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Thread: loci of hexagon`

  1. #1
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    loci of hexagon`

    How can I great hexagon that its' sides is a loci of an equation?
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  2. #2
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    Re: loci of hexagon`

    I have no idea what you are asking. If you are asking if there exist an "equation" such that the set of all points that satisfy the equation form a hexagon then the answer is "yes" if you allow that equation to have 6 separate parts, giving each if the six sides of the hexagon.
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  3. #3
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    Re: loci of hexagon`

    Fourier series + polar coordinates? That would be my guess.
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  4. #4
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    Re: loci of hexagon`

    Quote Originally Posted by HallsofIvy View Post
    I have no idea what you are asking. If you are asking if there exist an "equation" such that the set of all points that satisfy the equation form a hexagon then the answer is "yes" if you allow that equation to have 6 separate parts, giving each if the six sides of the hexagon.

    Can you give an example?
    Last edited by policer; Aug 17th 2018 at 07:46 AM.
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  5. #5
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    Re: loci of hexagon`

    Quote Originally Posted by policer View Post
    Can you give an example?
    $$f:[0,1] \to \mathbb{R}^2$$

    defined by:

    $$f(t) = \begin{cases}6t\begin{pmatrix}0 \\ 1\end{pmatrix}, & 0 \le t < \dfrac{1}{6} \\ (2-6t)\begin{pmatrix}0 \\ 1\end{pmatrix} + (6t-1)\begin{pmatrix}1 \\ 2\end{pmatrix}, & \dfrac{1}{6} \le t < \dfrac{1}{3} \\ (3-6t)\begin{pmatrix}1 \\ 2\end{pmatrix} + (6t-2)\begin{pmatrix}2 \\ 2\end{pmatrix}, & \dfrac{1}{3}\le t < \dfrac{1}{2} \\ (4-6t)\begin{pmatrix}2 \\ 2\end{pmatrix} + (6t-3)\begin{pmatrix}3 \\ 1\end{pmatrix}, & \dfrac{1}{2} \le t < \dfrac{2}{3} \\ (5-6t)\begin{pmatrix}3 \\ 1\end{pmatrix} + (6t-4)\begin{pmatrix}3 \\ 0\end{pmatrix}, & \dfrac{2}{3}\le t < \dfrac{5}{6} \\ (6-6t)\begin{pmatrix}3 \\ 0\end{pmatrix}, & \dfrac{5}{6} \le t \le 1\end{cases}$$
    Last edited by SlipEternal; Aug 17th 2018 at 09:17 AM.
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  6. #6
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    Re: loci of hexagon`

    Thanks!
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