User:Maitaman

I discovered the angle trisection method in 1957 when a teacher of trigonometry stated that Pythagorus "proved" that it could nor be done, using only a compass and straight edge. I said, "BS! It's a ratio, so figured the method on the basis of it being a ratio. I understood that the entire process had to include that angle, and only that angle. It would depend on three sections that were tied to that angle, and only that angle. Bisecting that angle was a thing that produced a result that was unique to that angle. Reasoning that I had to use three, I constructed a "data line" that was three measured sections of the bisector arc. Now to make it completely tied to that angle would be a matter of tying the data line to a point that was both connected to the particular angle and to the line. That seemed to be obvious. The point where the arc met the leg of the angle. I copied the data line from that point to where it met the other leg of the angle, That was a complete inclusion that fit that, and only that, angle in both operations I then drew lines from the data line to the point of the triangle. That gave me arc sections A, B, and C. It looked like section B was the trisector. I used the compass to ascertain that was, truly, the case. I noticed the difference in the three sections. Reasoning that B was the trisector, what was the relationship to A and C? Simple logic. If B was the trisector, then A and C added up to two thirds of the arc. That meant that adding A and C and dividing by two would give me B. It worked. I then noted that it only worked in acute angles. Bisecting was still on my mind, so I bisected the obtuse angles to get two equal acute angles. "Equal" was the point of it, so I trisected the half-angle, added two of the trisector, and tried it on the wider angle. It worked. I first published the exact process on the upload in 1961, and several times since. Mathematicians seemed to have the attitude that "Pythagoras proved it is not possible, and that's good enough for me!" "I tried it on a number of angles, and it SEEMS to work, but Pythagoras showed that it isn't possible." C'est la vie. I put it here on Wikipedia so they can now disprove it. I don't think they can

UPDATE: They could. Some people on a site that deals with such things has made a carefully drawn model and had it analyzed by computer, which discovered that the method was off about 1/15 of a degree. It is rather disappointing that, after 51 years, this was shown. I believe the method has a built-in way to correct that. It is a nagging feeling, somehow centered around the "compass and straight-edge" caveat. I will try to find where it is in my [excuse the expression] mind as soon as I finish the medical plant research I am working on. THE METHOD IS PROVEN FAULTY

                  Trisecting the Circle
            A proof of trisecting the angle

I am well-aware that there are several methods to trisect a circle. This is not proposed as a "new" idea. In 1957, I trisected the angle. It was dismissed by the teacher with the words, "There are a few methods that are very close for certain angles, but Pythagoras proved, for all time, that the angle can't be trisected using only a compass and straight edge." He had tried it with four or five random angles, and agreed that it "seemed" to work, then refused to investigate further. I became thoroughly disgusted with anyone who would make such a statement. In 1961, I first published the method - and was ignored I published it several times since. Only one time was any notice taken, except in 1991, when two mathematicians argued about it, still with the background idea that the Pythagoran Theory said it's impossible, so that's good enough for them! I recently posted it here on Wikipedia, and got a couple of responses. What I lacked was any kind of proof I could demonstrate. I am beyond caring about that kind of thing. My research in various fields seems to always come up with the same mindset. I finally, while editing a book I wrote in 1986, (yesterday, 17/07/2018) said the proof would be no harder than the original method to show. It was agreed that it always "seemed" to work on oblique angles. So! If it "seemed" to work on oblique angles, proof would come on wider angles, if it also "seemed" to work with them, right? The inconsistencies would be amplified on wider angles. The widest angle? 360 degrees. A Circle. So! All I have to do is trisect a circle using the method to present proof or disproof! So I tried it, as follows: To make it workable, I would have to use and angle that is within reason, so I bisected the circle, striking a diameter. That is a bit too wide, also, so I bisected that angle, giving me 4 equal 90 degree angles. There are a number of ways to trisect a 90 degree angle, so it would prove nothing, umless I use the method I'm trying to prove or disoprove. An added attraction is that the differences would be amplified by 4 increments. I then trisected one of the 90 degree angles, established a data line on which I established 4 points at junctures of the distance of the 90 degree trisection points. Reasoning: If I had true trisection of the first 90 degree angle, then found the second position, it should exactly determ,ine the trisection of 180 degrees. It did. Entonces, adding the third segment should exactly trisect 270 degrees. It did. Obviously, adding the last should be exactly at the starting point, at 0/360 degrees. If there was any inconsistency, it would be nultiplied 4 times, and should be obvious. It did. Exactly. So! We have now established that it works on small angles, and on 360 degrees, It also works on anything between. Now you can argue it all you like. I have published the method and the proof.