Proof Request: For which $n$ can we construct regular $n$ -gons with integer co-ordinates?

I've managed to prove this before but I expect much more elegant ways exist. If you see a way of doing this, please share :)

#Geometry

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Comments

I found the type of proof I was looking for (using complex numbers and Fields!) although it is a little beyond me right now. If anyone requests I will try write a nice accessible proof.

Roberto Nicolaides - 5 years, 4 months ago

Can u publish Ur proof?

Happy Melodies - 5 years, 4 months ago

Yes, I will start working on it during the weekend of Feb 6 - 7.

Roberto Nicolaides - 5 years, 4 months ago

Here is the first proof I became aware of but there are some really cool and diverse other ones using Galois Theory and Number Theory! If you come up with one or have any cool observations then please let me know :)

For now I'll just link the a proof I wrote a while back.

Roberto Nicolaides - 5 years, 2 months ago

@Happy Melodies, apologies for such a late response.

Roberto Nicolaides - 5 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Proof Request: For which nnn can we construct regular nnn-gons with integer co-ordinates?

Comments

Proof Request: For which $n$ can we construct regular $n$ -gons with integer co-ordinates?