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Math Help - create a 4-leaf clover by polar coordinates

  1. #1
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    create a 4-leaf clover by polar coordinates

    hi,
    what can be the polar equation whose graph is just like a 4-leaf clover as in the attachment?
    Attached Thumbnails Attached Thumbnails create a 4-leaf clover by polar coordinates-pfc.gif  
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  2. #2
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    Hello spring

    Welcome to Math Help Forum!
    Quote Originally Posted by spring View Post
    hi,
    what can be the polar equation whose graph is just like a 4-leaf clover as in the attachment?
    I produced the attached graph in Excel, using the polar equation
    r = \sin2\theta + \tfrac14\sin6\theta
    Is that close enough to what you wanted?

    Grandad
    Attached Thumbnails Attached Thumbnails create a 4-leaf clover by polar coordinates-untitled.jpg  
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  3. #3
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    cant be closer than this!
    i thought there must be something addition of two "sin"s and their coefficients should be different from each other. this solution makes me happy...
    thank you...

    but i want to know how can you produce a polar coordinated graph in excel?
    Last edited by spring; March 14th 2010 at 11:32 AM.
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  4. #4
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    Hello spring
    Quote Originally Posted by spring View Post
    ...but i want to know how can you produce a polar coordinated graph in excel?
    I'm using a fairly old version of Excel. (I bought Office 2007 and tried to like it but hated it, so I reverted to my earlier 2000 version.)

    1. Set up two columns of values: \theta and r=f(\theta). Use values of \theta from 0 to 2\pi.

    2. Create two further columns x = r\cos\theta and y = r\sin\theta.

    3. Use the XY (Scatter) graph-type using the x and y values, choosing the 'smoothed lines without markers' sub-type.

    Grandad
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  5. #5
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    attached graph in St. Patrick green ...
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  6. #6
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    hmm, got it!
    excel is incredible sometimes.
    i will try to produce the equation by skeeter.


    by the way,
    "work smart, not hard."
    like it.
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  7. #7
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    Quote Originally Posted by skeeter View Post
    attached graph in St. Patrick green ...
    Faith and begorrah! 'Tis a handsome colour. Yes, indeed!

    Grandad
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  8. #8
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    Re: create a 4-leaf clover by polar coordinates

    Hi there, first post, i'm in the middle of doing that very design but my clover isn't as tidy as yours, just wondering what i'm doing wrong.
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