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Math Help - Using Polar coordinates for leaf design

  1. #1
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    Using Polar coordinates for leaf design

    I am looking for a polar coordinate equation that would develop this leaf design.

    I have come up with is r= 1 + sin(x) + sin(x)2 , where x = degrees in radians but, it does not give the pointy tail. Too circular
    (and has a heart shape bump, but that's okay because most leaves have that heart shape).

    Anyone have any clue as to what infinite expansion I could use to get that bend to the point? i.e. r= a0 + a1sin(x) + a2sin(x)2 + a3sin(x)3 + ......that could be thrown my way? I only need to degree 4 or 5 in sin(x) as a loose approximation to get the flavor.

    Thanks!
    Walter Poelzing - Math Teacher
    Last edited by MathTeacher2012; June 11th 2012 at 08:04 AM. Reason: Forgot to enter the word "not" in a sentence. It would have been logically wrong without that word.
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  2. #2
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    Re: Using Polar coordinates for leaf design

    Something like 3 - sqrt(abs(cos(t))) + sin(t)/2 + sin(t)^3 ?



    Hope I'm not missing the point
    Last edited by tom@ballooncalculus; June 11th 2012 at 12:15 PM.
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  3. #3
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    Re: Using Polar coordinates for leaf design

    Thanks. That is very creative with the absolute value function in the sin function. Now, I'm going to see if I can create a stronger point! -W
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  4. #4
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    Re: Using Polar coordinates for leaf design

    only "leaf" design I could find ...

    Cannabis Curve -- from Wolfram MathWorld
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