misli Watch

point.ms
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#1
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A_1 - center ball
A_1  A_2 - radius ball
A_7A_8 - circular arc
A_9A_{10} - circular arc three times higher than A_7A_8 , A_7A_8=A_9A_{11}=A_{11}A_{12}=A_  {12}A_{10}
A_2A_5 - circular arc
A_2A_3=A_3A_4=A_4A_5 , points A_2 , A_3 , A_4 , A_5 on the best circle the ball (or sphere)
A_6A_2=A_6A_3=A_6A_4=A_6A_5 - circular arcs , are circular arcs on a spher
a 3d sfera.pnge

whether the circular arc that looks like straight?
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point.ms
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#2
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when we look at the top sphere of circular arcs A_6A_2,A_6A_3,A_6A_4,A_6A_5 - seem straight lines A_1A_2,A_1A_3,A_1A_4,A_1A_5 or A_6A_2,A_6A_3,A_6A_4,A_6A_5
b 3d sfera.png
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point.ms
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tendon A_7A_8 , A_9A_{10} ,A_{11}A_{12} arcs are parallel to each other
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#4
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- point A_1
- compass , from point A_1 , circular arc A_2A_5
- straightedge , in points A_1 , A_2 , straight line A_1A_2
- straightedge , in points A_1 , A_5 , straight line A_1A_5
- point A_7 , requirement A_1 A_7<\frac{A_1A_2}{3}
- compass A_1 , A_7 , from point A_1 , point A_8
- straightedge , in points A_7, A_8 , straight line A_7A_8
- bisection circular arc A_2A_5 , point B_1
- straightedge , in points A_1, B_1 , straight line A_1B_1 , point B_2

- compass A_1A_2 , from point A_1 , circular arc A_9B_3
- compass A_7A_8 , from point A_9 , point A_{11}
- compass A_7A_8 , from point A_{11} , point A_{12}
- compass A_7A_8 , from point A_{12} , point A_{10}- straighedge , in point A_9 ,A_{10} , straigt line A_9A_{10}
- bisection circular arc A_9A_{10} , point B_4
- straightedge , in points A_1, B_4 , straight line A_1B_4 , point B_5
111.png

To be continued ...
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#5
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that's the way, without the knowledge of what is happening in the sphere of

1a.png
- given the angle C_1C_2C_3
- straightedge and compass , straight line C_2C_3 , is divided into two equal parts, point C_4
- straightedge and compass , straight line C_2C_4 , is divided into two equal parts, point C_5
- compass C_2C_5 , from the point C_2, point C_6
- straightedge and compass, angle bisection C_1C_2C_3 , point C_7
- straightedge , straight line C_2C_7

- compass C_2C_3 , from the point C_2 , arc C_3C_1
- compass C_5C_6 , from the point C_3 , point D_1
- compass C_5C_6 , from the point D_1 , point D_2
- compass C_5C_6 , from the point D_2 , pointD_3
- straightedge , straight line C_3D_3
- straightedge and compass, angle bisection C_3D_3 , point D_4
- straightedge , straight line C_2D_4 , point D_5

YOU TRY TO KEEP ... Figure down

1b.png
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#6
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- straightedge and compass , perpendicular to the line a_1 straight line C_2C_7
- compass C_3D_5 , in point C_2 , points E_1 and E_2
- straightedge and compass , perpendicular to the line a_2 line a_1 , point E_3
- straightedge and compass , perpendicular to the line a_3 line a_1 , point E_3
- straighedge , straight line E_3E_4 , point E_5
- straightedge and compass , perpendicular to the line a_4 straight line C_5C_6 , point E_6
- straightedge and compass , perpendicular to the line a_5 straight line C_5C_6 , point E_7

YOU TRY TO KEEP ... Figure down
1cc.png
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- straightedge and compass , perpendicular  b_1 straight line C_2D_5
- straightedge and compass , perpendicular b_2 on the b_1 from point D_3 , straight line D_6D_3
- straightedge and compass , perpendicular b_3 on the b_1 from point D_2 , straight line D_7D_2
YOU TRY TO KEEP ... Figure down
F_1 is located on the arc C_3C_1 , C_3F_1=C_1F_1
1d.png
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#8
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- straightedge , straight line C_2F_1 , C_2F_1=C_2C_3
- compass C_2E_5 , from point C_2 , pointF_3
- straightedge and compass , straight line the normal to C_2F_3
- compass D_6D_3 , from point C_2 , pointF_4
- straightedge ,straight line extension C_2F_4
- compass D_7D_2 , from point C_2 , point F_5
- straightedge and compass , normal from point F_5 na duž C_2F_1 , point F_6

Solution - in the picture below
1e.png
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#9
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- compass C_2F_6 , from point E_6 , point A_{12}
- compass C_2F_6 , from point E_7 , point A_{13}
- straightedge , semi-line C_2A_{11}
- straightedge , semi-line C_2A_{12}

trisection is complete, any error !!!
this is true for angles 180^o<\alpha<0^o , larger angles of first division of the 180^o are you ready for the

process of construction of the regular polygon
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point.ms
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#10
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valid for the odd a={3,5,7,9,11,...}
Proper ninth angle
2.png
- straight line A_1A_2
- straightedge and compass ,\frac{A_1A_2}{10} , point A_4 , a+1 , a=9. followed by .9+1=10
- straightedge and compass , A_1A_3 normal A_1A_2 , angle C_3C_1C_2=90^o
- compass A_1A_4 , from point A_5
- straightedge , straight line A_4A_5 - straightedge and compass , bisection arc A_2A_3 , point A_6
YOU TRY TO KEEP ... Figure down
22.png
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