Answering Imhotep (AI) Trisect the pyramid


STEPS

  1. Extend the edges of the angle to some large length and inscribe a circle around the intersect with the compass.
  2. Ruler: Secant line across top intersect with circle
  3. Ruler: Secant line across bottom intersect
  4. Compass: circle around left top, length of chord
  5. Compass: circle around right top, length of chord
  6. Ruler: line from left circle intersect down to ∞
  7. Ruler: line from right circle intersect down to ∞
  8. More things are possible, but this is one way

Here is a step wise trisect done legally according to the international rules of geometrics. It is quite odd as I discovered two new ways to trisect while playing with this. I suspect there are many ways. There are many solutions to the Pythagorean Theorem geometrically and I have devised one myself. From this point in this method there are many ways to continue, and they allow any integer or integer fraction of splitting. This is about as much time as I intend to spend on this topic as it is getting boring. I see no application and though it may be of some value to somebody, there are better things to do. It was fun doing it in Inkscape, then gimp and creating the animated gif, but the fun is gone and I won't return to this subject unless somebody pays me to be bored to tears.

I found more entertainment in this, I decided I could make an angle trisection machine. I doubt I will actually make one, but I can see the design in my head and it has a grooved circle with a scissors in the middle and the second scissor is connected to the lower chord and free at the top where it would ride along the extended top chord. It seems that the lower scissor would have a rotating section that was radius in length. I am fairly sure it would work, but things don't always work out like they are planned, but this has so few moving parts I would guess that it would work. I see that somebody got a lot of attention for a trisect origami.

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