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Comments:
<0> well you could call it the set of all (hyper)planes in R^3 (if you want)
<1> oh ok
<0> but that is not telling much of what that set symbolizes in R^4
<1> ok so when phiste1: zaphy i mean u could have a space in which the points are not tuples of numbers but rather some other objects, like lines or groups or theories...
<1> what does it mean?
<2> ax+by+cz+d=0 considered as an equation in a,b,c,d will give u, when varying x,y,z, only some 3d hyperplanes in 4d
<0> i think it a a line in R^4
<1> x,y,z can be anything from R^3? or only a subset in R^3 ?
<0> read it as d(a,b,c)=-(ax+by+cz)
<2> zaphy, i can define for you a small space with only two points, the points being my shoes
<0> that would be a line through the origin in R^4
<1> ? :)
<1> go on phiste1 ?
<3> ....
<0> time for the trout - i wonder :-P
<2> ok
<1> u have amazingly small feet phiste1
<2> to not reinvent the wheel, its a good thing to work with _properties_ of objects, rather than with the objects themselves, because another day u may discover that some other objects may behave the same way
<2> ?
<2> aha :)
<3> @slap _kmh_
<2> @slap mbot
<4> why on earth would I slap mbot
<2> anyway zaphy, its been nice chatting, i gotta go to lunch
<3> bye phiste1
<1> thanks!
<2> bye pyenos
<5> '% Integrate[(sin[x])^2,0,pi]'
<5> mbot: '% Integrate[(sin[x])^2,0,pi]'
<6> % Integrate[Sin[x]^2,{x,0,Pi}]
<4> |Steve|: Pi/2
<5> mbot: '% Steps[Int[(sin[x])^2,{x,0,pi}]]'
<6> I'm unaware of a function Int.
<0> it is int in maple :)
<0> but Integrate in mathematica
<6> Given that this is Mathematica...
<6> What does Steps do?
<6> % Steps[Integrate[x,x]]
<4> |Steve|: Steps[x^2/2]
<6> Nothing.
<0> probably another wring attemot like Int ?
<7> @keal
<4> write an algorthim that generates the correct responses for a phone survey based on number of rings whether answered how quickly hung up on and the mood of the receiver
<0> maybe the idea is to have a riemann sum or something alike ?
<6> % Integrate[Sin[x]^2,{x,0,2Pi}]
<4> |Steve|: Pi
<6> % Integrate[Tan[x]^2,x]
<4> |Steve|: -x + Tan[x]
<0> when my laptop keybiard kills me, I'm constantly missing keys
<8> % D[Sin[x],x]
<4> Manyfold: Cos[x]
<8> % D[Sin^2[x],x]
<4> Manyfold: 0
<5> |Steve|: mathematica has a steps function which gives the steps to transfrom the input to output
<8> % D[Sin[x]^2,x]
<4> Manyfold: 2*Cos[x]*Sin[x]
<6> It doesn't seem to be called Steps though.
<1> is [x] ceil or floor ?
<5> % Integrate[Cos[x]^2 *Cos[2*n*x],{x,-Pi/2,Pi/2}]
<4> bouma: Sin[n*Pi]/(2*n - 2*n^3)
<5> which is zero for all integer n, the question is how can i deduce that by inspection
<6> zaphyBeeble: [x] is floor in older texts.
<5> the original question is what is the fourier series of cos[x]^2 .. the a_0 term is 1/2 and the b_n terms are all zero (cause the fs is even) but why is a_n also zero...
<6> % FourierSeries[Cos[x]^2]
<4> |Steve|: FourierSeries[Cos[x]^2]
<5> maby mbot needs to load the right package ?
<9> http://www.toothpastefordinner.com/gallery-matrix.jpg
<1> then cos[x] is 1,0,0,0,0.......................
<1> in 0, pi/2
<10> www.toothpastefordinner.com is hilarious
<1> or is it cos (floor(x))
<1> umm so floor(x) would be like a incremental step
<1> how does he do it? compute values or split into series
<1> though 0 to pi would add up to zero due to the periodic nature
<0> Table[Sin[Floor[k*Pi]],{k,1,25}]
<0> % Table[Sin[Floor[k*Pi]],{k,1,25}]
<4> _kmh_: {Sin[3], Sin[6], Sin[9], Sin[12], Sin[15], Sin[18], Sin[21], Sin[25], Sin[28], Sin[31], Sin[34], Sin[37], Sin[40], Sin[43], Sin[47], Sin[50], Sin[53], Sin[56], Sin[59], Sin[62], Sin[65], Sin[
<4> 69], Sin[72], Sin[75], Sin[78]}
<6> % Table[Sin[Floor[k*Pi]],{k,1,25}] // N
<4> |Steve|: {0.1411200080598672, -0.27941549819892586, 0.4121184852417566, -0.5365729180004349, 0.6502878401571168, -0.750987246771676, 0.8366556385360561, -0.13235175009777303, 0.27090578830786904, -0.
<4> 404037645323065, 0.5290826861200238, -0.6435381333569995, 0.7451131604793488, -0.8317747426285983, 0.123573122745224, -0.26237485370392877, 0.39592515018183416, -0.5215510020869119, 0.6367380071391379
<4> , -0.7391806966492228, 0.8268286794901034, -0.11478481378318722, 0.25382336276203626, -0.38778163540943045, 0.5139784559875352}
<0> % Table[Floor[Sink*Pi]],{k,1,25}]
<4> _kmh_: $Failed
<0> % Table[Floor[Sin[k*Pi]],{k,1,25}]
<4> _kmh_: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
<1> % Table[Sin[x],{x,0,Pi/2}]
<4> zaphyBeeble: {0, Sin[1]}
<6> Where did Sin[1] come from?
<1> well though the integral is easy... just do (pi/2 -1/pi)*cos(1)
<1> err integral cos[x] 0 to pi/2
<6> Do you mean Integrate[Cos[x],{x,0,Pi/2}] which is 1?
<1> is it?
<6> Of course.
<6> % Integrate[Cos[x],{x,0,Pi/2}]
<4> |Steve|: 1
<1> the 2nd [ ] is also mod ?
<6> Huh?
<1> the one for the integrate?
<1> integrate[...] does this give a mod?
<1> sorry a flor
<6> No.
<6> Did you want a floor?
<1> % Integrate[Sin[x],{x,0,Pi/2}]
<4> zaphyBeeble: 1
<6> % Integrate[Cos[Floor[x]],{x,0,Pi/2}]
<1> that's funny
<4> |Steve|: (2 - 2*Cos[1] + Pi*Cos[1])/2
<1> oh so what is Sin[x] ?
<6> The sine of x.
<1> geelps i thought that was sin floor[x]
<6> Don't mix notations. It's confusing me.
<1> |Steve|: zaphyBeeble: [x] is floor in older texts.
<1> so i thought ... :)
<6> Right.
<6> Mathematica isn't "older texts."
<1> ahh! :)
<6> http://raoulhl.dyndns.org/eq/?id=4t
<4> Title: Equation
<6> That's the more common notation.
<1> % Integrate[Sin[x],{x,0,Pi/2}]
<4> zaphyBeeble: 1
<1> % Integrate[Sin[Floor[x]],{x,0,Pi/2}]
<4> zaphyBeeble: (-2*Sin[1] + Pi*Sin[1])/2
<6> Heh, it took me a while to figure out how mathematica was doing that.
<11> MEOW
<11> :D
<1> how does he integrate the floor
<12> has anyone got a website which explains wtf the fourier series is? in simple english!.. I know how to figure it out, but I dont know wtf it is?
<6> zaphyBeeble: If you look at the graph of sin(floor(x)) for 0 <= x <= pi/2, it's pretty clear.
<6> % Integrate[Sin[1],{x,1,Pi/2}]
<4> |Steve|: -Sin[1] + (Pi*Sin[1])/2
<6> Look familiar?
<1> yes i agree but how does mbot do that, to me it simply is sin(1)(1/pi - pi/2)
<6> Where do you get 1/pi?
<1> can it pick rectangles? :)
<6> mbot is just using mathematica.
<6> And Mathematica can clearly figure it out.
<1> err sin(1)(pi/2 - 1/pi)
<1> oh wonder how...
<6> There's no 1/pi anywhere.
<6> It's sin(1)(pi/2 - 1)
<1> the required area is the value of the function, from x = 1/pi to x=pi/2 ?
<6> You did 0 to pi/2.
<6> I don't see 1/pi anywhere.
<11> implicit function is a function where I cant "isolate" a certain variable that for example i wanan be derive?
<11> like z=y+ln(x/y)
<11> like z=y+ln(x/z)
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