To any person reading this: In a perfect system (in mathemathics, not in real life on paper), having a perfect compass and a perfect ruler, and taking all the measurings perfectly, trisecting a random angle is not possible. Don't waste your time watching this video or trying to argue with this guy.

@emery5581

4 жыл бұрын

I wonder if he is really only trying to get hits on his presentation. Can he be as unintelligent as to believe in the full accuracy of his method, without proof?

@SledgerFromTDS.

2 жыл бұрын

@@emery5581 Well I need to Share My own Opinion on this Matter,

If done precisely....it isn't trisected. The two outer angles are the same. The middle one is -smaller- larger. [Editted this correction.]. It is close, though, so measuring it is unlikely to reveal the error. Calculating it, will.

@zacwilliams6740

6 жыл бұрын

The method will trisect the angle perfectly. Of course the math will always be precise with the inner circles radius set to the intersecting lines. “Pascal theorem” these circles will transfer the trisected line into the correct degrees where they intersect the arc between the lines. The difference in the radius’s is the golden ratio. With this method you can divided the Unite circle into any prime number as well. Have you tried this method with a compass and straight edge?

@Mephistahpheles

6 жыл бұрын

Starting at 3:12, you have a trisected line segment¹. Suppose that's "x", so the line segment is a total length of 3x. The arc between those same two points MUST be longer (3x + a). Since you 'copy' that length 'x' (at 3:29 to 3:50) on both sides, the arc is divided into 3 UNEQUAL sub-arcs: x, x and x + a. Not trisected, as desired. ¹ Assumed to be true. I didn't verify. ² I did err in my original post.....the middle angle is larger, not smaller. ³ Didn't examine (just watched) beyond the first angle. The algorithm shouldn't have so many exceptions/variations. I'm guessing this is a result of the error above becoming too obvious, necessitating an alternative that appears to work. ⁴ Trisecting an angle (in the general case...a few specific angles can be done) has been proven to be impossible. Granted, the proof might be wrong. :-)

@zacwilliams6740

6 жыл бұрын

Excuse me, in the video when I said “if done precise” was because my line was off. Didn’t want too reshoot video. The reason for the variations becomes obvious when you see the mechanics in my second proof titled “Riemann hypothesis”. If you want to see a precise execution of a 60 degree trisection, supposedly impossible, see “how to trisect any angle 60 degrees” by alien jester

@kxe6610

5 жыл бұрын

@@zacwilliams6740 given a line and all the possible circle arcs which transcribe that line, none have their length equal to the length of the original line.

@einsteingonzalez4336

4 жыл бұрын

You're right. That is stated by Pierre Wantzel in 1837. Also, have you ever heard of Galois Theory? This new theory formed by French mathematician Évariste Galois in his teens before his death in 1832 during a duel helped prove the impossibility of constructing cube roots, trisecting any angle, the impossibility of constructing certain polygons, such as the heptagon, and squaring the circle. The 3 problems I mentioned requires solving a cubic, and using a compass and straightedge can solve linear and quadratic equations only. The last problem implies that 𝜋 is not algebraic. The 3 problems require a new constuction called neusis, which is a construction by using a marking a straigtedge so that the marks are two points to create a distance and given a pole with two other curves until the two points on the ruler touch the two curves. Hopefully that explains a lot.

How to approximately trisect an angle *** This is not a precise trisection.

@zacwilliams6740

6 жыл бұрын

This method gives an exact trisection. The video is a quick drawing. I said in the construction when I messed the third circle. The nonagon at the end clearly shows 3 120 degree angles divided into 9 40 degree division perfectly. As is easily duplicated for your self by following the directions.

@emery5581

4 жыл бұрын

@@zacwilliams6740 Nonsense, Zak. You offer no logical proof. Do you understand what proving a theorem means? No disrespect intended, but you must advance your theoretical knowledge of geometry.

@zacwilliams6740

4 жыл бұрын

emery . It’s just presented in a way to be “click bate.” The point is to consider why you can’t. Still one of the most precise estimates on the internet... and if you understand the error of the method you generally are beyond the precision of a protractor

@emery5581

4 жыл бұрын

@@zacwilliams6740 "click bate"??? For what? Are you thinking straight? You have to state that the method is approximate only and come up with the error analysis. But don't just leave it as is. You will deservedly pass for an ignoramus.

@martinmazanek5192

3 жыл бұрын

@@zacwilliams6740 'This method gives an exact trisection' / 'one of the most precise estimates' - pick one, you can't have both. You should be ashamed of misleading so many and lying to the face of others by presenting your estimation as an 'exact trisection'.

This made my day. The truth is out there, I want to believe. If I get smaller paper, thicker pens and squint more, it looks about right.

@zacwilliams6740

5 жыл бұрын

Try Mathematica, accurate to a hundredth of a fraction. Most people are not that accurate by hand... please show me any method that is more accurate with a compass and straight edge...the inverse method will also give you the most accurate prime divisions of a circle beyond 5...

Not a trisection at all. Fundamentally mistaken.

this is in my geometry teacher's curriculum

Don't worry about precision of the drawing. Give me a written proof or disproof that it trisects. Only that will satisfy.

@k12byda5h4

4 жыл бұрын

Use geogebra and disprove it

Wish he would animate what he was doing, using colors, measurements and assign each point and areq a number or letter on a computer screen. Good effort though. That took a lot of thinking built on the minds of the ancients. My dad and I tried to solve this great ancient riddle for years when I was in grade school but it never would be perfect or exactly equal. A circle has infinite angles and sides. Even the circumference of a circle is based on a calculation that uses a number or value (π, pi) that can never be pinned down exactly. And because of that, no one can ever pin down an equal relationship between three angles on the same circle using a compass and a straight edge. Two equal angles, no problem. You can divide anything equally into two or equally into an even amount of segments. Three or an odd number amount, well that's an area where you enter at your own risk, lol.

this is awesome! very funny indeed.

Next video: How to build a perpetuum mobile ;-)

@capjus

2 жыл бұрын

lol :) hehe

@SledgerFromTDS.

2 жыл бұрын

@@capjus Actually I want to have a Conversation with you !

@capjus

2 жыл бұрын

@@SledgerFromTDS. hi, yes? Whats up

@SledgerFromTDS.

2 жыл бұрын

@@capjus What did you think about the Video ? In Your own Opinion

@capjus

2 жыл бұрын

@@SledgerFromTDS. Hi monke, thx for asking me. But why does my opinion matter? Im not so interested into this. Besides, there is a proof that trisecting is generally not possible with few exceptions

Zac: I tried duplicating it on CAD & the two outer angles were identical, but the center one was slightly smaller. It seems that the last step is an approximation, but it's good work regardless.

@zacwilliams6740

5 жыл бұрын

primero dinero, the next step is a squaring the circle problem. The point is it is accurate to the point that it exceeds human error in accuracy. The other video breaks down the accuracy to the point of infinity on CAD when dividing a 6o’ angle into prime divisions. Of coarse the real fun is analyzing the degree of error with trigonometry of prime divisions of the unite circle.

@Daniel-tl5wx

4 жыл бұрын

kzread.info/dash/bejne/iHaWmKlvc8Kfp7g.html

@Daniel-tl5wx

4 жыл бұрын

kzread.info/dash/bejne/iHaWmKlvc8Kfp7g.html

@robertv4076

2 жыл бұрын

@@zacwilliams6740 Are you admitting that your method is only an approximation to trisection?

Merci je retiens votre procédé !! Well done

Brilliant Work out there, So I gave a look at your own Method. In My own Opinion it's good to say the least/ most, But there could be a Small - Big amount of Inaccuracy. It's Good & Nice in terms of Estimations,

lets try guys more

For people watching this take into account that this is not an actual trisection, just an approximation. This is only acceptable if the drawing is small enough Trisecting any arbitrary angle exactly has been rigurously proved impossible At 3:10 you really can't "traspass the trisection of the line into the angle", you are just approximating. Do the math yourself and realise the middle arc is of a different length

@zacwilliams6740

5 жыл бұрын

Wurtt Mapper, it’s always a hundredth of a fraction or less, no matter the measure used miles or nanometers. Then it’s just Zenos paradox, just split hairs.

@wurttmapper2200

5 жыл бұрын

Zac Williams I don't know what you exactly mean, but I think that by Zeno's paradox you are telling me to continue spliting hairs infinitely until at the limit at infinity the arc is exactly trisected. Yes, you could get better approximations each time so it a really good method, but measuring and spliting hairs is sadly not allowed in compass and straightedge problems; also, doing infinite things is by some reason I don't know not allowed in straightedge and compass problems so anything related to Zeno's paradox can't be done. Think that doing infinite things would make every construction trivial, specially the cuadrature of the circle because you could do infinite segments of 3, 1/10, 4/100, 1/1000, 5/10000, 2/100000 ...etc to approximate pi until at infinity you have drawn a line of length pi exactly.

@zacwilliams6740

5 жыл бұрын

Wurtt Mapper, I’m simply making light of the fact that when using compass and straight edge on a standard size sheet of paper, human error is equal to the difference when done on a computer. Then of course you can bisect the difference until it reaches the needed accuracy. The interesting fact comes to light when dividing circles into prime number divisions and analyzing the difference to the Euclidean rendering gives a square fraction of the golden ratio, divided by.5

Some angles can be perfectly geometrically trisected and 2 are already documented in the comments below. This already debunks the validity of the mathematical "proof" that it cannot be done without qualification - the necessary qualification being that 90 degrees (at least) can be trisected with a compass and straight edge.

@SledgerFromTDS.

2 жыл бұрын

Can we talk to each other about this topic ?

Please explain me the procedure in details

THANK U SO MUCH

@redaabakhti768

6 жыл бұрын

lol

use the backside of the ruler to prove it is trisected without marks

If you try the same construction with GeoGobra software one will notice that this very close but not exact. For examples the angles came 17.62, 17.89, 17.62 degrees. But it's good approximation. Thanks for sharing.

@zacwilliams6740

6 жыл бұрын

Joseph Abela the funny thing is the more you expand the decimal the more accurate it becomes. Some software automatically rounds it right on. But nonetheless it becomes a “squaring the circle” problem. This problem is rooted in the base system of ten and the unit circle defined within a Cartesian plane. However when done with a compass and straight edge dividing a circle into any number of segments including primes, it will fall on all points exactly.

@schilduin

6 жыл бұрын

Zac Williams it has nothing to do with the base system of ten. When starting off with the points (0,0) and (1,0) in the plane, you can get additional points by adding circles and lines. These additional points are solutions of linear or quadratic equations with the already constructed numbers as coefficients. So any constructed point has to be the solution of such a series of quadratic or linear equations. But for trisected angles, the points are a solution of a cubic equation. Only for some special angles, this cubic equation can be solved with constructable numbers, but in general, solutions of cubic equations can't be solutions of such a series of quadratic and linear equations.

Trisection is 100% possible by use of a ruler and a pair of compass only and therefore any non decimal angle which is divisible by 5 can be accurately be constructed.

@robertv4076

2 жыл бұрын

The rules of construction forbid a ruler and only allow a straightedge. Markings are not allowed.

@SledgerFromTDS.

2 жыл бұрын

@@robertv4076 So I really have to chat with you about Something.

Hey Zac, thanks for the video. It is precise, as you say, and more than good enough to get any sailor home. (Yeah, and I actually got lost at sea once too. All I had to go by was my analog watch and the sun). Ignore your critics. this is actually one of the better methods I've seen. I have a similar idea that I'm testing out this morning (that's why I'm here now - looking to see what others have done). Your critics are young single frustrated males who think their obsession with Mathematical pedantic correctness is a suitable substitute for having an actual friend. They need to get a life and learn how to give credit where it is due. Maybe when they turn 30 they'll start to grow up....? ;-)

@SledgerFromTDS.

2 жыл бұрын

Do you need to have an Conversation between ourselves ?

at the start, you said you would construct a perpendicular bisector. that is an angular bisector. edit: oh, you mean a perpendicular bisector of the angle bisector. my mistake. ignore my comment.

Put the camera in a right way!

Great job for trisecting the line,the rest is not correct.But keep up,geometry is awesome!

@zacwilliams6740

5 жыл бұрын

Mixing mix, try it your self with compass and straight edge, it approximate to a thousand of a fraction, any angle. As far as the line it would be incorrect. You will not find a more precise method for any angle trisection on the internet

@zacwilliams6740

4 жыл бұрын

Obviously you didn’t try the method. Anyone can trisect a line. But you will not find a closer method on the internet. And once done the difference can easily be reduced to the point desired. But no other method will get you less than 1/100 of a fraction to start. But obviously you spoke without knowing considering the trisection of the line would be wrong and that’s easy to do

@zacwilliams6740

4 жыл бұрын

I know it’s not exact, that’s not possible. But if you have seen a more approximate method send me a link.. and you can keep bisecting the difference to the degree of accuracy desired... Zeno,s paradox

@robertv4076

2 жыл бұрын

@@zacwilliams6740 That disclaimer wasn't clear from the video.

54 degree ka bnao

This is a Neusis Construction.

@UCFupkb0V8CCmzkfIixN0V6Q @UCFupkb0V8CCmzkfIixN0V6Q @ D. D'Amato Sorry emery-you are right about Zac's demonstration- but wrong about the mathematical or graphical impossibility. My KZread presentation on Trisecting an angle and Squaring the Circle proves otherwise. Furthermore, my recent book "Trisecting Angles and Other Solutions" (Amazon) demonstrates both drawing and mathematical solutions to all five "insolvable" puzzles presented in Wikipedia. Included in this group is the calculation and drawing Pi as a straight line.

You did more work then needed.... the trisection was already finished once you did two more circles... you honesty just needed to place your trisection lines where the other circles crossed each other... also... you can’t completely trisect an angle unless the angle is divisible by 3. Otherwise the trisection will be off in one or two breaks of the trisection. And to those arguing precise... no ones numbers, math, ideas, or actions are ever completely precise... no one can be perfect.. so take your precise needs and shove them precisely where the sun don’t shine. We are only human after all if you strive to be perfect your in for a nasty “life slap”. Now striving for a challenge to trisect an angle with less than the necessary amount of mathematical moves is just genius. And to those who want to doubt are just mad they never bothered thinking outside of the box or challenge way they were taught to do things. Because in my math book... it lamely stated trisecting an angle was and I quote “impossible”... I broke it into three perfectly, no problem. Same moves with the circles but no extra lines after I just broke the angle and it worked out fine.

@SquirrelASMR

2 жыл бұрын

The point of math proofs are to be exactly precise tho

@SledgerFromTDS.

2 жыл бұрын

@@SquirrelASMR I want to Ask for, Your own Opinions on this (Video).

no se da la trisección

But there is least two ways I can do this. One is draw a arbitrary angle make a ark from the origin and than GUESS with your compass and I guarantee on the second try you trisected the ark precisely, second method again draw a arbitrary angle cut it out and than copy that arbitrary angle, make a arc from the origin making few copies trisect ,quadrisect or do what ever you want. Rules were NOT VIOLATED and we have achieved our goal. AMEN.

you can prove trisection of an arbitrary angle the same way that i can prove on paper with 1. a ruler, 2. a compass, 3. a piece of string that pi is rational and not irrational. Mathematicians have been wrong about this, and i've proved them wrong. I make a diameter of 10cm with my ruler, i then use a compass at 5cm to make a perfect circle of diameter 10. I then take my string and place it around the circle and i cut it 100% exactly the length of the circumference of the circle. I measure the length of the string and then i divide by 10. I know because i can measure the string with a ruler it must be a rational length. So a rational number divided by 10 is obviously a rational number and thus i've just proved to you that pi is rational. now you might say well what if my ruler or my eyes were slightly off, well then i'd say that i could have used a caliper that could measure to the nearest 1/1000 of a millimeter, it would still be a rational number and thus my proof still stands.

@SquirrelASMR

2 жыл бұрын

You're making fun of him right? Measuring a number to a certain number of digits is ways going to be rational for people that don't get the joke.

Contrary to what Galois and Wantzel claimed, it most certainly *is* possible to trisect any arbitrary angle using a compass and an unmarked straightedge. I have discovered a truly marvelous proof of this, which this comment box is too narrow to contain.

@SuperJimmyChanga

2 жыл бұрын

Murrmac's last theorem

You have to prove your drawing is correct by geometry, otherwise it is a joke.

Wasting time ! You better try zeta function rather than trying this one .

YOU MADE IT TOO COMPLICATED. MAYBE I HAVE FORGOTTEN ALL THE GEOMETRICAL CONCEPTS WHICH I HAVE BEEN TAUGHT IN SCHOOL

Fu**ing video quality

not helpful at all

@zacwilliams6740

3 жыл бұрын

Considering trisection of an angel is impossible and this is the most accurate method out there... how much help were you expecting

@UCFupkb0V8CCmzkfIixN0V6Q @UCFupkb0V8CCmzkfIixN0V6Q @ D. D'Amato Sorry emery-you are right about Zac's demonstration- but wrong about the mathematical or graphical impossibility. My KZread presentation on Trisecting an angle and Squaring the Circle proves otherwise. Furthermore, my recent book "Trisecting Angles and Other Solutions" (Amazon) demonstrates both drawing and mathematical solutions to all five "insolvable" puzzles presented in Wikipedia. Included in this group is the calculation and drawing Pi as a straight line.