Trisecting Any Angle

[Edwin Hackleman]

I found the discussion in Wikipedia to be nebulous to say the least. There is a simple way to do this. I discovered it about 15 years ago from a source that I cannot remember, so I decided to post it here.

   

I have used this method several times and found it to be on the nose. Give it a try and happy fourth of July!

[Bill Holt]

Now that is interesting!  Will I be able to remember it, who knows?

[Edwin Hackleman]

Now that is interesting!  Will I be able to remember it, who knows?

Print it and save it along with your other woodworking documents. Or, I think you can copy that image to a Pic file subdirectory. The text is all part of the image.

[FS7]

It is not possible to trisect an arbitrary angle with a compass and a straightedge. This was proven in 1837.

I'm honestly surprised this stuff still shows up.

ETA: I think this would technically be allowed since it involves a ruler and not a simple straightedge.

[Edwin Hackleman]

It is not possible to trisect an arbitrary angle with a compass and a straightedge. This was proven in 1837. I'm honestly surprised this stuff still shows up. ETA: I think this would technically be allowed since it involves a ruler and not a simple straightedge.

That's wrong. No ruler is required. The compass that was used to draw the circle can measure the length, BC, along the straight edge. Think about it.

[bhh]

It is not possible to trisect an arbitrary angle with a compass and a straightedge. This was proven in 1837.

I'm honestly surprised this stuff still shows up.

ETA: I think this would technically be allowed since it involves a ruler and not a simple straightedge.

In one of my last graduate classes in abstract math, we were studying a branch called "Galois Theory" named after a Frenchman who penned down the foundations prior to losing his life in a duel the next day (apparently a much better mathematician than marksman).   After a week or so of this esoteric study the professor announced "and that's why you cannot trisect an angle with straightedge and compass."   For years, math quacks had been publishing "proofs"to the contrary.   All us students just kind of stared at each other because it did not seem to have any direct relevance.   Prof spent the next 20 minutes explaining why.

https://en.wikipedia.org/wiki/Galois_theory

https://en.wikipedia.org/wiki/Angle_trisection

[Edwin Hackleman]

In one of my last graduate classes in abstract math, we were studying a branch called "Galois Theory" named after a Frenchman who penned down the foundations prior to losing his life in a duel the next day (apparently a much better mathematician than marksman).   After a week or so of this esoteric study the professor announced "and that's why you cannot trisect an angle with straightedge and compass."   For years, math quacks had been publishing "proofs"to the contrary.   All us students just kind of stared at each other because it did not seem to have any direct relevance.   Prof spent the next 20 minutes explaining why.

https://en.wikipedia.org/wiki/Galois_theory

https://en.wikipedia.org/wiki/Angle_trisection

Pierre Wanztel was wrong. Not everything published in 1837 was correct.

We also learned years ago that 22/7 was a good approximation for the ratio of the circumference of a circle to its diameter (pi ). In fact 355/113 supplies an easy to remember estimation for pi  that is about a million times more accurate -- that much less error.

[Admiral]

Wow, all of this is completely over my head.....

[daddo]

Math is not perfect. Try and divide a 7" bar into 3 equal sections mathematically and you can't. You get an infinite number and we all know there IS an exact measure for each 3 sections. The best we can do is measure to the tiniest quantum.
Dividing a 6" bar is quite different.

[DaveR1]

I just tested it in a CAD program. It was good to 6 places right of the decimal. I expect it's close enough for woodworking.