Wantzel was not wrong. I mentioned that the solution you posted uses a ruler and not an unmarked straightedge, so it technically is out of the realm of classical mathematics.
Trisecting Any Angle

When i was in Geometry class we proved that you can not trisect an angle with just straight edge and compass.
We also learned the Hackman method which is different because it uses marks on the straightedge. We also proved the Hackman method is sound. For practical purposes the easiest way to trisect an angle is trial and error with dividers. If it takes a whole minute you don't know what you are doing. (07042019, 10:44 PM)DaveR1 Wrote: 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. I'm reminded of a story about a professor who frequently used the term "for all intents and purposes...". When asked to explain, he suggested that he could draw a line down the center of the classroom and then ask the boys to stand along the left wall and the girls to stand along the right wall. He could then ask everyone to walk half way to the center line and then walk halfway of the remaining distance and then do it again and again. Continuing in this fashion, he said, no one will ever get to the line. However, "for all intents and purposes" you will be close enough. Regardless of how accurate this method is or isn't, it is a great tool for the shop and for all intents and purposes, it will be close enough. Thanks for this. (07052019, 09:51 AM)Willyou Wrote: I'm reminded of a story about a professor who frequently used the term "for all intents and purposes...". When asked to explain, he suggested that he could draw a line down the center of the classroom and then ask the boys to stand along the left wall and the girls to stand along the right wall. He could then ask everyone to walk half way to the center line and then walk halfway of the remaining distance and then do it again and again. Continuing in this fashion, he said, no one will ever get to the line. However, "for all intents and purposes" you will be close enough. Anybody who learned high school geometry ought to be able to prove that this is fact. Not just six decimal places. No wishy washy "all intents and purposes". (07042019, 10:47 PM)FS7 Wrote: Wantzel was not wrong. I mentioned that the solution you posted uses a ruler and not an unmarked straightedge, so it technically is out of the realm of classical mathematics. However, the straightedge is not really a ruler because the mark that is made on the straightedge is done with the same compass that was used to draw the circle. I think a ruler has predefined marks all along its length based on a specific unit of measurement. Just MHO.
Rip to width. Plane to thickness. Cut to length. Join.
(07052019, 10:52 AM)Edwin Hackleman Wrote: However, the straightedge is not really a ruler because the mark that is made on the straightedge is done with the same compass that was used to draw the circle. I think a ruler has predefined marks all along its length based on a specific unit of measurement. Just MHO. ^^^^^^^^^^^ Dittos! Doug
I believe we're dealing with a technicality on this.
When you make a mark on the straightedge it now becomes a ruler and falls out of the original parameters of the problem. Frank S in IA
You're right, and to me it seems like the Euclidean method of requiring only an unmarked straightedge is rather arbitrary and this method (Archimedes, I believe) allows for marks. Why a mark made on one of the tools with the other makes it outside the realm of the original limitations is beyond me.
07052019, 12:54 PM
(This post was last modified: 07052019, 03:45 PM by DaveR1.)
Re: Trisecting Any Angle by Edwin Hackleman (I found the discussi...)
I think this argument has run its course now. Time for the next one. Pins or tails first.
I once bought a fresh apple pie and enjoyed a slice like line AOX. Then my wife came along and trisecected it like line AC because she wanted more of the delicious crust. Boy! Did that ever pee me off! Never thought about math and angle but only a now jacked up pie. No wonder I never excelled in the maths? I don’t like when people desecrate a pie!
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