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Math Forum » Discussions » Math Topics » geometry.pre-college.independent

Topic: construction of angles
Replies: 2   Last Post: Mar 30, 1998 11:07 AM

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Peter Ash

Posts: 13
Registered: 12/6/04
Re: construction of angles
Posted: Mar 29, 1998 7:58 AM
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rajuyr@giasbga.vsnl.net.in wrote:
>
> I KNOW HOW TO CONSTRUCT ANGLES LIKE 30,45,90,60 DEGREES BUT I ALSO
> WANT TO KNOW HOW TO CONTRUCT 20 AND 50 DEGREES. I HOPE U SEND ME THE
> METHOD TO ME AT MY EMAIL.


Rajuyr,

You may have heard that it is, in general, impossible to trisect an
angle using compass and straightedge. Well, it happens that a 60 degree
angle is impossible to trisect; that is, it is impossible to construct a
20 degree angle using the allowed tools. This means it is also
impossible to construct a 50 degree angle as well (20 = 50 - 30, so if
you could construct a 50 degree angle, you could construct a 20 degree
angle, which you can't).

To understand WHY you can't construct a 20 degree angle, you need to
understand some Galois theory. This is something I didn't learn until
graduate school, and I don't know offhand of a good elementary
treatment. Perhaps someone else in the forum will suggest a reference.

--Peter





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