Angle trisection famously cannot be accomplished by straightedge and compass. But it can be accomplished by compass and a straightedge with two marks, or by conic sections. However, none of these devices are adequate to quintisect an arbitrary angle. Is there any interesting set of geometric tools that suffices to quintisect an arbitrary angle in a finite number of steps? If so, what is that set of tools?
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One interesting tool that can divide any angle into any number of equal parts is linkages. Cf. here. – Parcly Taxel May 21 '21 at 04:08
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@ParclyTaxel That seems to be roughly equivalent to the Mecanno geometry considered by Gerard ’t Hooft (see also here), which is a world more easily explained to children (but possibly harder to prove stuff in, as the world is not truly "flat", and so is only "roughly" equivalent). – user1729 May 21 '21 at 09:05