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Thread: misli

  1. #1
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    misli

    misli-1a.png
    - given the angle $\displaystyle C_1C_2C_3$

    - straightedge and compass , straight line $\displaystyle C_2C_3$ , is divided into two equal parts, point $\displaystyle C_4$
    - straightedge and compass , straight line $\displaystyle C_2C_4$ , is divided into two equal parts, point $\displaystyle C_5$
    - compass $\displaystyle C_2C_5$ , from the point $\displaystyle C_2$, point $\displaystyle C_6$
    - straightedge and compass, angle bisection $\displaystyle C_1C_2C_3$ , point $\displaystyle C_7$
    - straightedge , straight line $\displaystyle C_2C_7$


    - compass $\displaystyle C_2C_3$ , from the point $\displaystyle C_2$ , arc $\displaystyle C_3C_1$
    - compass $\displaystyle C_5C_6$ , from the point $\displaystyle C_3$ , point $\displaystyle D_1$
    - compass $\displaystyle C_5C_6$ , from the point $\displaystyle D_1$ , point $\displaystyle D_2$
    - compass $\displaystyle C_5C_6$ , from the point $\displaystyle D_2$ , point$\displaystyle D_3$
    - straightedge , straight line $\displaystyle C_3D_3$
    - straightedge and compass, angle bisection $\displaystyle C_3D_3$ , point $\displaystyle D_4$
    - straightedge , straight line $\displaystyle C_2D_4$ , point $\displaystyle D_5$


    YOU TRY TO KEEP ... Figure down
    misli-1b.png
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  2. #2
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    Re: misli

    - straightedge and compass , perpendicular to the line $\displaystyle a_1$ straight line $\displaystyle C_2C_7$
    - compass $\displaystyle C_3D_5$ , in point $\displaystyle C_2$ , points $\displaystyle E_1 and E_2$
    - straightedge and compass , perpendicular to the line $\displaystyle a_2$ line $\displaystyle a_1$ , point $\displaystyle E_3$
    - straightedge and compass , perpendicular to the line $\displaystyle a_3$ line $\displaystyle a_1$ , point $\displaystyle E_3$
    - straighedge , straight line $\displaystyle E_3E_4$ , point $\displaystyle E_5$
    - straightedge and compass , perpendicular to the line $\displaystyle a_4$ straight line $\displaystyle C_5C_6$ , point $\displaystyle E_6$
    - straightedge and compass , perpendicular to the line $\displaystyle a_5$ straight line $\displaystyle C_5C_6$ , point $\displaystyle E_7$

    YOU TRY TO KEEP ... Figure down
    misli-1cc.png
    Last edited by msbiljanica; Jan 1st 2017 at 05:13 AM.
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  3. #3
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    Re: misli

    - straightedge and compass , perpendicular $\displaystyle b_1$ straight line $\displaystyle C_2D_5$
    - straightedge and compass , perpendicular $\displaystyle b_2$ on the $\displaystyle b_1$ from point $\displaystyle D_3$ , straight line $\displaystyle D_6D_3$
    - straightedge and compass , perpendicular $\displaystyle b_3$ on the $\displaystyle b_1$ from point $\displaystyle D_2$ , straight line $\displaystyle D_7D_2$

    YOU TRY TO KEEP ... Figure down
    $\displaystyle F_1$ is located on the arc $\displaystyle C_3C_1 $, $\displaystyle C_3F_1=C_1F_1$
    misli-1d.png
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  4. #4
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    Re: misli

    - straightedge , straight line $\displaystyle C_2F_1$ , $\displaystyle C_2F_1=C_2C_3$
    - compass $\displaystyle C_2E_5$ , from point $\displaystyle C_2$ , point$\displaystyle F_3$
    - straightedge and compass , straight line the normal to $\displaystyle C_2F_3$
    - compass $\displaystyle D_6D_3$ , from point $\displaystyle C_2$ , point$\displaystyle F_4$
    - straightedge ,straight line extension $\displaystyle C_2F_4$
    - compass $\displaystyle D_7D_2$ , from point $\displaystyle C_2$ , point $\displaystyle F_5$
    - straightedge and compass , normal from point $\displaystyle F_5$ na duž $\displaystyle C_2F_1$ , point $\displaystyle F_6$

    Solution - in the picture below
    misli-1e.png
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  5. #5
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    Re: misli

    Do you have a question? What is supposed to be true of these? What was your point in posting them?
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  6. #6
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    Re: misli

    - compass $\displaystyle C_2F_6$ , from point $\displaystyle E_6$ , point $\displaystyle A_{12}$
    - compass $\displaystyle C_2F_6$ , from point $\displaystyle E_7 $, point $\displaystyle A_{13}$
    - straightedge , semi-line $\displaystyle C_2A_{11}$
    - straightedge , semi-line $\displaystyle C_2A_{12}$

    trisection is complete, any error !!!

    this is true for angles $\displaystyle 180^o<\alpha<0^o $, larger angles of first division of the $\displaystyle 180^o$

    are you ready for the process of construction of the regular polygon

    ------
    HallsofIvy -question
    1.if my trisection possible ?
    2.from the picture below, if you can figure out which actions the ball (sphere) applied in the plane ?
    arc $\displaystyle A_7A_8=A_9A_{11}=A_{11}A_{12}=A_{12}A_{10}=\frac{A _9A_{10}}{3}$
    misli-3d-sfera.png
    misli-y3d-sfera.png
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  7. #7
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    Re: misli

    valid for the odd $\displaystyle a={3,5,7,9,11,...}$


    Proper ninth angle
    misli-2.png
    - straight line $\displaystyle A_1A_2$
    - straightedge and compass ,$\displaystyle \frac{A_1A_2}{10}$ , point $\displaystyle A_4$ , $\displaystyle a+1$ , $\displaystyle a=9. followed by .9+1=10$
    - straightedge and compass , $\displaystyle A_1A_3$ normal $\displaystyle A_1A_2 $ , angle $\displaystyle C_3C_1C_2=90^o$
    - compass $\displaystyle A_1A_4$ , from point $\displaystyle A_5$
    - straightedge , straight line $\displaystyle A_4A_5$
    - straightedge and compass , bisection arc $\displaystyle A_2A_3$ , point $\displaystyle A_6$

    YOU TRY TO KEEP ... Figure down
    misli-22.png
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