Visualizing Cyclotomic Polynomials

[@The9thDoctor]

Great video! Earned a spot in the math playlist for sure. I hope more people find this channel.

[@draido-dev]

im about to spam this in projecteuler threads, thanks for making these videos! you don't know how much reading you saved my poor soul from doing :3

[@luizmenezes9971]

This makes math look like dark magic

[@izak5775]

math is literally the magic system of our universe.

[@LucasAnbessaCastillo]

13:12 fun fact the shape of 15 is the exact channel/profile picture of your channel!!

[@rxlnj]

hi, could you share the notes you said you have for covering the topic in more detail? id love to learn from them oh, and what a captivating video!

[@noblearmy567]

I'm 13 and watched through the entire video. Suprisingly entertaining.

[@DanishHafiz-gt4sq]

its entertaining, as math is. lets study for future!! of all

[@paridhaxholli]

Im 12

[@noblearmy567]

@ nice

[@area51xi]

I need a little more hand holding on this. Got the overall feel but need to go back a notch and review some more fundamentals of nth roots and number theory. Thanks.

[@PunmasterSTP]

Cyclotomic? More like "Cool; this video is slick!" 👍

[@slawless9665]

this is way over my head but I'll take a stab at your question at the end of the video - my guess is because 11 and 19 are 1 off from a multiple of 5

[@LillianRyanUhl]

Bingo :)

[@luisalejandrohernandezmaya254]

Excelent video. I have a question maybe you can answer it. The cyclotomic polynomial when n=p = prime is Φ_p(x)=x^{p-1}+x^{p-2}+...+x+1 I have to prove Φ_p is irreducible. Hint: Use Eisenstain criterion. The problem is that all a_k = 1 so there is not a prime q such that q|a_k for all k

[@TheGrayCuber]

Take (x + 1) as a an input of Φ_p, then you can use the binomial theorem to get primes

[@luisalejandrohernandezmaya254]

@@TheGrayCuber Oh! Thank you so much!! God bless you!

[@cosimobaldi03]

​@@TheGrayCuberclassic proof ❤❤

[@pawebielinski4903]

You do realise, however, that cyclotomic polynomials can in fact have coefficients other than --1, 0, 1?

[@TheGrayCuber]

Yes, those cases are more complicated to break down into regular polygons, but for example with 105 there are two points that are part of both a pentagon and a triangle

[@pawebielinski4903]

@@TheGrayCuber I see, I was curious what you'd do in that case.

[@PunmasterSTP]

@@TheGrayCuber Ah that's interesting; I didn't think of how you could assign those points to more than one shape!