classical trisection of an angle

May 2010
7
2
Has anyone heard of the lost theorem and its relevance to trisection of an angle using classical method?
I have a 10 min video on it as well as a trisection method, although not using the lost theorem.....But I am looking for some feedback from anyone knowledgeable in this area.....
Thank you.... Jeremy
YouTube - trisecting this

PS I know about Wantzel....this is briefly addressed.
 
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Oct 2009
255
20
St. Louis Area
Has anyone heard of the lost theorem and its relevance to trisection of an angle using classical method?
I have a 10 min video on it as well as a trisection method, although not using the lost theorem.....But I am looking for some feedback from anyone knowledgeable in this area.....
Thank you.... Jeremy
YouTube - trisecting this

PS I know about Wantzel....this is briefly addressed.
Did you watch this video? You cannot trisect a 180 degree angle with the method he was using. Pi = 3.14159 not 3. If you take the compass you cannot construct a true hexagon with this method. It is only an approximation and is not accurate.
 
May 2010
7
2
Did you watch this video? You cannot trisect a 180 degree angle with the method he was using. Pi = 3.14159 not 3. If you take the compass you cannot construct a true hexagon with this method. It is only an approximation and is not accurate.
But the arc of a half circle is divided into thirds by the radius....creating three equilateral triangles, each angle at the vertex, (center of the circle) is equal to 60 degrees.
 

HallsofIvy

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Apr 2005
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Well, this guy was more honest than most! He constructs two arcs and a straight line, for which he can trisect (the arcs correspond to 180 and 90 degrees) and uses those three points to construct a circular arc. He then says that, since the circular arc trisects those three arcs it seems "reasonable" that it would trisect any arc between them, "would it not be a steady progression" but then ends up saying "I don't know".

No, that circular arc does NOT trisect any arc.
 
May 2010
7
2
Hi, ....I take it you do agree they trisect the 180 and the 90 degree arc. Can you give an explanation why the arc of a circle center thusly would not trisect other arcs as postulated? I don't doubt it so much as I am just wondering. Also, can you at least give a guess as to what kind of arc between these points would perform this task. Or is there no arc? But this seems unlikely, I would think there would be some kind of progressive arc that would trisect the ever decreasing arc of the ever decreasing angle. Could it be the arc of a circle that is centered somewhere else than where I chose? And how might that center be determined?
This is the crux of the problem....there should be a steady progression from G to I to P and from H, J,and Q that trisects any arc from 180 to 0. Can we find the arc that defines that progression?
 
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Oct 2009
255
20
St. Louis Area
But the arc of a half circle is divided into thirds by the radius....creating three equilateral triangles, each angle at the vertex, (center of the circle) is equal to 60 degrees.
I apologize. I was totally out of line with my reply. You are correct about the 180 degrees. But there is no way to trisect an angle in general.

You did not deserve the reply I gave you. I should not take my own frustrations out like that.
 
May 2010
7
2
thanks for the apology, but I didn't take it personally, I just thought you made a mistake and would realize it upon reflection. No problem. Kind of you to write. (besides, I've gotten much worse from some who wouldn't even look at the construction)
And I realize there is not supposed to be a classical solution to trisecting an angle, but I think this construction offers an interesting mental exercise, as I describe in my last post reply to HallsofIvy. And I have updated the video with a caption as well, that examines this question. It is thus.....
Shouldn't some kind of curve (2 actually) define all the trisecting points as the angle transfers from 180 to 0 degrees on this template? What kind of curve?
Any thoughts?
 
May 2010
27
5
Hi linelites, really nice to see your video. I was unaware of the problem so I fiddled some with it.

I took your idea and use the fact that a square can be divided in three equal parts, and Im sticking the square to the base of the bisected angle. Could you have a look at this diagram? what am I doing wrong or not understanding? since I have no problem trisecting any angle with this?
 

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May 2010
7
2
I see you are using the Brunnes Starcut....are you familiar with Malcolm Stewart's new book Patterns of Eternity? Really good.
I think you making the mistake of thinking that trisecting the chord of an angle will trisect the arc. Is this what you are thinking?
J
 
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May 2010
27
5
ah, yes I am, now I see it. tricky problem isn't it.
I'll see if I can find anything on 'the Brunnes Starcut' or Malcolm Stewart's book. Thanks for the tip and help. :)