Trisection of angles-similarly

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Re: Trisection of angles-similarly

Post by JO 753 » Wed Dec 28, 2011 10:28 pm

Yes, its better to call that point C.

The way I draw this, I start with a horizontal line and the point on the left, which I hav been thinking uv az C duznt hav to be associated with the radius uv SRKL1. Sorry for all the sloppy discriptionz and improper terminology.

By 'the top uv SRKL4' I mean the top intersection uv SRKL4 and a line perpendicular to CD from the center uv SRKL4.

Believe it or not, I found a slitely different method that seemz to be even closer.

My computer wuz barely able to zoom in far enuf to see a tiny difference between the computer generated 15 deg. point on line CD and the line I made that crossez it.

Then it froze up & I had to force the program to shut down.

Trying out the method on a 27 degree angle today, I found that both AG- and AG+ were above the computer generated 9 degree line; so both were actually AG- . But the line extended frum R still crossed CD in ALMOST the rite place.

I figured the 2nd new line, LM, shoud cross UV a little further down, so now it starts at the bottom of SRKL1.

I zoomed in again on the rezulting line segment R and the comp locked up before I coud see any deviation. I tried to zoom back out but it wuz stuck. I left it for about 20 minutes and it had extracated itself finally. I'm going to try to zoom in a lot slower wen I get real close.

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Re: Trisection of angles-similarly

Post by JO 753 » Sat Jan 07, 2012 6:02 pm

I found that the displayed decimal places can be chosen in the C.a.R app.

The 60 degree trisection turns out to be 19.9999999927 degrees and its the first 'Z' line. Too close for my computer to do the refinement step. All the other angles Ive tryed are similarly close.

Im thinking that to be so consistently close over the whole range meanz that therez sum fundamental concept involved that will enable an exact trisection. I'm not the guy whoz likely to figyr that out; all Im doing iz finding coincidental points and srklz. I may still find a way to perfect it without having to learn trig!

Herez the webpage I made for my little project: TRiSeK

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Re: Trisection of angles-similarly

Post by Harte » Sat Jan 07, 2012 7:53 pm

JO 753 wrote:
Im thinking that to be so consistently close over the whole range meanz that therez sum fundamental concept involved that will enable an exact trisection.


What it actually means is that there is some fundamental process that ensures you can't do it.

It's called "constructability," as was pointed out earlier.

Some specific angles can be trisected. But not just any angle in general.

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Re: Trisection of angles-similarly

Post by JO 753 » Sat Jan 07, 2012 8:11 pm

Sorta, maybe.

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Re: Trisection of angles-similarly

Post by xouper » Sun Jan 08, 2012 3:50 am

JO 753 wrote:Sorta, maybe.

On the one hand, I applaud and encourage your enthusiasm and curiosity as this will lead you to learn more about geometry. Regardless the outcome, you will know more than when you started. I see that as a useful result of your efforts.

On the other hand, I don't want to encourage a false hope that you can actually accomplish the trisection of the angle.

Let me tell you a story about another puzzle. Suppose you want to find whole numbers M and N such that M divided by N equals the square root of two. You can try various values for M and N and you may find that you can get closer and closer to the actual square root of two. For example:

17 / 12 is correct to 2 decimal places.
577 / 408 is correct to 5 decimal places.
665857 / 470832 is correct to 11 decimal places.

From that you might suspect that it will only be a matter of time before you stumble upon the correct M / N that equals the square root of two with no error. Except it has already been proven that no such whole numbers can be found. You can get as close as you like to hundreds of decimal places, but you can never find values for M and N such that M / N exactly equals sqrt(2).

http://en.wikipedia.org/wiki/Hippasus
http://en.wikipedia.org/wiki/Square_root_of_2

Likewise for the trisection of the angle. You can get as close as you like to as many decimal places you like, but you will never get the error down to zero, which is required by the original puzzle.

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Re: Trisection of angles-similarly

Post by xouper » Sun Jan 08, 2012 3:54 am

JO 753 wrote:Herez the webpage I made for my little project: TRiSeK

Aha!! There is evidence on that website that you DO know how to write in English. So why do you persist in annoying us here on this forum with your non-English writing? Really, it is very annoying.

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Re: Trisection of angles-similarly

Post by Gord » Sun Jan 08, 2012 8:24 am

xouper wrote:Let me tell you a story about another puzzle.

Good analogy. Or maybe "analogy" isn't close enough; good example, then.
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Re: Trisection of angles-similarly

Post by JO 753 » Sun Jan 08, 2012 12:39 pm

Good analogy, but I'm not 100% convinced that it applies.

I know how exasperatingly ignorant that seems. You know you're right, and even though I know far less than you about the math, I keep working on it.

Sorry about the irritation. It's the cement in your head crumbling.

I'll make a deal with you. I'll write basicly perfect English, aside from normal typos and a few words I can't memorize (tommorrow, nesessary) when conversing with you. BUT! If I ever come up with a true trisection procedure, you have to learn, use and help promote Nooalf.

Deal, xouper?

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Re: Trisection of angles-similarly

Post by JO 753 » Wed Jan 18, 2012 4:46 pm

HA! Not 100% sure that I wont do it!

I've updated the TRiSeK page.

Now you can see & play with the CaR constructions. My fave iz MQVUBL.

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Re: Trisection of angles-similarly

Post by xouper » Wed Jan 18, 2012 9:35 pm

JO 753 wrote:Mathematicians can still claim that the angle is not being perfectly trisected. But if it is not possible to measure the deviation, what does that mean? Better computers and more expensive software can probably find the error and refine the angle many more times than my setup can. I'm still experimenting here - coming up with refinements and variations on this proceedure and completely new ideas. Joe also occasionally sends me a new idea to test, and who knows how many young wippersnapper trigonometry savants are out there who could find an exact method. Because I'm not amazingly smart and yet have come so close, I suspect that it can be done.

I have already addressed those issues in post #35 and #45.

viewtopic.php?p=266169#p266169
viewtopic.php?p=267057#p267057

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Re: Trisection of angles-similarly

Post by JO 753 » Wed Jan 18, 2012 10:01 pm

And yet, you didnt take the bet.

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Re: Trisection of angles-similarly

Post by xouper » Wed Jan 18, 2012 10:44 pm

:roll:

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Re: Trisection of angles-similarly

Post by JO 753 » Tue Jan 24, 2012 7:41 am

BOK BOK BOKBOK

BOK BOK BOKBOK

BOK BOK BOK!

BOK BOK BOKBOK!

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Re: Trisection of angles-similarly

Post by xouper » Tue Jan 24, 2012 8:33 am

I've been trying to be nice. Don't ruin that.

This guy might be interested in seeing your results.
http://en.wikipedia.org/wiki/Underwood_Dudley

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Re: Trisection of angles-similarly

Post by JO 753 » Tue Jan 24, 2012 12:29 pm

Thanks for the link. I'll hav to get that book.

Frum juj Posner: "A crank is a person inexplicably obsessed by an obviously unsound idea—a person with a bee in his bonnet. To call a person a crank is to say that because of some quirk of temperament he is wasting his time pursuing a line of thought that is plainly without merit or promise."

Nicely worded, but I gess I dont qualify since my obsession iz explicable and the 'line uv thot' iz not plainly without merit or promis.

I gess you alredy suspect I may hav produced a trisection method.

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Re: Trisection of angles-similarly

Post by xouper » Tue Jan 24, 2012 1:52 pm

JO 753 wrote:Thanks for the link. I'll hav to get that book.

Frum juj Posner: "A crank is a person inexplicably obsessed by an obviously unsound idea—a person with a bee in his bonnet. To call a person a crank is to say that because of some quirk of temperament he is wasting his time pursuing a line of thought that is plainly without merit or promise."

Nicely worded, but I gess I dont qualify since my obsession iz explicable and the 'line uv thot' iz not plainly without merit or promis.

Sorry, but trying to trisect an angle with only compass and straightedge is an idea without merit or promise. It cannot be done. You have not done it. Nor will you ever do it. You are not yet a crank, but you seem to be going in that direction. I think it's great that you are exploring this issue and trying things. That's an excellent way to learn more about geometry and mathematics. But I would advise caution against crossing the line into full crankery.

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Re: Trisection of angles-similarly

Post by fromthehills » Tue Jan 24, 2012 3:17 pm

JO 753 wrote:HA! Not 100% sure that I wont do it!

I've updated the TRiSeK page.

Now you can see & play with the CaR constructions. My fave iz MQVUBL.


I got
Not Found

Sorry, the requested URL /TRiSeKTOTRoN.avi was not found on this server.
from clicking on the photo in your site.

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Re: Trisection of angles-similarly

Post by fromthehills » Tue Jan 24, 2012 3:26 pm

But hey, I started taking pre- Algebra through the Khan Academy. I plan on working up through Trig and Calc so I can understand physics. Pre algebra was my highest math course in high school, but that was 23 years ago. I do some sort of math as a carpenter using a tape measure to find arcs and angles and square, but I don't know what it is, I just know it works. Some I picked up from other carpenters, and some I figured out on my own.

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Re: Trisection of angles-similarly

Post by xouper » Tue Jan 24, 2012 3:55 pm

In carpentry (and drafting), the easiest and fastest way to trisect an angle is to use a protractor.

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Re: Trisection of angles-similarly

Post by JO 753 » Wed Jan 25, 2012 1:34 am

Sorry about that, From. This interweb thingy needz a few more hourz uv development work. Stuff works. Then it duznt. I'll try to fix it later.

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Re: Trisection of angles-similarly

Post by Gord » Wed Jan 25, 2012 4:36 am

I blame SOPA.
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Re: Trisection of angles-similarly

Post by JO 753 » Wed Jan 25, 2012 5:12 am

.AVI had reverted to .avi sumtime during an update. It will play now. Unfortunately, the Canon video editing software duznt hav anything to make it smaller aside frum chopping off chunks, so it playz a little choppy frum being too big.

And I cant get Joe Keatingz new thing to load up.

Anyway, the TRiSeK V4 iz still not dun, but I hav the shortcut version there. Its currently only good to about 13 decimal placez, but its simpler than the V3.

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Re: Trisection of angles-similarly

Post by fromthehills » Wed Jan 25, 2012 5:59 am

xouper wrote:In carpentry (and drafting), the easiest and fastest way to trisect an angle is to use a protractor.


I honestly don't know about trisecting an angle. The last time we talked about this, I thought I knew what was going on, I did the work with a framing square, then realized I was so far off base that it didn't relate. But I do understand that what I do with a tape measure, with a larger measurement, is what one does with a protractor. I know the concept is the same, I just don't know the principles. If that makes sense at all. Alas, I build stuff, the math that comes into play makes sense to me. As I mentioned, I'm starting with what you got in 8th grade, and that {!#%@} is hard for me.

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Re: Trisection of angles-similarly

Post by JO 753 » Wed Jan 25, 2012 4:45 pm

I got Joez new thing to work now.

Sumthingz goofy with my comp. Sumtimez it will hav 14.9999999999999 for the trisection uv 45 and later show 15. You will notice in the V4USiND that it showz up az perfect.

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Re: Trisection of angles-similarly

Post by xouper » Wed Jan 25, 2012 7:17 pm

JO 753 wrote:I got Joez new thing to work now.

Sumthingz goofy with my comp. Sumtimez it will hav 14.9999999999999 for the trisection uv 45 and later show 15. You will notice in the V4USiND that it showz up az perfect.

If it shows up as perfect, that is due to aliasing errors in the graphics, not because the angle was perfectly trisected by your method.

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Re: Trisection of angles-similarly

Post by JO 753 » Wed Jan 25, 2012 9:38 pm

I mean the number it showz. I gess its too close for the software to clearly decide.

I just updated USiNDaNGL, wich iz V3, to show the angle and it alwayz iz off by sum billionths or millionths uv a degree. (rite klik on the big angle to change it in the edit box)

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Re: Trisection of angles-similarly

Post by xouper » Thu Jan 26, 2012 4:26 am

If the error is larger than zero, it is not a perfect trisection and does not qualify as a solution to the problem.

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Re: Trisection of angles-similarly

Post by Tom Cara » Sun Jan 29, 2012 7:08 am

xouper wrote:If the error is larger than zero, it is not a perfect trisection and does not qualify as a solution to the problem.


Just a quick query: Is this about software approximations or geometry?
Is it saying the diagram geometrically does not trisect the chance angle?

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Re: Trisection of angles-similarly

Post by xouper » Sun Jan 29, 2012 11:41 am

Tom Cara wrote:
xouper wrote:If the error is larger than zero, it is not a perfect trisection and does not qualify as a solution to the problem.

Just a quick query: Is this about software approximations or geometry?

The original problem is about geometry. See for example:
http://en.wikipedia.org/wiki/Angle_trisection

If the problem were about approximations, then it is simpler and faster to use a protractor.

Tom Cara wrote:Is it saying the diagram geometrically does not trisect the chance angle?

Correct, that is what I am saying. Jo's method does not do a perfect geometric trisection of all angles.

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Re: Trisection of angles-similarly

Post by JO 753 » Sun Jan 29, 2012 5:12 pm

Joe wuz asking about hiz new trisector. It duz the same thing hiz frst wun duz in a completely different way. It iz perfect, but its not a given angle.

An amazing thing about the CaR program iz that there duznt seem to be a limit to how big you can go. You can zoom out so far that your construction turnz into a dot & then pan all over to see where the linez go.

This enablez a test to see if an angle iz off. Even tho it will only show 16 decimal placez maximum on anglez, you can asine (HAHA! spelling 'asign' in a slitely more sensibl way makes a pun here!) a specific test angle and go reeeeeelly far away to see if your angle divergez frum it. With the V4 at 45 deg., I used a radius frum the A point at 1,4142 kilometerz* away and coud barely see a tiny sliver uv gap wen zoomed az far in az it will go.

Uv course, this assumez the specified angle iz perfect, so I am wondering how it calculates and creates anglz. I hav found discrepensiez, so its not a certain thing. If you draw a line parallel to your final line, for example, it will measure off by about 1.2 billionths degree.


*The final line in the V4 iz duz not cross thru the A point, so I did the softwarez equivelent uv seting the compass and moving it to a new place. I drew a perpendicular line 1000 kilometerz away on line CD and zoomed in on the intersection with the final trisek line and put the circle there.

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Re: Trisection of angles-similarly

Post by Gord » Sun Jan 29, 2012 5:22 pm

JO 753 wrote:Joe wuz asking about hiz new trisector.

I thought you were Joe. :scratch:
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Re: Trisection of angles-similarly

Post by JO 753 » Sun Jan 29, 2012 6:02 pm

No! Joe iz Tom Cara! I'm JO! I dont know who Jo iz. Probably a hot co-ed/stripper in xouper'z advanced trig class and he'z fantasizing that I'm her. (assuming he'z a math prof at a college)

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Re: Trisection of angles-similarly

Post by xouper » Sun Jan 29, 2012 8:24 pm

JO 753 wrote:I'm JO! I dont know who Jo iz.

My apologies. Wherever I typed "Jo", I meant "JO". Sorry if that confused anyone. In the future I shall type it with the proper capitalization.

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Re: Trisection of angles-similarly

Post by Tom Cara » Mon Jan 30, 2012 4:48 am

xouper wrote:
Tom Cara wrote:Is it saying the diagram geometrically does not trisect the chance angle?

Correct, that is what I am saying. Joe's method does not do a perfect geometric trisection of all angles.[/quote]

Please explain the error in Diagram -1 at:
< http://users.tpg.com.au/musodata/trisec ... _angle.htm >.
Tom.

( I use the name 'Tom Cara' because when I tried to register my own, it was refused.
'Tom Cara' here means Joe Keating as at the above www-link.)

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Re: Trisection of angles-similarly

Post by JO 753 » Mon Jan 30, 2012 5:22 am

Why 'Tom Cara'?

Funny coincidence - Peter Griffin rode in a boomarang on tonites Family Guy.

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Re: Trisection of angles-similarly

Post by xouper » Mon Jan 30, 2012 10:59 am

Tom Cara wrote:
xouper wrote:
Tom Cara wrote:Is it saying the diagram geometrically does not trisect the chance angle?

Correct, that is what I am saying. JO's method does not do a perfect geometric trisection of all angles.

Please explain the error in Diagram -1 at:
< http://users.tpg.com.au/musodata/trisec ... _angle.htm >.
Tom.

Your construction method is backwards. You construct angle HIJ from previously known points, and thus angle HIJ is not an arbitrary angle. This violates the conditions of the original puzzle.

If you want to trisect any acute angle HIJ, you must show how to construct the other points starting from only the points H, I, and J.

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Re: Trisection of angles-similarly

Post by Gord » Mon Jan 30, 2012 11:39 am

JO 753 wrote:Probably a hot co-ed/stripper in xouper'z advanced trig class and he'z fantasizing that I'm her.

No, that was me.

(Stop reading my mind before you stumble on "things best left unstumbled-on".)
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Re: Trisection of angles-similarly

Post by Tom Cara » Tue Jan 31, 2012 12:37 am

Please explain the error in Diagram -1 at:
< http://users.tpg.com.au/musodata/trisec ... _angle.htm >.
Tom. [/quote]

xouper replied - post 76:
Your construction method is backwards. You construct angle HIJ from previously known points, and thus angle HIJ is not an arbitrary angle. This violates the conditions of the original puzzle.
If you want to trisect any acute angle HIJ, you must show how to construct the other points starting from only the points H, I, and J.[/quote]

The link explains the diagram is for a 'chance' angle, not a 'given' angle.
Regardless of which point or line comes first, there is no elementary geometrical error in the model, otherwise it would not work.
The point behind the diagram is the question: Can a 'given' angle, in the context of the true trisection problem, be inserted within the chance angle automatic trisecting model, employing only "an unmarked straightedge and compass"?

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Re: Trisection of angles-similarly

Post by xouper » Tue Jan 31, 2012 7:55 am

Tom Cara wrote:The link explains the diagram is for a 'chance' angle, not a 'given' angle.

Word games won't help you here.

The original puzzle says for any given arbitrary angle, trisect it using only compass and straightedge.

That means that I give you an angle and then you trisect it. It does not mean you get to construct the angle from a set of preexisting points, and then trisect THAT angle. You are not allowed to have a set of preexisting points in addition to your angle. You must start with only the angle.

And your method does not do that.

If you still disagree, then start with points H, I, and J and show us how to construct points C and D. In other words, once you have built angle HIJ, erase all the points not on the angle and then reconstruct your method starting from only points H, I, and J. Only then will you have trisected the angle HIJ.

Tom Cara wrote:Regardless of which point or line comes first, there is no elementary geometrical error in the model, otherwise it would not work.

That's not correct. You are only allowed to start with the angle to be trisected. You are not allowed to use any points not on the angle that were used to construct the angle. Otherwise, I can trisect any "chance" angle using a much simpler method than you use.

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Re: Trisection of angles-similarly

Post by Tom Cara » Tue Jan 31, 2012 10:34 am

xouper wrote:
Tom Cara wrote:The link explains the diagram is for a 'chance' angle, not a 'given' angle.

"Word games won't help you here."

Correct: Word games won't help you here.