# Thread: Trisection of an angle

1. ## Trisection of an angle

Hello,

My friend has come up with a method of trisecting any angle with a compass and straight edge after years of trying. But we are not sure what we should do next. The proof and the geometrical constructions are all complete. Now we want to know how we should go about publishing it. We have no idea about how we should go about securing the copyrights or whatever is applicable in this case. He has not published anything before so have no idea.

I am sorry if the questions sound a little vague but like I said as neither of us have any experience in this matter, we are unsure of what course to take next. I would be thankful if someone can guide us further.

Thank you

2. ## Reality Therapy

The very, very first thing you should do is go back to a math class with a competent teacher and just keep attending until you figure out why your proof is incorrect.

The next thing you and your friend shoud do is get a better hobby.

Finally, if you really are interested in mathematics, you can stick with the program long enough to learn what a proof really is. A proof that some thing cannot be done does NOT mean that we're just not clever enough, or if we keep trying, we'll get it. A proof of non-existence is absolute. You will not solve this particular problem. There may be a few special cases that you can solve, but you have not solved the general case. This is because it is known that it cannot be done.

3. ## Trisecting an angle

Originally Posted by TKHunny
The very, very first thing you should do is go back to a math class with a competent teacher and just keep attending until you figure out why your proof is incorrect.

The next thing you and your friend shoud do is get a better hobby.

Finally, if you really are interested in mathematics, you can stick with the program long enough to learn what a proof really is. A proof that some thing cannot be done does NOT mean that we're just not clever enough, or if we keep trying, we'll get it. A proof of non-existence is absolute. You will not solve this particular problem. There may be a few special cases that you can solve, but you have not solved the general case. This is because it is known that it cannot be done.
Much has been written on this going back to Archimedes.

Thomas Hutcheson has written an article

Math Teacher vol 94,no 5 2001

I have not read this but its referenced to a cylinder and string and i would guess the idea would be to measure lenght of arc with string,and put the lenght on a straight line, trisect the line and scribe the equal lenghts on the arc.

bjh

4. Wow. It's solved!

Wait, string, cyllinder, measuring tape, and marking pen aren't allowed.

Choco, let's hear the proof. Someone will be quite able to tell you why it violates the allowable tools or where your mathematics wandered off.

5. ## TKHunny

I am not the one who has the proof neither do I understand it. I am no mathematician. But I can assure you my friend isnt one of those who does this as a casual 'hobby' as you call it. Its out of a deep love for the subject so i would appreciate if you would answer my questions if you can, rather than being condescending and suggesting to find a new hobby or attend maths classes. This friend of mine, after all these years of relentless work, has the humility to attend maths classes if need be but thats beyond the point at the moment.

What I am asking now is that he has come up with something which he honestly thinks could have some value (the method uses nothing except a compass and straight edge). He has the mathematical proof for it ready and just wants to know what is the next step in terms of sending it to be published. If its worthless, he will naturally be turned down which would be alright.

Thank you.

6. I would have thought posting it here would be a good start.

I don't think the idea would be stolen and claimed as someone elses work. You could post it to several friends beforehand as evidence. If it's true it would be big news so your friend would be aware of any false claims and could challenge this.

7. Originally Posted by chocopuff78
Its out of a deep love for the subject so i would appreciate if you would answer my questions if you can, rather than being condescending and suggesting to find a new hobby or attend maths classes. This friend of mine, after all these years of relentless work, has the humility to attend maths classes if need be but thats beyond the point at the moment.
There you have it. If there is a deep love, then pursue the mathematics until it is understood what an existence (or nonexistence) proof is all about.

Recall from your studies "alchemy"? That is where you are living. Your very best choice, if you really, truly believe you have something, is to present it to proper investigation. However, I must warn you, mathematics departments in colleges and universities across the world have files jam packed with proofs submitted by those who do not understand what they are doing. (Well, to be honest, some just discard them when the file gets too big.) There are many, many, many such attempts. Since there is already a proof on non-existence, all the proofs in the file are wrong for some reason - every one of them. Yours will be joining them.

I do appreciate the time that has been spent on the investigation. A few good things came from alchemy, too. If you learned something along the way and broadened your understanding, that's great. On the other hand, if your sole purpose was this solution and you accomplished absolutely nothing else in the effort, you were wasting your time. Perhaps the greatest lesson we could learn, today, it for you to listen to what I'm saying and go find the error(s) yourself. You would learn something doing that.

8. Originally Posted by lemonbreath
I would have thought posting it here would be a good start.
Yes but the problem like i said before is i dont have the proof. And i dont understand it properly either. So i wont know what to post. And unfortunately i dont think my friend would be willing to do it

Originally Posted by TKHunny
Your very best choice, if you really, truly believe you have something, is to present it to proper investigation.
That is exactly what we want to do and thats what my questions were directed at from the beginning. Do you have any ideas on who we should send it to for investigation?

9. You're not really reading my posts, are you? My point was that you need to stop believing you really, truly have something. You don't. My suggestion was not one of encouragement to have some qualified mathematician tell you why your proof is incorrect. The most benefit to you and your friend, and the world, would be for you to find the error yourself and then don't try to fix it. Realize, instead, that there is NOT a solution to this problem and take up some other pursuit. Really, that's why I called this a hobby. Unless you choose insanity, there will soon be an end to it. You will have to think of something else to do. As far as mathematics in general, well, that still would be worth pursuing. Trying to solve the three ancient problems that are known to have no solution, well, that is a hobby you should abandon. Certainly, it might be fun to try to solve them, but you can be certain that every time you think you have solved them, you missed something. This might give you an opportunity to learn something new.

Recap
1) You didn't solve the general trisection problem.
2) Stop believing that you did.
3) It doesn't matter where you send it for adjudication, it will be refuted.
4) If you refute it yourself, it will be less painful and you may gain from the experience.
5) If you insist on sending your proof to a competent publication, it will be refuted, but you may still believe it is true. This has the potential to lead places you do not want to go. I have seen a few go down this path. It is doubtless far more serious than you imagine.

10. ## relationship of prime numbers and dividing an arbitrary angle into equal angles

I believe I have discovered a way of constructing a "prime number fraction" of an arbitrary angle giving equal angle results. i.e.: 2(divide an angle into 2 equal parts), 3(divide an angle into 3 equal parts), 5(divide an angle into 5 equal parts), 7(divide an angle into 7 equal parts), 11(divide an angle into 11 equal parts)......so on and so on....using only a compass and a straight edge.

I know this is supposed to be impossible and I wanted to share this with you so that I may know where I made the error.

I believe it will work properly with any acute angle.

It has been over 40 years since I took plane geometry, so please bare with me on this.

1) Draw an angle using 2 lines, first one horizontal for easy reference labeled BA, and the other line BC to form an acute angle with common point B as the vertex, and label it angle CBA.

2) From vertex B, use a compass to draw a full circle(labeled B) and label intersection of BC point D, and intersection of BA point F.

3) Draw a perpendicular line to BA from point B and label it BG.

4) Draw a line that extends radius BD equivalent to 4 radius's (3+1, 3 being the number of desired equal angles here plus one more), always adding one more radius to the desired number of equal angles, and label the end point H.

5) Draw a parallel line to BA that completes H to BG and label intersection point K.

6) Complete line KF, and label intersection of circle B point E.

7) Angle EBA should + 1/3 angle CBA.

Originally Posted by chocopuff78
Hello,

My friend has come up with a method of trisecting any angle with a compass and straight edge after years of trying. But we are not sure what we should do next. The proof and the geometrical constructions are all complete. Now we want to know how we should go about publishing it. We have no idea about how we should go about securing the copyrights or whatever is applicable in this case. He has not published anything before so have no idea.

I am sorry if the questions sound a little vague but like I said as neither of us have any experience in this matter, we are unsure of what course to take next. I would be thankful if someone can guide us further.

Thank you

11. Originally Posted by carparts1952
I believe I have discovered a way of constructing a "prime number fraction" of an arbitrary angle giving equal angle results. i.e.: 2(divide an angle into 2 equal parts), 3(divide an angle into 3 equal parts), 5(divide an angle into 5 equal parts), 7(divide an angle into 7 equal parts), 11(divide an angle into 11 equal parts)......so on and so on....using only a compass and a straight edge.

I know this is supposed to be impossible and I wanted to share this with you so that I may know where I made the error.

I believe it will work properly with any acute angle.

It has been over 40 years since I took plane geometry, so please bare with me on this.
Hi,
for us to point out where your error lies, you should provide a proof of why you think your construction trisects the angle. If you don't have a proof but just a "hunch", you can prove by yourself that it is wrong: for instance, you should look at the case when ABC is 60° (i.e. $\displaystyle \frac{\pi}{3}$) and compute all the lengths explicitely using Pythagoras theorem.

By the way, following your instructions, I got an angle EBA greater than CBA, so there must be something unclear (a sketch is good)...

12. Thread closed before more 'proofs' are posted. MHF is not the place for these sorts of 'proofs'.