Zero Deviation Euclidean Trisection

Approaching a proof, I'd been working on modeling constructs capturing larger segments of the primary angle arc and came up with a more simplified trisection method. This produced an astounding reference-construction deviation of only 0.000000000000001 and was worthy of what I thought would be my final video, the "Ultimate Trisection" of February 15, 2026. With a 12-inch base, it produced a deviation equivalent to one thirty-third the diameter of a hydrogen atom's nucleus—it couldn't get better than that!

But it could and it did. I didn't throw in the towel and on March 18, 2026, hit on new final steps leading to zero deviation between my constructed angle and the computer derived reference point. This was a little embarrassing, as I'd already put the matter to bed. I started to make another video, flip-flopped, put it off until yesterday. 

                                     Zero Deviation construction (click to enlarge).

As with the Ultimate Trisection, the final point is placed on the primary angle's arc. But unlike the Ultimate Trisection's minuscule "sub-atomic" deviation, the computed reference Point D' of the Zero Deviation trisection falls on exactly the same point as constructed Point P.

Whew! I'm finally finished with Euclidean trisection. Well, for now, anyway. 

Here's the video demonstrating its construction: 


 

  

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