Comment by Terr_

5 months ago

> Folds are powerful. One can trisect or n-sect any angle for finite n.

Does that mean folding allows you to construct (without trial-and-error) an accurate heptagon, even though you can't with a straight-edge and compass?

Intuitively, that seems wrong, I would expect many of the same limitations to apply.

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Terr_

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avhon1  5 months ago

Seems like you can

https://origamiusa.org/thefold/article/diagrams-one-cut-hept...

The one cut is to remove the perimeter of the square that lies outside the heptagon. Without the cut, you could make a crease, and fold the excess behind the heptagon.

  • Terr_  5 months ago

    My reading is that it's a convenient near-7 approximation someone developed, like using 22/7 for pi.

    Certainly good enough for practical handheld construction purposes, but not geometric-proof-y stuff.

    • srean  5 months ago

      Checkout

          Scimemi, Draw of a regular
    heptagon by folding.
    Proceedings of the 1st
    International Meeting of
    Origami Science and 
    Technology. 1989

      Simultaneous folding is mathematically a strictly more powerful primitive.

      Are you familiar with Lill's method of finding real roots of polynomials of any degree ? Simultaneous folds are a realization of the same idea

      https://en.m.wikipedia.org/wiki/Lill%27s_method#Finding_root...

srean  5 months ago

Yes.

But remember one is dealing with idealized / axiomatized folding. The situation is similar with compass and straight edge geometry -- those physical lines and circles marked on paper are approximate but mathematically, in the world of axioms we assume the tools are capable of perfect constructions.