Visualizing Cyclotomic Polynomials

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This is about Cyclotomic Polynomials and an interesting way to view them visually.
Part 2: • Visualizing Cyclotomic...
Another Follow-up: • Modifiers of Cyclotomi...
There are some unjustified jumps in logic within the video. I did that to keep the length down - a video that covers every detail would be less entertaining - but I do have detailed notes written to support these 'claims'.

Опубликовано:

7 сен 2024

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Комментарии : 21

@draido-dev Месяц назад

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

@The9thDoctor 10 месяцев назад

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

@luizmenezes9971 Месяц назад

This makes math look like dark magic

@izak5775 Месяц назад

math is literally the magic system of our universe.

@wargreymon2024 3 месяца назад

This channel is gold

@noblearmy567 Месяц назад

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

@DanishHafiz-gt4sq 17 дней назад

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

@rxlnj Месяц назад

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!

@area51xi 6 месяцев назад

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 Месяц назад

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

@slawless9665 20 дней назад

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 6 дней назад

Bingo :)

@luisalejandrohernandezmaya254 3 месяца назад

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 3 месяца назад

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

@luisalejandrohernandezmaya254 3 месяца назад

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

@cosimobaldi03 29 дней назад

@@TheGrayCuberclassic proof ❤❤

@pawebielinski4903 9 месяцев назад

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

@TheGrayCuber 9 месяцев назад

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 9 месяцев назад

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

@PunmasterSTP Месяц назад

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