[Hal.]

John Cuthber, on 12 September 2011 - 06:12 PM, said:

This isn't a development because it can't go anywhere or do anything.

This is an attempt at a development which is what I admire .

Quote

It's not "supposed" impossible; its proven impossible.

I am supposing it is impossible , as I did not see a proof of impossibility , I do know who I am willing to believe if they say it is impossible .

Quote

It would be better if he spent his time helping little old ladies across the road or, at least, trying to do something where he might succeed.

You could be surprised how a person could receive an A+ for trying to prove something which is impossible to prove as it doesn't really matter sometimes if somebody is right or wrong , it is about the persistence of an argument . Take law as an example , people are committing crime all day long and lawyers are convincing people of their innocence even if only their guilt can be proven . Maybe the original poster could take a lesson from the legal profession in so far as trying not to prove the geometry but trying to convince people of it's proof first which could be much easier .

[John Cuthber]

Hal., on 12 September 2011 - 09:57 PM, said:

as I did not see a proof of impossibility ,
it is about the persistence of an argument

Then you should have followed the link in the 4th post in this thread.
and
It is indeed about persistence of an argument.
If you persist after it has been proved that you are wrong then, at best, you are a fool.

[Hal.]

I supposed correctly , Cuthber , from the posts of two people and you aren't one of them .

[imatfaal]

Rockas - I have not had time to read your paper fully, but two things:

1. It can be proven that one cannot in general trisect the angle
2. I think from the brief glance I gave your work that it merely shows that an angle that is constructed is half the size of the original angle. This is not, I believe, something new - what you need to be able to show in geometric steps is how to trisect an angle between two lines and (this time shouting for emphasis) THIS IS IMPOSSIBLE

Could you just confirm that you are working from merely two lines call them A and B which intersect? Any points on the lines, tangents, circles around points etc must be uniquely identifiable and given in simple steps.

It also seems that your proof that angle D1 is half of D2 is a bit over the top.
from your construction DG=DG'=DE - they are points on a circle of which D is centre.
G'G=GE - two radii of circle centred at G.
thus the two triangles DG'G and DGE are congruent isosceles triangles.
the line DZ is easily shown to bisect the angle G'DG.
As the angle ZDG is half the angle G'DG it must be half the same angle of the congruent triangle ie GDE.
The total angle ZDE is then clearly 3 times larger than ZDG - but that is not because you have trisected an angle, it is because you have mirrored an angle, bisected it, and then taken the sum of the original and the half angles.

it is impossible to do this the other way around!

[doG]

rockas30, on 19 January 2012 - 05:01 PM, said:

Read my work about trisection at http://bestsitetopbu...le-English.docx

Waste of time...the problem was algebraically proved impossible by Wantzel (1836).

This post has been edited by doG: 19 January 2012 - 06:01 PM

[DrRocket]

John Cuthber, on 12 September 2011 - 06:12 PM, said:

It would be better if he spent his time helping little old ladies across the road or, at least, trying to do something where he might succeed.

I am fond of some little old ladies and would prefer a more reliable source of aid.

[michel123456]

michel123456, on 8 September 2011 - 03:32 PM, said:

90° is feasable too.

Curiously, I was never interested in the question.
Yesterday I made a simple thought: it is possible to make a circle, draw 3 smaller circles (of random radius) upon its circumference, and create an arc, divided in 3 equal parts, forming a random angle.
I wondered why the reverse construction was impossible (beginning from the angle and dividing the arc). As if geometry had a direction that cannot always be reversed, like entropy and time...

Now I took some time to draw that.

Step 1. a circle.


Step 2. a smaller circle with a center on the circumference of the big circle.


Step 3. a 2nd small circle, identical, with center at the intersection of the 2 circumferences.


Step 4. segments joining the center of the big circle with the intersections on the circumference.


Step 5. erasing the circle, keeping the arc.


The angle is trisected, but there is no way to make the construction backwards. Isn't that remarkable?

This post has been edited by michel123456: 10 February 2012 - 06:18 PM

[imatfaal]

Yes - it is a nice construction and as you point out not reversible which is a shame and not unexpected. doG included a great link to a math profs page of quasi-trisections of an angle - repeated here . I think the various different failed/half-hearted attempts show how fascinating and doomed the quest is - and how close we can come even when we know it is impossible

This post has been edited by imatfaal: 10 February 2012 - 06:38 PM