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Author Topic: Is this a valid way to trisect an angle?  (Read 2158 times)

Offline f.point

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Is this a valid way to trisect an angle?
« on: 07/01/2016 10:44:16 »
Required accessories - pencil, compass, unmarked straightedge


Odd proportion angles (there is a proportion of the steam angles) of the element 3 (which may be 5,7,9, ...) and the base angle 77f80f95807de378e713d5c330bc37ef.gif (which can be any angle which is obtainable by means of compass and straightedge)


The angle CAB  26044431401f41fccfc64f0b65bdb83e.gif  can be obtained with a compass and unmarked ruler, he added angles (each have  26044431401f41fccfc64f0b65bdb83e.gif) DAC and EAD, obtained angle EAB e0f75903caa131f167df4a8bce88e666.gifis the starting angle


Merge points E (D, C, B) and get a longer ED (DC, CB)


Along the DC from the point C draw is normal that intersects the segment AB, the intersection is a point G


Divider AG and from point G draw a circular arc to a longer EA and H get the point, and the arc GH, join the dots G and H and get along GH


Longer GH (ED, DC, CB) are equal, the arc EB's first circular arc can be made smaller or larger with a constant radius AB, arc GH is the second circular arc can be made smaller or larger with a constant radius AG


INCREASING THE ANGLE
the starting angle EAB add angle FAE e03f50112e457dc4a243a12bab9babca.gif get the angle FAB b157590e3fd5f709a3cd84ecef476bb8.gif - continued in the next post
« Last Edit: 13/01/2016 14:15:47 by chris »


 

Offline chris

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Re: proportioned angles
« Reply #1 on: 07/01/2016 11:19:11 »
And your question is?
 

Offline f.point

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Re: proportioned angles
« Reply #2 on: 12/01/2016 15:58:08 »
- previous post was in error -



Required accessories - pencil, compass, unmarked straightedge

basic angle - can be any angle that can be construction using compass and unmarked straightedge, angle CAB 77f80f95807de378e713d5c330bc37ef.gif

starting angle - sum of 2, 3, 4, 5, ... basic angles , EAB 8d683c9c0d121441c43a4f7afa48b2f3.gif
sum angles CAB 77f80f95807de378e713d5c330bc37ef.gif DAC 77f80f95807de378e713d5c330bc37ef.gif EAD 77f80f95807de378e713d5c330bc37ef.gif

difference angle - the angle which increases or decreases the starting angle. difference starting angle and the angle of whom do not know the measure , this angle is known to see a procedure HAB 217a0f1dfb61eefd29d5fa9b095065a8.gif

straightedge AB is divided into three parts AF , how we have a basis in the angles starting angle

divider AF from point A the circular arc FG

section straightedge AH the circular arc FG , point I

straightedges FG , ED
--------------------------------------
will continue - if there are errors
 

Offline evan_au

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Re: proportioned angles
« Reply #3 on: 13/01/2016 08:20:21 »
It is often useful to start a proof with a statement of what you are trying to prove.

This website is about asking and answering questions, so please phrase the thread as a question (even if it is "Is this a valid way to trisect an angle?").
 

Offline f.point

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proportioned angles
« Reply #4 on: 20/01/2016 09:53:28 »
basic angle CAB 1ec6981abf6bb2a5d4ed72db7f740256.gif

starting angle EAB 0719f3a59e1bb14f3338bfc60214bbd0.gif consists of the sum of the angles CAB 1ec6981abf6bb2a5d4ed72db7f740256.gif DAC 9dd0345b4d306b33fb5bb5f3e793e280.gifEAD 1ec6981abf6bb2a5d4ed72db7f740256.gif

DC straightedge the normal to the point D , gets the point F

AF divider from point A, we get the point G

divider AB from point F, divider AB from point G, we get the point H

HG divider from point H, creates a circular arc FG

difference angle IAB 5089c3ad1f14e3026766c28db2d7c735.gif

section IA and longer circular arc FG is a point J

 

Offline Bored chemist

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Re: Is this a valid way to trisect an angle?
« Reply #5 on: 20/01/2016 21:10:10 »
In the particular case of 45 degrees it's easy to trisect it.
You construct a triangle of 60 degrees and the difference is 15 which is a third of 45.
However that's not generally very useful.
Being able to construct an angle like 135 degrees by trebling some other angle, then dividing it back into three parts is even less use.

What would be interesting would be a general way of splitting an angle into 3 equal parts.
However that problem has been proven to be impossible.
Why spend time on it?
 

Offline alysdexia

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Re: Is this a valid way to trisect an angle?
« Reply #6 on: 21/01/2016 13:43:12 »
Instructions unclear.  Pencil stuck in toaster.

Being able to construct an angle like 135 degrees by trebling some other angle, then dividing it back into three parts is even less use.

What would be interesting would be a general way of splitting an angle into 3 equal parts.
However that problem has been proven to be impossible.
Why spend time on it?

Only with a compass and edge, not with a ruler.  What if one uses two or three compasses at a time?

Anyway one could triple any angle, put a set of those angles in a table, then use that table as the ruler.
 

Offline f.point

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Re: Is this a valid way to trisect an angle?
« Reply #7 on: 30/01/2016 16:50:15 »
applies this photo

bisection angle DAC is obtained by point J
along AJ
GF section circular arc and along the AJ, obtained point L
AF divider, from the point J, we get the point O
divider AF, from point A circle c1
divider GL, from the point J, the circuit d1, get the points P and Q
 

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Re: Is this a valid way to trisect an angle?
« Reply #7 on: 30/01/2016 16:50:15 »

 

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