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Jul
9
comment Closed-form solution to polynomials of this special form?
@DavidButlerUofA: Ohh I see haha ok sorry.
Jul
9
comment Closed-form solution to polynomials of this special form?
@DavidButlerUofA: Yeah, there are direct solutions for arbitrary polynomials up to degree 4, so I'm not sure why you're going this route. The question is this can be done for arbitrary degrees.
Jul
8
comment Closed-form solution to polynomials of this special form?
@NotNotLogical: Are they that weak? We already know the roots of the two polynomials and we already know the interval in which it must lie, I felt like that would be quite strong.
Jul
8
comment Closed-form solution to polynomials of this special form?
@NotNotLogical: Great point, I didn't really spend time thinking about the formal justification for why it must exist.
Jul
8
comment Closed-form solution to polynomials of this special form?
@DavidButlerUofA: Yup I'm already aware of that, but thanks anyway.
Jul
8
asked Closed-form solution to polynomials of this special form?
Jul
8
comment Formulation and computation of “the” unique median of an even-sized list
@MichaelGrant: Haha yes but I meant what inherently makes them useful? On another note, it seems like the median can be defined as the number that equalizes the product of its distance to the numbers below it with that of the numbers above it, which I think is pretty cool!
Jul
7
comment How to make a perpendicular construction in 3 moves?
I'm almost certain that I learned this in elementary or middle school, then totally forgot it until I saw your hint... (though I didn't spend too much time thinking about it)
Jul
7
comment Does the phrase “instantaneous frequency” make sense?
@J.M.: I entirely missed your comment until now (which is 3 years later)! Yes it does! haha :)
Jul
7
revised Stopping the “Will I need this for the test” question
edited body
Jul
4
awarded  Peer Pressure
Jul
4
comment What is the significance of the slope of the tangent line of a function? Why is the derivative so important?
@Downvoter: Care to comment?
Jul
3
comment Why do determinants have their particular form?
@Eupraxis1981: I'm not sure if you were really looking for a proof of the cofactor expansion method or if you were instead looking for the meaning of a determinant, but if it's the latter case, I think my answer should answer your question quite directly and elegantly, so I encourage you to take a look at it. (But if it's the former please let me know.)
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jul
2
awarded  Popular Question
Jun
28
comment Formulation and computation of “the” unique median of an even-sized list
It also makes me wonder why first-order approximations are so special. A second-order approximation would seem correct but unhelpful, whereas a zeroth-order approximation would tell us nothing. So what's so special about first-order that gives us the answer we want exactly in the limiting case? Maybe I should ask that as a question...
Jun
28
accepted Formulation and computation of “the” unique median of an even-sized list
Jun
28
comment Formulation and computation of “the” unique median of an even-sized list
+1 Holy cow, this looks exactly like the kind of answer I was hoping for! So you used approximated $m^* - x_k$ to first-order to be equal to its linearization $1 + \epsilon \log(m^* - x_k)$, because it's equal in the infinitesimal case? It seems so obvious in hindsight but it's very clever, I wouldn't have thought of it for quite a long time! Thanks so much, I learned something new today from your answer. :)
Jun
27
comment Formulation and computation of “the” unique median of an even-sized list
My edit got rejected... would you mind trying to add it (or something to the same effect) again? I'll accept it after that's clarified, but until then it's too unclear for me to accept it.