Trisection of an angle

[A.Pechatnik]

Angle trisection

Probably the most accurate method of dividing any angle into three equal parts. Simple and accurate

[video=youtube;48YSOt5Kiyo]https://www.youtube.com/watch?v=48YSOt5Kiyo[/video]

www.sacredgeom.org

 

[topsquark]

That is a beautiful presentation. It's also wrong. The figures you drew are "Euclidean" in the sense that they can be made with a straightedge and compass. It is impossible to trisect and angle using those tools.

Personally I like using a protractor.

-Dan

 

[JeffM]

That is a beautiful presentation. It's also wrong. The figures you drew are "Euclidean" in the sense that they can be made with a straightedge and compass. It is impossible to trisect and angle using those tools.

Personally I like using a protractor.

-Dan

With a certain level of skill, one can present almost any analysis in a plausible but misleading manner. It is the stock in trade of politicians, lawyers, magicians, and other con men. A bunch of unexplained graphs do not constitute a proof. Furthermore, I am cynical enough to believe as being close to certainty that a proof presented through music and unexplained diagrams is actually known to be false by the presenter.

 

[mmm4444bot]

͏

From wikipedia:

For any nonzero integer N, an a͏ngle of measure ​2π⁄N radians can be divided into n equal parts with straightedge and compass if and only if n is either a power of 2 or is a power of 2 multiplied by the product of one or more distinct Fermat primes, none of which divides N. In the case of trisection (n = 3, which is a Fermat prime), this condition becomes the above-mentioned requirement that N not be divisible by 3.

 

[Dr.Peterson]

Technically, the video probably isn't wrong; it doesn't claim to present an exact trisection. At the end it shows something like this:

\(\displaystyle \phi=88^{\circ}, \phi/3=29.33333...^{\circ}\)
\(\displaystyle <ZNB (\phi/3) = 29.29279...^{\circ}\)

So they are admitting that the construction does not really create a trisection. (That last line, appearing to call the resulting angle \(\displaystyle \phi/3\), is basically a lie, but the rest seems to be honest).

But then, who cares? The construction is perhaps relatively "accurate", but it is also not at all simple. There is no benefit in using a compass and straightedge construction to do something that is not exact; using a real compass, every step adds error. The only benefit in compass and straightedge construction is in theory -- that in principle it does exactly what it claims to do. It doesn't accomplish anything useful. An inexact construction, no matter how close it might be, is utterly worthless.

I should add that a construction isn't really a construction unless it is accompanied by a proof of what it does. There is no way to prove that this is "the most accurate method" (in what sense? compared to what?); and it can't be proved that it is exact, because it is not (and because no such construction can be).

 

[Denis]

A pencil is a writing implement or art medium constructed of a narrow,
solid pigment core inside ... Because the pencil core is still referred to
as "lead", or a "lead", many people have the misconception that the
graphite in the pencil is lead, and ...

...and the fatter the lead is, the easier to trisect an angle

 

[mmm4444bot]

[the video] doesn't claim to present an exact trisection.

The OP makes that claim in their op and on the youtube page.

Probably the most accurate method of dividing any angle into three equal parts. Simple and accurate

---

I agree about comparing "accuracy" of methods; I wondered why the OP claims this method is more accurate than other methods (many mentioned at wikipedia).

 

[Dr.Peterson]

The OP makes that claim in their op and on the youtube page.

---

I agree about comparing "accuracy" of methods; I wondered why the OP claims this method is more accurate than other methods (many mentioned at wikipedia).

Admittedly, when I look up "accurate", all dictionaries define it as "exact". But the OP, in using the phrase "most accurate", makes it a relative term (presumably meaning "close to exact"), and clearly states that it is not exact, if you read that "fine print".

My remark was really meant to point out the inconsistency. I don't think the OP knows what "accurate" or "exact" even means, or why it matters.

 

[Steven G]

Probably the most accurate method of dividing any angle into three equal parts. Simple and accurate

[video=youtube;48YSOt5Kiyo]https://www.youtube.com/watch?v=48YSOt5Kiyo[/video]

I now longer entertain anyone showing me methods of trisecting angles until the presenter proves that the theorem that states it can't be done is wrong.

 

[Dr.Peterson]

I now longer entertain anyone showing me methods of trisecting angles until the presenter proves that the theorem that states it can't be done is wrong.

Here is what I tell a naive trisector, when I am feeling very generous, and want to help them understand. Many people who get the idea that trisecting an angle is a worthwhile goal just don't get the idea of proof in the first place, or don't know what construction is all about. Some just won't listen to anything, so it's not worth answering them at all.