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Comments:
<0> Actually, there'd be two inverse functions: one like a root and one like a natural log.
<1> Hmm
<1> Have you seen lg^* before?
<1> Because that sounds like it's sort of what you're looking for
<2> Zemyla: Yes, there is.
<3> sdfasdfsdf: just got here, what's the question?
<2> But I don't remember what it's called.
<4> my book defines an element of a solid angle as d(Omega) = sin(theta) d(theta) d(phi) .. how did they get this?
<4> i'm thinking i need to use a Jacobian, but I don't know how to relate a solid angle to polar coordinates.
<3> sdfasdfsdf: that sounds more like area than volume
<4> yes, its is
<4> what am i saying that means volume?
<5> wolfram mathworld has a nice picture of it.
<3> sdfasdfsdf: "solid"
<3> sdfasdfsdf: but that doesn't mean anything, i just wanted to be clear
<4> oh ok
<4> evoli, thanks that does look good, i'll read that
<3> sdfasdfsdf: i'm not sure, if you had the surface of a sphere parametrised in t and p as x=sin(p)cos(t) y=cos(p)cos(t) z=sin(t) maybe
<3> sdfasdfsdf: um maybe that's backwards
<0> I think that's how it is.
<4> TRWBW, could u just repaste that line, my IRC client turned it into emoticons
<3> sdfasdfsdf: i'm not sure, if you had the surface of a sphere parametrised in t and p as x=sin(p)cos(t) y=cos(p)cos(t) z=sin(t) maybe
<4> i thanks
<1> :)
<3> sdfasdfsdf: i can't do the jacobian in my head, but i'd guess something like that. some polar style parameterization of a spheres surface
<4> yes i've done that before
<4> but even having it in terms of x,y,z how does that help me relate it to the solid angle?
<6> can someone help me solve the integral of exp(x)/(sqrt(exp(2x)+1))
<4> the solid angle isn't defined as some integral dxdy..
<5> u = exp(x), substitute
<7> x = cos(phi)*sin(theta), y = sin(phi)*sin(theta), z = cos(theta)
<4> hmm.. i just saw Wolfram defined it differently using d(area)
<4> ok i thanks for the help :)
<8> does anybody know a simple proof that the euler phi function is multiplicative? My google foo seems to be weak..
<5> *gasp*!
<9> Thanks for the help with the homework yesterday, guys -- I dominated my quiz today
<2> sorje: first prove that phi(p^a q^b) = phi(p^a) * phi(q^b).
<2> sorje: then by induction for phi(p1^a1 p2^a2 p3^a3...) etc.
<8> for q and p prime?
<2> Yes.
<2> sorje: that's my best offhand guess, anyway.
<2> or maybe that phi(n * p^a) = phi(n) * phi(p^a) when n is not divisible by p. Or something like that.
<2> I think you should be able to do tha tsimply by considering the divisors of n*p^a explicitly.
<2> Since they're clearly (divisors of n) U (p * divisors of N) U (p^2 * divisors of N) ... = (n+1) * phi(n)
<2> Blah blah blah.
<8> hmm
<4> back again.. can someone please explain where the cos(phi) comes from in Equation (3) on this page: http://mathworld.wolfram.com/SolidAngle.html
<4> isn't "da" already in Cartesian coordinates?
<10> hi
<10> I don't understand the difference between a Continuous function function F and a uniform continuous function.
<10> aren't they the same?
<2> No. 1/x is continuous on (0, oo), but not uniformly continuous.
<2> For a continuous function, someone can come to you and gives you a point x and number e. Then you find a d such that, as long as x' is in (x-d, x+d), it does not vary by more than e.
<10> yea
<2> But the d that you give them will depend on x, because otherwise how do you know how much f can vary?
<2> Right?
<10> yep
<2> Well, a uniformly continuous function is so well-behaved that you can give d ahead of time, without knowing what x is.
<10> I got it , thanks
<2> Sure.
<11> How do I argue about an algorithms "correctness"?
<11> Like, what makes an algorithm incorrect? :/
<11> I have an ***ignment where I should "argue about the correctness of those algorithms by either induction or a loopinvariant"
<2> Trixsey: If it produces the wrong answers on some inputs, or if it fails to produce any answers at all on some inputs.
<11> oh ok
<12> Trixsey, google denotational sematnics
<12> @go denotational semantics
<12> bah
<12> stupid bot
<13> which one? :)
<12> the non-bot
<10> hi
<10> can any one help me find x, where x^2 = (123)(45)( 67) in S_7 by not bruteforcinf?
<2> jin: Didn't you just ask almost the same question a couple of days ago?
<10> that was another one
<2> (132)(4657) will do.
<10> okay, I have the answer byself by trying
<14> hi, probably not entirely math related but does anybody know how to compute the projection center given a projection matrix?
<2> Is that some kind of Freudian thing?
<14> yrlnry: the projection matrix you mean?
<2> joke, sorry.
<15> Could someone shed some light on this problem: http://www.mathbin.net/7352 .. I see that the sequence looks like 1,2,1,2, ...etrc., or 2/1,2/(2/1), 2/(2/(2/1)), 2/(2/(2/(2/1))) .. etc. I'm having a little difficulty finding how to generate the 1,2,1,2 or in the "spirit" of the recursive function the 2/(2....2/1). any hints?
<15> it's supposed to be "find the explicit" formula
<16> Tommorow I have exam in linear programming, all I nede is to p***, and the nightmare is over!
<16> The material is "cute", but the proffesor is ****, he is crap at teaching, or at any contact with other humans.
<17> nonix4: I can do an animation of that if you want
<18> % Solve[x^2+1==0,x]
<19> Can anyone prove that if a = bq + r, 0<=r<b, then HCF(a,b)=HCF(b,r)?
<19> HCF is the highest common factor.
<19> :/
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