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29 views

Dummit & Foote: Construction of the regular $17$-gon

In the last step of the exercise where we construct the $17$-gon, I have to draw a circle with a diameter whose endpoints are $(0, 1)$ and $(\eta_1', \eta_4')$ and show that it intersects the positive ...
4
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1answer
61 views

Proof of necessary condition for constructibility of a number

I'm reading a proof of the necessary condition for a real number to be constructible, and it seems to leave out a few details that I can't really fill in. This is what I understand so far. We have to ...
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43 views

proving that this family of angles, cannot be trisected

Given a field $ \Bbb Q \subset K \subset \Bbb C$. One can prove that $\beta \in \Bbb C$ is constructible over $K$ iff the galois group of the minimal polynomial over $K$, $m_{\beta}(x)\in K[x]$ is a ...
2
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1answer
63 views

Construction of a field

Given the polynomial $$f(x)= x^4-16x^2+4$$ which has $a=\sqrt 3+\sqrt 5$ as one of its roots in $\Bbb C$, can you use $f(x)$ to construct a field $E$ of the form $Q[x]/I $ for some appropriate ideal ...
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1answer
82 views

Contracting an angle (using straightedge and compass)

In my field theory lecture notes I have it that a regular polygon with $n$ sides is constructable iff $\zeta_{n}=\frac{2\pi}{n}$ is constructable. Shouldn't this be $\frac{\pi}{n}$ instead of ...
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359 views

Constructible angles

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 ...
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1answer
289 views

geometric construction of a given angle

Given any angle how can you say that it is constructable or not?