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I watched in one of the lecture series on YouTube that it is not possible to construct a 20 degree angle using only a compass and ruler; is there a formal proof for this ?

user366398
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  • Yes, for instance see https://en.wikipedia.org/wiki/Angle_trisection#Proof_of_impossibility – Watson Nov 03 '16 at 16:59

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60 degrees construction possible by Ruler & Compass. Further angle trisection proved already not possible by Euler.

Narasimham
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  • Of course, a $60^0$ angle cannot be 3-sected into three $20^0$ angles. I think the argument has a logic problem. Let’s start with angle of $\theta^0$ and we try to have it n-sected. For example, if $\theta = 40^0$, then we can 2-sect it into two $20^0$ angles. Clearly, a 2-sect action is geometrically constructable. The question becomes “can the $40^0$ angle be constructed in the first place?” Similarly, an $80^0$ angle can be 2-sected three times into four $20^0$ angles but then we have to prove that the $80^0$ angles can never be formed. The list goes on forever. – Mick Nov 04 '16 at 16:21
  • For an input $ 60^0$ a method should exist outputting $20^0$ – Narasimham Nov 04 '16 at 17:36
  • The input ($60^0$) is valid but the method (trisecting it) is not possible. Bisection is valid but can we prove that all angles of ($40^0$, $80^0$, .... ) are NOT constructable in the first place? The list is infinite to be exhausted. – Mick Nov 04 '16 at 18:11