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Topic: Non-constructible numbers of degree 4
Replies: 8   Last Post: Dec 8, 2013 3:27 AM

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Jose Carlos Santos

Posts: 4,872
Registered: 12/4/04
Re: Non-constructible numbers of degree 4
Posted: Dec 8, 2013 3:27 AM
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On 06/12/2013 10:22, quasi wrote:

>> Can anyone tell me where to find examples of impossible
>> constructions which lead to algebraic numbers of degree four
>> (or, more generally, some power of 2)?

>
> Here's one:
>
> Construct a cyclic 10-gon with 9 sides of length 1 and
> the remaining side of length 2.
>
> The radius r is a non-constructible number with algebraic
> degree 8 over Q.


Thanks a lot. I was looking after examples such as this one and the one
you mentioned after it.

Best regards,

Jose Carlos Santos




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