[Visual] Complex Trigonometric Functions Visualised

[@zakerysimpson5363]

This animation is second to none in expressing how supremely smooth functions are where they're analytic. Brilliant work!

[@dereathacross1991]

I'm so glad I discovered these.

[@J.M.S.Simoes-Pereira]

Eu sou matemático, professor na Universidade de Coimbra! Parabens pelo trabalho!

[@FlyingSavannahs]

I love the rendering! It looks to me like the work of a master glassblower with mad skills in a much higher plane of existence. My "they always want more" thought, though, was wishing we would fly through one of the sin and cosine arches. Or better yet, a slalom route around all the zeros! ...And a swoop into the valley, too! Ok, fire up the compute farm and get ready to spend $160 in electricity! Thanks as always for the beautiful work!

[@TheMathemagiciansGuild]

Thanks!! Expect a cos fly-through in the next video of the main series. (It won't be glass though, something a little new). I love the slalom idea!

[@jennycotan7080]

The sine and cosine complex surfaces seem to be an epic challenge for stunt skaters.

[@cypheruniversity3074]

Thank you for your labor. I definitely have already applied this to my theory crafting and storytelling. You have done a remarkable service 🐕‍🦺

[@zigzagzwag]

Your videos and effort go tragically unappreciated. Not sure what to make of this information but this is far out✌️

[@KaliFissure]

Surface(cos(u/2)cos(v/2),cos(u/2)sin(v/2),sin(u)/2),u,0,2pi,v,0,4pi Notice that 4 pi are needed to complete the surface. This is a single sided closed surface. The radially symmetric Klein bottle.

[@brendawilliams8062]

Gorgeous

[@UwU-rn8xo]

Those are some beatiful shots. Also i finally know what this stuff is my PC is rendering on SheepIt all the time :D

[@guill3978]

Can we integrate them like a function z=f(x,y)? How must we do that?

[@Kasamori]

If f(t) = u(t)+iv(t) where u(t) gives the real part and v(t) gives the imaginary part then ∫ f(t) dt = ∫ (u(t) + i v(t)) dt = ∫ u(t) dt + i ∫ v(t) dt.

[@Kasamori]

Assuming t = x+iy in your example

[@Kasamori]

Now i'm wondering if this actually helps, I need to take some time on this :D

[@guill3978]

@Nimbo Stratus The key should be to derive it.

[@NonTwinBrothers]

Must've taken ages to render!

[@TheMathemagiciansGuild]

Yes it did!!! 4-5 mins per frame on a 64-core CPU. There are around 10,000 frames. Mostly, it was done on a render farm, I did around 2000 myself.

[@theunknown4834]

@@TheMathemagiciansGuild Can you show us a way to get this?

[@LaVoie26]

Now try the mandorbolt 😅😅😅 and watch it predict were you wanna go

[@TheMathemagiciansGuild]

I will do the Mandelbrot at some stage. :-)

[@alexanderwermlund3145]

Am i a true math lover now? Jokes aside that render is impressive

[@TheMathemagiciansGuild]

Yes you are!

[@amansingh-ww2qc]

Bhai galgotia m aaja ek din k lie sab maths le lenge

[@jeremx7094]

That’s weird