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visits member for 1 year, 8 months
seen 19 hours ago

Aug
18
answered Log concavity of binomial coefficients: $ \binom{n}{k}^2 \geq \binom{n}{k-1}\binom{n}{k+1} $
Aug
4
comment Negative number modular positive number ?
This question appears to be off-topic because it is about a different programming language than Mathematica or about mathematics. If it about how Mathematica defines the function Mod (not MOD), then why write %?
Jul
26
comment Intuition on the curl formula
@LucasZanella Maxwell observed that the observed properties of the electromagnetic field were similar to the dynamics of rotating fluids in small cells. The book Maxwell on the Electromagnetic Field: A Guided Study contains excerpts that describe how he deduced his equations. Too long to cover the details in a comment, really.
Jul
5
comment Calculating a limit in two variables by going to polar coordinates.
@Crumbs Given: In polar coordinates, $f(x,y) = r \cdot [\cos\theta \sin^2\theta /(\cos^2\theta + r^2\sin^4\theta)]$, $\theta$ fixed, $r \ne 0$, $r \rightarrow 0$. Hence: If $\cos\theta = 0$, then the second factor equals $0$ for all $r$ (given $r \ne 0$); if $\cos\theta \ne 0$, then the limit of the second factor is $\sin^2\theta/\cos\theta$. In both cases the limit of the second factor exists. The first factor approaches $0$, so the limit is $0$.
Jun
6
comment Is there a difference for discount per unit and discount per purchase total?
This question appears to be off-topic because it is not about Mathematica
Apr
29
revised Calculating a limit in two variables by going to polar coordinates.
Responded to downvote
Apr
19
answered If there are obvious things, why should we prove them?
Apr
1
comment How do you find the general solution to a higher order nonhomogeneous differential equation?
Is this a question about the software product Mathematica?
Mar
15
comment Why are the axes in coordinate geometry perperndicular?
It may be of interest to note that Descartes did not use perpendicular axes in his Geometry. He used distances to given lines, the given lines being at whatever angles and sometimes more than two in number. So having coordinate axes at angles other than 90 degrees came first. Descartes used his method to solve a problem of Pappus that the ancients Greeks could not, and thus proved a new theorem.
Mar
15
comment Why are the axes in coordinate geometry perperndicular?
@Kartik Euclidean and non-euclidean geometries are not equivalent. Two coordinate geometries are. You just get different formulas with different coordinate systems, formulas for things like distance, translations, rotations. Some of these are simpler in one coordinate system than another.
Mar
15
comment Crazy $\int_0^\infty{_3F_2}\left(\begin{array}c\tfrac58,\tfrac58,\tfrac98\\\tfrac12,\tfrac{13}8\end{array}\middle|\ {-x}\right)^2\frac{dx}{\sqrt x}$
@ClaudeLeibovici, @VladimirReshetnikov Oops, I mistyped one of the coefficients. The answer I get is (25 MeijerG[{{-(1/8), 3/8, 3/8}, {9/8}}, {{1/8, 1/8, 5/8}, {-(5/8)}}, 1])/(32 Sqrt[2] Gamma[5/4]^2) with Integrate[HypergeometricPFQ[{5, 5, 9}/8, {4, 13}/8, -x]^2/Sqrt[x], {x, 0, Infinity}] on Mma V9.0.1. Sorry for the error.
Mar
13
comment Finding the point that a normal line goes through
@RickyMutschlechner Thanks for the accept. I wish you the best with the rest of the course.
Mar
11
comment I don't like Wolfram Alpha's evaluation of an integral
+1. You're more generous toward W|A than I would be. :) I would have said it was just wrong at $x = n\pi$, since the antiderivative is not differentiable at those points, no matter how sgn is defined. Since the integrand is continuous everywhere, there is an antiderivative that is differentiable everywhere, which of course you have given. The W|A antiderivative cannot be used to apply the Fundamental Theorem of Calculus, which seems a shortcoming worth pointing out. (W|A and Mathematica often give symbolic results that are only generically correct.)
Mar
11
comment Finding the point that a normal line goes through
@RickyMutschleckner You don't have to solve for $f$. It is given. See my answer for details.
Mar
11
answered Finding the point that a normal line goes through
Mar
11
comment Finding the point that a normal line goes through
Solve $f'(a) = -a/f(a)$. (Slope of tangent is negative reciprocal of radial line from origin.)
Mar
9
comment solving a trigonometric differential equation
This is covered in standard textbooks on differential equations. Perhaps it's in yours?
Jan
21
awarded  Necromancer
Jan
11
comment Why is Euclid's proof on the infinitude of primes considered a proof?
@MarcvanLeeuwen FWIW, Euclid used the word ἄπειρον, unbounded or infinite, sometimes in geometry (e.g. Post. 5), but not in this proposition. He used the word πλῆθος, multitude, which incidentally is the word used to define number. A number is a multitude of units. In IX.20, Euclid stated, "The prime numbers are more than any proposed multitude of prime numbers" -- he is just that close to saying a "number of prime numbers."
Dec
29
awarded  Yearling