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Math Help - polar coordinates, berger's butterfly

  1. #1
    Senior Member pacman's Avatar
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    polar coordinates, berger's butterfly

    Is there anyone who can solve this? i have polar form plot of this as attachment, its very beautiful but i can not solve it. Any help? A credit to this goes to Henri Berger of UCLA, i can arrive with the correct factorization.

    r = sin^4 (4 theta) + cos (3 theta) for theta = 0 to 2pi)
    Attached Thumbnails Attached Thumbnails polar coordinates, berger's butterfly-berger-butterfly.gif  
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by pacman View Post
    Is there anyone who can solve this? i have polar form plot of this as attachment, its very beautiful but i can not solve it. Any help? A credit to this goes to Henri Berger of UCLA, i can arrive with the correct factorization.

    r = sin^4 (4 theta) + cos (3 theta) for theta = 0 to 2pi)
    Solve what? You have not asked a question.

    CB
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  3. #3
    Senior Member pacman's Avatar
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    Captain Black, what i need was the correct factorization of this sin^4 (4 theta) + cos (3 theta), so that it will be easy for me to generate the above graph by hand . . . . thanks.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by pacman View Post
    Captain Black, what i need was the correct factorization of this sin^4 (4 theta) + cos (3 theta), so that it will be easy for me to generate the above graph by hand . . . . thanks.
    I'm not sure how you are attempting to produce the graph, but it does not seem to me that you need to do anything to the equation in order to plot the curve.

    CB
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  5. #5
    Senior Member pacman's Avatar
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    i think you are right captain black, factoring it wont make it better, more complicated, and it seems i am moving toward uncertainty . . . .

    sin^4(4x) + cos 3x = (1/8)[8cos 3x - 4cos 8x + cos 16 x + 3], whew!!!

    Thanks for taking a blink on this

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