>>777
>こういう説明は「素人臭い」と言われても仕方がない

・まあ、議論の基礎ですから
　基礎の共有認識がないと、議論がかみ合わず、すれ違いになります
・なお下記”Root of unity”、先に進むと ”Cyclotomic fields” the Kronecker–Weber theorem "Class Field Theory" に至る
　（私はあまり分かっていませんが ；ｐ）
・十七角形の三角関数を使った導出は
　下記”Heptadecagon”の”Trigonometric Derivation using nested Quadratic Equations”
　にあります

(参考)
https://en.wikipedia.org/wiki/Root_of_unity
Root of unity
Cyclotomic fields
Main article: Cyclotomic field
In these cases Galois theory can be written out explicitly in terms of Gaussian periods: this theory from the Disquisitiones Arithmeticae of Gauss was published many years before Galois.[17]
Conversely, every abelian extension of the rationals is such a subfield of a cyclotomic field – this is the content of a theorem of Kronecker, usually called the Kronecker–Weber theorem on the grounds that Weber completed the proof.
References
Milne, James S. (1998). "Algebraic Number Theory". Course Notes.
Milne, James S. (1997). "Class Field Theory". Course Notes.
Neukirch, Jürgen (1999). Algebraische Zahlentheorie. Grundlehren der mathematischen Wissenschaften. Vol. 322. Berlin: Springer-Verlag. ISBN 978-3-540-65399-8. MR 1697859. Zbl 0956.11021.
Neukirch, Jürgen (1986). Class Field Theory. Berlin: Springer-Verlag. ISBN 3-540-15251-2.

https://en.wikipedia.org/wiki/Heptadecagon
Heptadecagon
In geometry, a heptadecagon, septadecagon or 17-gon is a seventeen-sided polygon.
Construction
Publication by C. F. Gauss in Intelligenzblatt der allgemeinen Literatur-Zeitung
As 17 is a Fermat prime, the regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass and unmarked straightedge): this was shown by Carl Friedrich Gauss in 1796 at the age of 19.[1] This proof represented the first progress in regular polygon construction in over 2000 years.[1]

Trigonometric Derivation using nested Quadratic Equations
Combine nested double-angle formula with supplementary-angle formula to get the nested quadratic polynomial below.
略

https://ja.wikipedia.org/wiki/%E5%8D%81%E4%B8%83%E8%A7%92%E5%BD%A2
十七角形