# constructible angles with integer values in degrees

## Primary tabs

Synonym:
constructible angle
Type of Math Object:
Theorem
Major Section:
Reference

## Mathematics Subject Classification

### very nice, but

where is the proof that the angle of 20 degrees can not be constructed?

### Re: very nice, but

in pretty much any galois theory book

the proof relies on 20Âº not being constructible.
This is a corollary from the proof that
60Âº can't be trisected
which is the STANDARD proof that
the trisection of angles is impossible

so.. I'm relying in a known fact
everytime yo prove something you take some things for granted

I could add it, but it has a completely different
(and non elementary) context, so I left it out as known fact

And realize this is always done, If I had written the actual proof
would you request to add inside the proof to the galois theory results
it uses? and then the proof the the results used on those proof and ad infinitum?
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

### Re: very nice, but

Well, it really would be nice if "trisection of the angle is impossible" were an entry in PM, possibly along with doubling the cube and squaring the circle; all three could be examples somethere in Galois-theory-land.

As for needing proofs for all the Galois theory results, that's a problem for the entries on the actual results --- but it makes sense to hope that those results actually have entries.

### Re: very nice, but

Yes, that's what I meant

The style and techniques used in proving the trisection of angle don't go very well with this entry, I try to keep things in a n elementary level as possible

So yes, a "trisecting angle" entry should be added (with sysnonyms mentioning impossibility at all, it could even become a topic and then we could attach this entry and several others to it
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f