A Complex Way to Graph

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TheGrayCuber

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Man, this is asmr for my ears, eyes and mind at the same time...

frendlyleaf

This is a great visualization technique, it really gets you thinking about complex roots of polynomials. I like it when I'm able to "package up" mathematical concepts and "carry them around in my pocket, " and this definitely scratches that itch.

theneongoomba

this is so greately visualised and super intuitive! love it!

thepro

8:05 I am beyond excited that 105 was included because it's the first cyclotomic polynomial with a coefficient as large as 2! I'm sure there was a lot of toying with conjectures on special cases like 105=3*5*7

tcaDNAp

This was so interesting. Love your channel

ajs

Always totient of n roots to the nth cyclotonic. Very cool

brandonklein

Is the last animation made with a linear interpolation between each polynomial? I would be curious to see these animations with different methods of interpolation! like maybe exponential interpolation (t -> a(z)^(1-t) * b(z)^t )

applimu

I love your graph, could you open what is special about x8 + x4 + x3 + x + 1, since it is used in SHA512.
Do you insight for that special case?

Peccomment

How do you interpolate between the polynomials at the end? What is the eth polynomial?

sachs

So glad i found this. The animation's absolutely gorgeous, how did you make it?

fr

Makes me wonder if cyclotomic shapes could be a way to identify large primes…

kdicus

Could you do this for the zeta function?

CodecYT-wn

Is there a way to calculate the length of these weird shapes? With contour integrals or soemthing

BirdsAreVeryCool

Why people keep saying that we need 4d to graph C to C functions? There's already a lot of tools that can plot these functions using color schemes where hue is angle and brightness is intensity at each point.

escher

How do you interpolate between cyclotomics in your animation?

elijahberegovsky

Is this an entertainment video or an education video?

lumpyspaceprincess

how are computed the intermediate curves between two cyclotomic curves in the ending animation?

Abraccuda

is the title are reference to "a better way to count"

yoavboaz

Why didn't you graph other functions? Polynomials aren't that cool...

oKrybia

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