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ORIGAMI RINGS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 92 / Issue 3 / June 2012
- Published online by Cambridge University Press:
- 02 November 2012, pp. 299-311
- Print publication:
- June 2012
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- Article
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Motivated by mathematical aspects of origami, Erik Demaine asked which points in the plane can be constructed by using lines whose angles are multiples of
$\pi /n$ for some fixed 
$n$. This has been answered for some specific small values of 
$n$ including 
$n=3,4,5,6,8,10,12,24$. We answer this question for arbitrary 
$n$. The set of points is a subring of the complex plane 
$\mathbf {C}$, lying inside the cyclotomic field of 
$n$th roots of unity; the precise description of the ring depends on whether 
$n$is prime or composite. The techniques apply in more general situations, for example, infinite sets of angles, or more general constructions of subsets of the plane.
