Talk:Angle trisection

Initial draft

I, user:dino, wrote this from a re-direct. Yes, the diagrams are not so hot. But I wanted something "out there," perfect or not. Anyone with better software than the Dia (software) I used is welcome to replace them.

dino 18:51, 4 August 2007 (UTC)

2π/5

The article states that "For example, 2π / 5 radians (72°) may be constructed, and may be trisected. Also there are some angles, that are not-constructable, but (if somehow given) trisectable, e.g. 2π / 5." Surely 2π/5 cannot be both constructable and non-constructable? -Elmer Clark (talk) 10:05, 6 January 2008 (UTC)

Sure, correct example is 3π/7. It is not constructable, but (if somehow given) it is trisectable. —Preceding unsigned comment added by 213.171.48.226 (talk) 21:33, 23 January 2008 (UTC)

Angle trisection up to 60 degree

        I can trisect the angles up to 60 degree.
         my amail address:- apdeokule@yahoo.co.in  —Preceding unsigned comment added by 59.95.34.139 (talk) 13:13, 4 August 2008 (UTC) 

mistake in the statement of the "general theorem"

The correct statement of the theorem is: The angle $\theta$ may be trisected if and only if $q(t)=4t^{3}-3t-cos(\theta )$ is reducible over the field extension $Q(cos(\theta ))$. I think the confusion arises because in the theorem we want to construct $\theta /3$ from $\theta$, whereas in the previous section (where the important trigonometric identity appears) we construct $\alpha$ from $3\alpha$. Right? —Preceding unsigned comment added by 87.165.223.61 (talk) 16:30, 22 January 2009 (UTC)

No criticism?

Haha, only on Wiki. —Preceding unsigned comment added by 80.213.165.232 (talk) 18:45, 29 January 2010 (UTC)

Solution of a polynomial

What is a solution of a polynomial? I suspect you mean root of an irreducible polynomial of second order, or something related? Could you please also explain why? Quiet photon (talk) 20:30, 23 March 2010 (UTC)

"The proof would take us afield"? this is not encyclopedic.. proof is required :P --187.40.247.75 (talk) 04:23, 14 April 2010 (UTC)

New material OK?

I'm planning on adding to this article significantly; I hope that's OK with everyone? I intend to cover not only Wantzel's proof that angle trisection cannot be done with compass and straightedge, but also the mathematical methods by which it can be done. I'm going to have to be slow, so please be patient with me! :) Help would be appreciated – thanks! Willow (talk) 02:07, 4 May 2010 (UTC)

90 Degree

Any right angle, divided or multiplied by 2 is trisecable, right? Jokem (talk) 21:33, 13 May 2010 (UTC)

Indeed, with SE&C you can construct on a given line any multiple of 30°, or construct 30° and bisect it as many times as you like. -- Smjg (talk) 10:53, 14 May 2010 (UTC)

Trisecting analytically

Near the beginning the article says "Also, it is possible to trisect any angle analytically." Depending on how one interprets it, this sentence is either misleading or wrong. Trisecting analytically requires solving a cubic equation which has three real roots. But this cannot in general be done analytically unless you express the solution in terms of the cube root of a complex number; this is the casus irreducibilis. You can take the cube root of the complex number trigonometrically, but then you end up using an expression of the form cos[(1/3)cos^{-1}z]. So the analytic trisection ends up being expressed in terms of the analytic trisection, which is circular.

Does anyone object to my removing the indicated sentence?Duoduoduo (talk) 22:15, 18 May 2010 (UTC)

What the blazes?

Cosine of a cosine? Yes, it should probably go, unless the is good support somewhere.

dino (talk) 00:13, 19 May 2010 (UTC)

Some angles may be trisected

I believe that the statement "Further, an angle of k degrees (k an integer) can be trisected if and only if 3 divides k" is incorrect, the correct statement should read "... 9 divides k. An angle of 60 degrees is a counter-example.

In general, an angle x can be trisected if x/360° is a rational number whose denominator (in lowest terms) is not a multiple of 3. --Jwillekens (talk) 09:09, 23 May 2010 (UTC)

You're right, it's mistaken. The original source says it's constructible (not trisectible) if 3|k. I've deleted it. I'll leave it to you to put in something about 9|k if you want to, along with a reference. I'm not sure whether that is if and only if, or just if. Duoduoduo (talk) 15:44, 23 May 2010 (UTC)

marked straightedge

I suppose it would be cheating to just hold the compass on the straightedge in such a way as to indicate the distance CD? Technically you are still just using a strightedge and compass, though. Jokem (talk) 16:05, 10 June 2010 (UTC)

That is called a neusis construction and is mentioned in the article. 67.119.12.216 (talk) 18:52, 14 September 2010 (UTC)