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What are the constructible angles ?

Wikipidia sais:

The only angles of finite order that may be constructed starting with two points are those whose order is either a power of two, or a product of a power of two and a set of distinct Fermat primes.

I don't understand the exact meaning of this, does it say that an angle is constructible if and only if it is a power of two or a product of a power and $?$ (this part I didn't understand either)

J. M. ain't a mathematician
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Belgi
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    That is the theorem, yes, if and only if. A less fancy way of putting it is for $n$ a positive integer, the angle $2\pi/n$ is constructible iff $n$ is a power of $2$ (possibly equal to $1$) times a product (possibly empty) of distinct Fermat primes. The order stuff generalizes this in an unimportant way. – André Nicolas Apr 20 '12 at 14:09
  • @AndréNicolas not really. The angle 98 degrees = 6π/10 is constructible, but your way doesn't include it. – Ekuurh Apr 20 '12 at 14:18
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    @Ekuurh: $6\pi/10$ is $108^\circ$... – J. M. ain't a mathematician Apr 20 '12 at 14:30
  • @Ekuurh: Our disagreement would be over whether going beyond the constructible polygons is an important generalization. – André Nicolas Apr 20 '12 at 14:44
  • @J.M. Honest mistake :) Yea, I think the set of all constructible angles should be classified. – Ekuurh Apr 20 '12 at 18:12
  • 98 degrees can not be constructible. We know that 90*11/10=99 degrees is constructible , and if 98 degrees is constructible, then 1 degree would be constructible, and 20 degrees would be constructible, which contradicts the classic proof of the impossibility of trisecting an arbitrary angle with a compass and straightedge. – Michael Ejercito Feb 01 '24 at 08:02

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It means an angle is constructible if and only if its order is either a power of two, or a power of two times a set of Fermat primes. For example, 10 = 2*5, and 2 is a power of two and 5 is a fermat prime, thus you can make an angle of 360/10 = 36 degrees. but 40 degrees = 360/9 cannot be constructed, because 9=3*3, and 3, 3 are not distinct.

Ekuurh
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