tri-sected angle explained...

[Days]

tri-sected angle explained...

If you begin with the tools, you can not get there. But if you reproduce the angle itself, and set the angle three times in itself, it has to tri-sect the angle. That's absolute, the question isn't whether reproducing the angle 3 times and setting it within itself tri-sects - that absolutely tri-sects - the question is; did you reproduce the angle 3 times and did you set the 3 angles within itself?

Now, remember, we are talking about the angle, not the hypotenuse.

from my blog: (posted 10 years ago)

I still have this drawing somewhere in a desk drawer. This image was made with my wife's old cannon scanner, long since trashed, cuz the technology gets old. But I still have the pencil on paper... can you see where the angle is reproduced 3 times within itself? If you look for bi-section, you will think you are seeing bi-section, but it isn't there, the key is to look for the reproduction of the angle itself and the setting of that angle within itself 3 times; think angle, what is the angle? The angle is the arc produced by the compass intersecting the 2 straight lines that created the original angle; think of that arc, look for the reproduction of that arc 3 times... can you see it?

 

[Days]

Nobody sees it.

I'll tell you how to look for the arc, how the angle was tri-sected. Remember, the theory that this is impossible to do was based upon geometry; it is impossible to triple a cube using just a straight edge and a compass... but I don't use geometry, I use the mechanic method, I looked at what is there and I figured out how to reproduce it with the tools given. When I was in high school I did it with geometry, what I did then was make three parallel lines for each straight line and kept reproducing the angle on top of itself in a series. What I do here is move out each line of the original angle and keep reproducing the arc, until I get three arcs out. At that point, I reproduce the arc off the one line and off the other, what is left in the middle has to be the 3rd arc, now, can you see it?

 

[Days]

Look for these arcs...

 

[Days]

View attachment 39196
Look for these arcs...

Now, I'm going to show you the middle arc; the bi-section of the angle reproduces the original angle exactly in the middle of the third layer - this is easier to see than it is to describe:


okay, I'm going to add more highlighter...


... even the biggest moron, liar of the fray can not deny that I did reproduce the exact angle in the middle of the the 3rd layer; what did that guy say 12 years ago on BotF? Remember? The middle angle was slightly smaller than the outside angles... remember that? And that's the same thing they told me when I did it a completely different way in high school; but that is just a total bogus lie; remember how they told that lie? You can't see it with your eyes but we measured it with high tech measuring instruments and it it is this tiniest fraction smaller; LIARS! This was the exact same scan that I posted on BotF, I just didn't argue with the Liars, cuz I was so used to their lying all the time. But look at this, don't you think I couldn't have pointed it out 12 years ago? I knew they were lying, but I went along with it because I also knew that if I proved it was the exact same angle geometrically, then they would steal it from me. So, I went along with their lie and said, oh, yeah, I see where it is impossible to do.... but look at it, folks, it was tri-sected PERFECTLY, geometrically, all along.... and so was the tri-section that I did in high school pre-calculus (analysis) class, but they told me the same lie, they make up those lies to protect their religion, or whatever it is that makes them feel superior to the rest of us. There's a word for that type of religion; higher learning... or more simply: snobbery.

 

[Days]

Now, I'm going to show you the middle arc; the bi-section of the angle reproduces the original angle exactly in the middle of the third layer - this is easier to see than it is to describe:

View attachment 39201
okay, I'm going to add more highlighter...

View attachment 39202
... even the biggest moron, liar of the fray can not deny that I did reproduce the exact angle in the middle of the the 3rd layer; what did that guy say 12 years ago on BotF? Remember? The middle angle was slightly smaller than the outside angles... remember that? And that's the same thing they told me when I did it a completely different way in high school; but that is just a total bogus lie; remember how they told that lie? You can't see it with your eyes but we measured it with high tech measuring instruments and it it is this tiniest fraction smaller; LIARS! This was the exact same scan that I posted on BotF, I just didn't argue with the Liars, cuz I was so used to their lying all the time. But look at this, don't you think i couldn't have pointed it out 12 years ago? I knew they were lying, but I went along with it because I also knew that if I proved it was the exact same angle geometrically, then they would steal it from me. So, I went along with tyheir lie and said, oh, yeah, I see where it is impossible to do.... but look at it, folks, it was tri-sected PERFECTLY, geometrically, all along.... so was the tri-section I did in high school pre-calculus class, but they told me the same lie, they make up those lies to protect their religion, or whatever it is that makes them feel superior to the rest of us. There's a word for that type of religion; higher learning... or more simply: snobbery.

Now, just for the fun of it, I'm going to explain this geometrically; if the angle is reproduced exactly as the original - which it obviously is - and if it is exactly in the middle of the original angle - which it has to be , because it was created by bi-secting the original angle - than it is all by itself a proof of tri-section because it is exactly 1/3 of the angle and it is located dead center, so the two angles on each side of it have to be equal due to the middle angle being exactly in the middle and if the middle angle is exactly 1/3 of the original angle, then the two equal angles on each side of it have to be 1/3 also.

So it is a proof; the angle was trisected.

 

[Days]

2000 years is a long time to be stumped...

Euclid's Big Problem - Numberphile

 

[Days]

globetrotter extra for the hard core cynics (you know who you are)!!

Did the drawing reproduce the original angle and set it within itself 3 times?


can you see it now?

yep, the bloody angle was tri-sected all along, and I knew it was 12 years ago. But heck, mankind was stumped for 2000 years, what's 12 more years gonna matter?

What I wish I could recover was the 6 part formula that I came up with in 6th grade for the formula of a circle... without using Pi. My teacher didnot grasp the importance of that formula, all he cared about was teaching the day's lesson; how to calculate the area of a circle (using Pi... he taught us Pi).

 

[Days]

 

[Days]

Those don't look like the exact same arcs reproduced over and over, but they are.

 

[Days]

View attachment 39206

Those don't look like the exact same arcs reproduced over and over, but they are.

So, let's analyze the Lie they told and see why it was a Lie. They said the middle angle in the 3rd tier was different; slightly larger or slightly smaller, but not the same as the two angles beside it. Now, think about this; isn't that angle exactly the same as the two angles beside it? Aren't all 6 angles exactly the same angle? They are all exact copies of the original angle created by randomly drawing two lines with a straight edge. So, they told a lie... they knew they were lying, they created this lie just to lie, that's what liars do, they fabricate lies.

Does the second row of angles bisect the angle? Of course we know it does. Then does the third row of angles tri-sect the angle? It is an exact repeat of the second row. If I had done another row of circles, it would have divided the angle into four equal angles; and no one thinks that is impossible, so no one would dispute it, but by continuing the progression and having it repeat equal angles and result in equal division of the angle, it proves that the third row also divided the angle equally, because the 4th row would be based upon the 3rd row, the same as the 3rd row was based upon the 2nd row, the same as the 2nd row was an equal division of the original angle. You could continue the division forever because the method works. So you can divide the angle into equal angles 5 times, 7 times, 9 times, 11 times, 13 times, etc.

If you remember how this happened, I was talking about my experience in analysis, three decades earlier (now it's been 4 decades) on a friday and I said I would try to remember how to do it over the weekend, and I couldn't remember how I did it, but I came up with this method instead. Now, when I showed my teacher in high school (it is part of the course study in analysis) he took the method to university profs and a couple weeks later, he told me they had measured the angles with very exact instruments and the middle angle was slightly different... exactly what someone responded on the fray to this method. But now we have analyzed that Lie and proven it false, because if nothing else; all the angles are exactly the same. They are all exact reproductions of the original angle I produced with the very first arc I swept with my compass.

Not only is the scan in the top post the exact same scan that I posted on the fray a dozen years back; I then used two printouts of that scan that I found in my drawer. I had to go over the circles with a compass to get them to show up when I scanned them again for this thread, you can see how the circles didn't show up on the first printout I worked with... I can see the circles on the paper, but after I scan it into the computer, you can't see them; so I took the second printout and darkened all the circles by going over them with my compass, so you could compare the two. I then used my color pens to hand draw in the arcs to show you where they were in the drawing. So all of this thread was using the exact same original scan that I posted on the fray 12 years ago; just in case the weasel that lied back then tries to use that as an out; he was responding to the scan in the top post; I uploaded the scan to my blog ten years ago and then downloaded it here; it is the same scan I made to post on the fray.

 

[Days]

I made a copy of the 2nd printout and you can see how the circles fade when I scan a 2nd generation of graphite pencil; but where I inked over the arcs, that still shows up. Then i knocked out a bunch of parallel lines... in high school I did it the right way with a compass, but here I just slapped them off with a ruler, because here I had the intersection of the circles to guide me where the lines go. The whole reason I made whole circles was to show where the parellel lines are formed... when you keep using the original arc over and over, which i obviously did. So, I did make the parallel lines with the compass, I just did it in two steps; first I did all the compass circles then i joined the intersections with a straight edge; and voila... parallel lines. Even if my work is sloppy, the lines are geometrically parallel.

So here you see the method I used in high school produced the same results; it reproduced the original angle over and over. This is another proof that they were lying when they said one of the angles had a slightly different degree from the other angles; geometrically impossible for that to have happened, all the angles are identical. They were formed with parallel lines to the original angle... I knew they were lying to me in high school also, because I was staring at the proof that the angles were identical. There are triangles, rhombuses, and arcs all perfectly reproduced over and over, and you can continue to reproduce them into infinity; so I used the original angle as an unit, and then reproduced it to form 3 units ... all exactly equal to each other. That was the method I used to tri-sect and then they respond to the method and say the units were not equal to each other... I was like, "the hell you say! That's exactly what the method did; reproduce identical units!" My teacher just looked at me stupid, because he could see through the Lie also. whatever.

can you see it now?

 

[Days]

Now, I'm going to do the third set of parallel lines; forming the triangles and completing the grid...




Now, pay attention to these 3 triangles...



identical triangles; proving the angle between all 3 tri-section lines are equal.

That's a mathematical proof, whether you can see it or not; the tri-section is geometrically proven.

where's my money?

 

[Days]

Now, I'm going to do the third set of parallel lines; forming the triangles and completing the grid...

View attachment 39211


Now, pay attention to these 3 triangles...

View attachment 39212

identical triangles; proving the angle between all 3 tri-section lines are equal.

That's a mathematical proof, whether you can see it or not; the tri-section is geometrically proven.

where's my money?

so if we rotate the top and bottom triangles so that they point down the center of their angle the same way the center triangle does... their corners would just barely edge out, hence, the center slice of the tri-section is slightly smaller than the two outer angles; so the establishment had it correct and I was wrong.

sigh.

this tri-sected the hypotenuse, not the angle.

 

[Days]

the moral of the story is this:

non-euclidean geometry is false.

 

[Days]

So, hey, now that I finally figured out why the center angle is slightly smaller, maybe i can still pull off the tri-section. Nobody ever explained to me that it was a tri-section of the hypotenuse instead of the angle. If the establishment would actually teach you the truth, maybe you could resolve all these riddles, right? But they keep you in the dark, they don't teach you, and you don't know why they say what they say... until you figure out the whole planet on your own, in your old age, and then your eyes are so bad, you can't see the lines on the paper you are trying to make with a straight edge and a compass.

(expletive)

Don't go away yet, I'm looking at this and wondering if it still can't be done. Got an idea here... would if I took my compass and swiung the same arc as all the arcs from the right corner of the base line; 3 compass arcs over. Now use your compass to measure the original arc and swing that arc from the right corner, creating the same angle in the opposite direction. Now, tri-sect that hypotenuse. Did we just align those triangles down the middle and really tri-sect the angle???

 

[Days]

I'm learning to use the contrast on the edit feature of the windows 10 scan software...



so here you see I swung the arcs from the right corner and created the same angle going back against itself. Check out the intersection of the original angle: exactly at the intersection of the second arc; I don't know if that works every time or just happened on this particular random angle?

At any rate, my idea of trisecting this hypotenuse won't tri-sect the angle, obviously.

But it seems I have something to work with here, give me a weekend, okay? Maybe it will come to me.

 

[Days]

I'm learning to use the contrast on the edit feature of the windows 10 scan software...

View attachment 39222

so here you see I swung the arcs from the right corner and created the same angle going back against itself. Check out the intersection of the original angle: exactly at the intersection of the second arc; I don't know if that works every time or just happened on this particular random angle?

At any rate, my idea of trisecting this hypotenuse won't tri-sect the angle, obviously.

But it seems I have something to work with here, give me a weekend, okay? Maybe it will come to me.

first step to solving 2000 year old riddles:

make a fresh pot of coffee

... it's brewing

 

[Days]

oh yes, the coffee is done, man, that first sip of the fresh brewed pot tastes good!

So, let's look at this together. What has to be done? The answer is to work with the middle arc; we need to adjust the radius at which we make the arc until it matches the two outside arcs... with me? So if the middle arc is too small, we need to bring it in toward the center of the arc until it grows large enough to match the angle of the two outside angles. The two outside angles are equal, they remain equal as long as the center arc remains in the center.

So first off, let's draw a center line with our straight edge and then see if we can figure out a way to determine exactly where the middle arc needs to be located on that center line...

let's do the center line in green ink...

another sip of coffee...




okay look at the 3rd center arc (in blue) and here's the battle; we need to pull that arc in towards the center, staying on the green center line.

My first great idea is this; let's use the hypotenuse and strike back the arc down the green centerline, then draw the arc again; that will pull it in a slight amount, maybe too much?
Nope, it looks pretty good, people. The frickin' paper tore on me, so I couldn't finish the small circles that reproduce the arc, but you can see their placement, remember, it's the method, does the method work?

So I tried to run the new tri-section lines in blue - but they practically run exactly on top of the original method lines; which is where they should be.



impossible to see, I know, but think about the method explained... does that tri-sect the angle? It sure as heck does to the human eye, but so did the original method, this method should be even closer, whether it is geometrically perfect or not, it probably meets the test of being within the accepted range for an accurate measurement (some tiny degree of error accepted) ... but where are the mathematical authorities? This may in fact have tri-sected the angle. I know I have to do it all over from scratch so we can see the method... arrrgh, first, more coffee.

 

[Days]

Well, that's my new tri-section method; it may take me awhile to draw it up fresh, but the method is there; I've got to get back to my work on the hoist.

 

[Days]

okay, so the answer to the top post was this:

But if you reproduce the angle itself, and set the angle three times in itself, it has to tri-sect the angle. That's absolute, the question isn't whether reproducing the angle 3 times and setting it within itself tri-sects - that absolutely tri-sects - the question is; did you reproduce the angle 3 times and did you set the 3 angles within itself?

Now, remember, we are talking about the angle, not the hypotenuse.

the question is; did you reproduce the angle 3 times
yes

... and did you set the 3 angles within itself?
no

Now, remember, we are talking about the angle, not the hypotenuse.
man, did that ever come back to bite me on the ass.

But we adjusted the setting of the angles within itself... could the final method actually solve this 2000 year old riddle? Maybe we have to resurrect Euclid to find out for sure.