Non-Euclidean Geometry Explained - Hyperbolica Devlog #1

I present the easiest way to understand curved spaces, in both hyperbolic and spherical geometries. This is the first in a series about the development of Hyperbolica.

Chapters:
0:00 Intro
0:24 Spherical Geometry
2:33 Hyperbolic Introduction
3:53 Projections
5:37 Non-Euclidean Weirdness
8:31 Non-Euclidean Formulas
10:20 Outro

Hyperbolica

Henry Segerman

HyperRogue

If you like the things I do and want to support the channel:

Music:
"Glass Waves" By Phil K

[Roter_Wolf]

"Honey, can you knit me some non-euclidean planes?"

[outdateduser]

When you stop paying attention in calculus for 3 seconds

[lordvincenteperez]

can you just imagine beings of 4D using our 3D to explain 5D

[Starnoxiar]

"But first we have to talk about parallel universes" nice.

[MilesMetal]

"So I hope that's given all of you a little better understanding of curved spaces..."

...he says as the last remnants of my brain leak out of my ear.

[entitydotexe]

CodeParade: "Stay Hyperbolic"
Me: *proceeds to occupy the entire volume of the universe*

[efeersoy]

"Hey honey, do you think you could knitt me a projection of a hyperbolic tiling in 3D?"

[etourdie]

Greenland looks like it's about the size of Africa, but in reality it's about the size of Greenland
-Map Men

[rosearachnid]

“Hyperbolic crochet”
Come on in, sir. That’s the right password.

[TheVoidIsBees]

I feel like I just gained 100 braincells but lost 300 points psychic damage.

[PleasentDddd]

“All the angles are 0 and the area is pi.”

As someone who loves geometry, this statement really through me off.

[verylostdoommarauder]

Now I understand the lovecraftian horror of non-euclidean geometry better now. If it's this confusing to us, imagine what geometry would be like for an eldritch horror.

[michaelzopff]

Oooh! Holonomy is the reason why, when rotating a 3D object with a mouse, the orientation quickly gets messed up, isn't it? That would explain why my trick of moving the mouse in small circles clockwise or counter-clockwise works, too.

[carykh]

whoa, that's crazy that you can figure out the areas of triangles just by knowing its angles. It feels like there's something missing in the formula but there's not!

[kylies]

'isnt that neat?' while talking about non euclidean formulas almost made me tear up. This man's gentle, genuine enthusiasm really is so endearing and lovely. Thanks for this vid, can't wait to check out more.

[koda_pop]

The parallel universe bit caught me off guard lmao

[cynicap]

"Courtesy of mrs. Parade"

Awww, what a sweet, weird quality time

[kirbee]

Bro the "First I'll have to talk about parallel universes" had me DEAD LMAO. Shoutouts to pannenkoek2012!

[woodant]

I actually just got non Euclidean tiling in my bathroom.

[thecheesybagel]

No one:
My brain at 1 am: let’s try to understand non Euclidean geometry when I already have a hard time with algebra