21
reviewed Approve suggested edit on Inverse Trigonometric Integrals
Oct
21
reviewed Approve suggested edit on Find the free variables in the given sentences.
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.