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Thread: Surface Area of a Sphere

  1. #1 Surface Area of a Sphere 
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    I was wondering if there was any geometric meaning to this integral/area element... what does it mean on a sphere? A very small circle, when added up (0 to 2R), the area is that of the sphere's surface area?



    Well, it equals , but maybe it's meaningless.

    The most commonly seen integral that's meaningful is , where the area element is a strip of the sphere.


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  3. #2  
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    if i remember correctly pir^2 integrated
    is the volume of a sector of a sphere (pir^3)/3
    4 times this is the total volume of the sphere 4/3pir^3
    which when diffentiated gives 4pir^2 its surface area


    Last edited by fiveworlds; March 6th, 2013 at 01:03 PM.
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  4. #3  
    Genius Duck Moderator Dywyddyr's Avatar
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    Feel free to ignore Fiveways. He's not exactly an authority on maths, nor particularly coherent.
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    Quote Originally Posted by fiveworlds View Post
    if i remember correctly pir^2 integratedis the area of a sector of a sphere (pir^3)/34 times this is the total area for the sphere 4/3pir^3which when differentiated gives 4pir^2
    You do realize that I am talking about the surface area, not the volume. is what you are talking about.
    Last edited by Wise Man; March 6th, 2013 at 02:16 PM.
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    you do realise that 4pir^2 is the surface area and an area is a specific amount of space so i am not incorrect to call it area instead of volume sadly i have never called myself the authority on maths nor would i call it one of my goals for somebody to view me as such i certainly dont want to be
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  7. #6  
    Genius Duck Moderator Dywyddyr's Avatar
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    Quote Originally Posted by fiveworlds View Post
    an area is a specific amount of space
    No it's not.

    i am not incorrect to call it area instead of volume
    You are actually.
    Each of those terms has a specific definite meaning. They are not interchangeable.
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  8. #7  
    Quagma SpeedFreek's Avatar
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    Surface area = the amount of surface.
    Volume = the amount contained inside the surface.
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  9. #8  
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    yet you really dont know the meaning of it obviously. Ps wise man you dont use newtons formula here the only time you would need it is for finding pi so you are incorrect in its application. Note how sombody took the time to write surface in front of area...
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  10. #9  
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    Okay, fiveworlds, what you said in post #2 goes like this:






    This is nothing more than a curious set of statements ending with the expression for the surface area of a sphere. You didn’t answer the OP’s question, namely what is the geometrical interpretation of the integral .
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    Quote Originally Posted by Nehushtan View Post
    Okay, fiveworlds, what you said in post #2 goes like this:






    This is nothing more than a curious set of statements ending with the expression for the surface area of a sphere. You didn’t answer the OP’s question, namely what is the geometrical interpretation of the integral .
    Right. My question is whether has a geometric meaning or is it a curious set of statements ending with the expression for the surface area of a sphere, as Nehushtan said.

    fiveworlds, what you said is that the derivative of the volume is equal to the surface area of a sphere... that doesn't mean anything, not that I can think of.
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  13. #12  
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    Quote Originally Posted by fiveworlds View Post
    yet you really dont know the meaning of it obviously. Ps wise man you dont use newtons formula here the only time you would need it is for finding pi so you are incorrect in its application. Note how sombody took the time to write surface in front of area...
    #1 Can you use proper grammar? I find it hard to read your post.
    #2 What did I do wrong? Which part?
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    Quote Originally Posted by fiveworlds View Post
    You never reasoned your proof, or gave us that link in the first place. And besides, as I said, that doesn't answer me question.

    Though I thank you this proof, I never saw it before. Next time be sure to give us a full proof or a link to one instead of making claim out of no where.
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  15. #14  
    Ophiolater Nehushtan's Avatar
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    Quote Originally Posted by Wise Man View Post
    I was wondering if there was any geometric meaning to this integral/area element... what does it mean on a sphere? A very small circle, when added up (0 to 2R), the area is that of the sphere's surface area?



    Well, it equals , but maybe it's meaningless.
    May I ask where you got the integral from? Your question got me intrigued; I’ve been searching everywhere for an answer without success. I wondered if it might have something to do with solid angles, but apparently not (plus I can’t make out why the limits should be 0 and 2R).
    Last edited by Nehushtan; March 7th, 2013 at 07:51 AM.
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  16. #15  
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    Quote Originally Posted by SpeedFreek View Post
    Surface area = the amount of surface.
    Volume = the amount contained inside the surface.
    Reminds me of the terminology used by my then-teenaged Nephews when relating tales of their experiences with girl friends: they managed to "get some surface".......

    jocular
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  17. #16  
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    Quote Originally Posted by Nehushtan View Post
    Quote Originally Posted by Wise Man View Post
    I was wondering if there was any geometric meaning to this integral/area element... what does it mean on a sphere? A very small circle, when added up (0 to 2R), the area is that of the sphere's surface area?



    Well, it equals , but maybe it's meaningless.
    May I ask where you got the integral from? Your question got me intrigued; I’ve been searching everywhere for an answer without success. I wondered if it might have something to do with solid angles, but apparently not (plus I can’t make out why the limits should be 0 and 2R).
    Well, it was really something I came up with ... I'm trying to see if it corresponds to some geometric shape.

    It seems that the area element is a small circle, with a radius of , and the area adds up to 2R...hmm... I think it doesn't make sense.
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  18. #17  
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    Ah, okay.

    To find the surface area of a sphere by summing areas of elements on the surface, I suppose one could proceed as follows. Divide the sphere into latitudes and longitudes; let the equator be 0 latitude, choose an arbitrary merdian and call it 0 longitude. Now, at latitude the circle of latitude has radius . So the surface element between latitudes and and longitudes and has area . Hence the surface area of the sphere is


    which should work out to be .
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  19. #18  
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    also and albeit very uniterestingly by multiplying pir^2 by a factor of D you are changing the amplitude of a waveform graph unless you can specify the exact uses of this and know what you are doing you are easily incorrect
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  20. #19  
    Genius Duck Moderator Dywyddyr's Avatar
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    Please stop posting drivel.
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    umm well..
    x= a line
    xx=a square
    xx+x-xx=a square wave
    x(xx)=a cube
    but drivel...not likely
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  22. #21  
    Genius Duck Moderator Dywyddyr's Avatar
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    Yup, nonsensical drivel.
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  24. #23  
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    Quote Originally Posted by fiveworlds View Post
    umm well..
    x= a line
    xx=a square
    xx+x-xx=a square wave
    x(xx)=a cube
    but drivel...not likely
    Quote Originally Posted by fiveworlds View Post
    What on earth goes on inside your skull? Every time you post it's like walking into Dali painting or a Becket play.

    x= a line
    xx=a square
    xx+x-xx=a square wave
    x(xx)=a cube
    Would you care to explain this, apparently meaningless notation?

    And what the heck does it have to do with a purveyor of laser systems?
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  25. #24  
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    Quote Originally Posted by fiveworlds View Post
    also and albeit very uniterestingly by multiplying pir^2 by a factor of D you are changing the amplitude of a waveform graph unless you can specify the exact uses of this and know what you are doing you are easily incorrect
    Wrong. Everyone knows that you have to multiply by E, not D. Then -- and only then -- the waveform graph will be sinusoidally rectified. Contumely.
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    dywyddr is always on about me making coherent replies links to coherent
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  27. #26  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by fiveworlds View Post
    dywyddr is always on about me making coherent replies links to coherent
    Doh. Even your jokes are incomprehensible.

    You need to take a course in communication skills or something. Posting in shorthand isn't really doing you any favours.
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  28. #27  
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    ABLSGR8TaNo
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  29. #28  
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    Quote Originally Posted by fiveworlds View Post
    ABLSGR8TaNo
    Regrettably, that's about the most coherent thing you've posted.
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  30. #29  
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    75,13,3,39,16,8? protons
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  31. #30  
    Genius Duck Moderator Dywyddyr's Avatar
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    2, 4, 6, 8?
    Garden gate.
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    fun. Tk might i ask you refer to E and not D since both could be a number surely it would be irrelevant what you called it. x^2 for example is the same as x*x or a*a or b*b provided a=b=x of course. Secondly i dont see why it is even necessary for a waveform to be sinusoidally rectified in order to be a waveform but surely Asin(@) applies where A is the amplitude of the wave. This would still hold for x*x etc where x is a certain distance between two points ie length and breadth for a square or length*amplitude. You are doing the exact same with the asin(@) transformations. The main difference being that sinx is bounded on the x axis between 0 and 2pi.
    Last edited by fiveworlds; March 7th, 2013 at 05:32 PM.
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  33. #32  
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    Some threads regrettably regress rather than progress, which results in consummate waste of electronic storage capacity. jocular
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  34. #33  
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    Quote Originally Posted by fiveworlds View Post
    fun. Tk might i ask you refer to E and not D since both could be a number surely it would be irrelevant what you called it. x^2 for example is the same as x*x or a*a or b*b provided a=b=x of course. Secondly i dont see why it is even necessary for a waveform to be sinusoidally rectified in order to be a waveform but surely Asin(@) applies where A is the amplitude of the wave. This would still hold for x*x etc where x is a certain distance between two points ie length and breadth for a square or length*amplitude. You are doing the exact same with the asin(@) transformations. The main difference being that sinx is bounded on the x axis between 0 and 2pi.
    What you are failing to take into account is the distributivity of hyperbolic functions with complex arguments that are Abelian, but not perfunctory. If you parse the bases without orthogonality, you are led ineluctably to a Class 3 Hausdorff homeomorphism.

    Now is that clearer?
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    a little something i didnt know could you redirect me to the solution to this problem
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  36. #35  
    Brassica oleracea Strange's Avatar
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    You might find what you want here: New on the snarXiv
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  37. #36  
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    so basically instead of awnsering my question redirect to paper generator snarXiv - Wikipedia, the free encyclopedia basically this website i may have to get rid of a few more incorrect mathsbooks
    Last edited by fiveworlds; March 8th, 2013 at 06:09 PM.
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  38. #37  
    Brassica oleracea Strange's Avatar
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    It makes as much sense as 90% of what you write.
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    its a pity that its typed so
    Last edited by fiveworlds; March 9th, 2013 at 07:46 AM.
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  40. #39  
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    Quote Originally Posted by fiveworlds View Post
    its a pity that its typed so
    The quality of the typing appears to be symptomatic of the "thought processes" behind it.
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  41. #40  
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    then perhaps the 'thought processes' could learn something for a change. Can you explain to me the chemical reactions grass undergoes as it passes through a cows digestive system?
    Last edited by fiveworlds; March 12th, 2013 at 01:55 PM.
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