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Sep
29
comment Napier's Rules applied to spherical distance calculations
Correction to that last comment of mine: all the meridians/longitudes are great circles, but among the latitudes, only the equator is a great circle.
Sep
29
comment Napier's Rules applied to spherical distance calculations
Yes, the Napier formulae are meant only for spherical triangles, triangles whose sides are arcs of great circles. Remember that only the equator and the prime meridian are the great circles on the globe.
Sep
29
comment Generalizing values which Euler's-totient function does not take
In general, when you encounter some sequence of integers in your work, it is always a good idea to look first at OEIS; the refs there usually provide interesting leads.
Sep
29
answered How do I combine “error of order” terms in numerical analysis?
Sep
29
comment Image of sin(z) over a complex set
Hans, those pics look awesome. May I know what you used to plot these?
Sep
28
comment Factoring a Cubic Polynomial
Cardano is a bit of a sledgehammer here; the only other thing I'll note is that synthetic division may be more convenient than long division, depending on the user.
Sep
28
answered WolframAlpha Returns only 2 Roots for a Polynomial Equation of 6 Degree
Sep
28
comment WolframAlpha Returns only 2 Roots for a Polynomial Equation of 6 Degree
It's actually a decic (tenth-degree) that you have; with two roots of multiplicity 5.
Sep
28
comment Solve cryptogram - ciphertext given
Well, that too... wow, has it really been that long ago? I guess I'm getting old. :D
Sep
27
comment Solve cryptogram - ciphertext given
Up to 3 blocks... okay, it is dated, but it still looks interesting.
Sep
27
awarded  Disciplined
Sep
27
comment Solve cryptogram - ciphertext given
I have not heard of the Sinkov book until now, so the +1 is a thank you of sorts. :)
Sep
27
comment Karush-Kuhn-Tucker condition - Lagrange multiplier
Shorter version: KKT is not an (practical) algorithm; it's what a solution to a constrained optimization problem has to satisfy. A probably simpler starting point than Nocedal/Wright or Fletcher would be the book by (Griva/)Nash/Sofer.
Sep
27
revised Karush-Kuhn-Tucker condition - Lagrange multiplier
edited tags
Sep
27
comment Extension of previous problem, involving $\ell^p$ norm circles
That's already the expression for the total area; the trick is to just compute the area of a single quadrant (i.e. have the area integral range from 0 to $\pi/2$) and then multiply the result by 4.
Sep
27
comment Good computer programs for dealing with sparse matrices
Well, you can solve linear systems with Arnoldi, but it's a bit like using a gold brick to swat flies...
Sep
27
answered Good computer programs for dealing with sparse matrices
Sep
27
comment How do I find the lowest $n$ for which $a^n \equiv 1 \pmod{b}$?
@Eugene: That one's from Cohen's "A Course in Computational Algebraic Number Theory"; a good book, if you can find it in your nearest library.
Sep
26
comment What is the proper geometric description of a the oval used for a horse racetrack?
So maybe not always something entirely composed of clothoid arcs, but track/road designers do use it at turns. (Just to be clear on the picture: the black outline is the clothoidal track; I only drew the full clothoid in gray for illustration, but no designer in his right mind would use the spiraling portion of the curve. ;P )
Sep
26
comment What is the proper geometric description of a the oval used for a horse racetrack?
After more digging around: apparently for the "cheaper" :P tracks, they use the clothoid sections only for joining straight (zero curvature) and circular (nonzero constant curvature) sections of track. I guess it depends on what the engineers were thinking when they were designing the tracks.