Is this a valid way to trisect an angle?

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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 [TEX] 45 ^ o[/TEX] (which can be any angle which is obtainable by means of compass and straightedge)


The angle CAB  [TEX]45 ^ o[/TEX]  can be obtained with a compass and unmarked ruler, he added angles (each have  [TEX]45 ^ o[/TEX]) DAC and EAD, obtained angle EAB [TEX]135 ^ o[/TEX]is 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 [TEX]15 ^ o[/TEX] get the angle FAB [TEX]150 ^ o[/TEX] - continued in the next post
« Last Edit: 13/01/2016 14:15:47 by chris »

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Offline chris

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Re: proportioned angles
« Reply #1 on: 07/01/2016 11:19:11 »
And your question is?
I never forget a face, but in your case I'll make an exception - Groucho Marx

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Offline f.point

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

[attachment=20771]

Required accessories - pencil, compass, unmarked straightedge

basic angle - can be any angle that can be construction using compass and unmarked straightedge, angle CAB [TEX] 45 ^ o[/TEX]

starting angle - sum of 2, 3, 4, 5, ... basic angles , EAB [TEX] 135 ^ o[/TEX]
sum angles CAB [TEX] 45 ^ o[/TEX] DAC [TEX] 45 ^ o[/TEX] EAD [TEX] 45 ^ o[/TEX]

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 [TEX] 30 ^ o[/TEX]

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

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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?").

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Offline f.point

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proportioned angles
« Reply #4 on: 20/01/2016 09:53:28 »
basic angle CAB [tex]45^o[/tex]

starting angle EAB [tex]135^o[/tex] consists of the sum of the angles CAB [tex]45^o[/tex] DAC [tex]45^o [/tex]EAD [tex]45^o[/tex]

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 [tex]30^o[/tex]

section IA and longer circular arc FG is a point J

[attachment=20820]

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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?
Please disregard all previous signatures.

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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.

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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
[attachment=20871]
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
[attachment=20873]