alt Hacker News> 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.
Replies
jo-han • today at 6:00 AM
This paper discusses constructing heptagons, with some history and the maths.
http://origametry.net/papers/heptagon.pdf
It shows both a single sheet and a modular version.
avhon1 • today at 1:38 AM
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.
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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.