Golf Is So Much Better With Extra Dimensions

Рет қаралды 1,369

Күн бұрын

4D Golf is a miniature golf game with a delightful extra-dimensional twist! It's available on steam here: store.steampowered.com/app/21...
From the Steam page:
4D Golf is a mind-bending golf game unlike any other because it's set entirely in a 4-dimensional space. Complete fun and unique golfing challenges as you gain hands-on experience of the 4th dimension and beyond!
Join my discord to get stream announcements, participate in community events, make content suggestions, and generally hang out with like-minded nerds! / discord
Catch me live on my stream here!
/ samettheturk
0:00 World 3b
48:50 World 4a
1:03:47 Math Digression (Sphere Packing)
1:26:42 World 4a Continued
2:09:10 Math Digression (Products of Circles)
2:14:12 World 5a
2:36:38 World 5b

Пікірлер: 25

@monkyyy0 Ай бұрын

aw yes a 20 minute math lecture in the middle of a 4d golf stream

@yuvalne Ай бұрын

my favourite 4d jokes is that USB-A ports are actually 4D objects performing double rotation, which is why you always go try flip over try flip over try when you connect them.

@sargentgullible2794 Ай бұрын

holy shit. actual 4D USB-ANYTHING sounds like a total fucking nightmare.

@brinleyhamer729 Ай бұрын

@@sargentgullible2794 it would rotate in the 5th dimention

@justagayguyfromrussia5294 Ай бұрын

Btw, you should also check out the Mezzanine Tour in the extras next time! In there, your volumetric view slice is at the height of your eyes when you're walking in a gravity-affected slice, allowing you to see all of the 4d exhibits from Mezzanine in volumetric view!

@DDvargas123 Ай бұрын

for the math digression, i think duocylinder is the product of two disks and torus is the product of two circles

@johngalmann9579 Ай бұрын

Fun fact: the boundary of the duocylinder is two filled tori glued along their boundary (similar to how a sphere is two disks glued along their boundaries)

@KacaBiru Ай бұрын

I love how you try to solve the sphere packing problem

@dliessmgg Ай бұрын

I looked a bit into torus vs duocylinder, and as far as I can tell the difference is that the generating circles for a torus by necessity share a dimension, while the generating circles for a duocylinder don't. Or in other words: torus = (circle in xy-plane) x (circle in xz-plane) duocylinder = (circle in xy-plane) x (circle in zw-plane)

@dliessmgg Ай бұрын

The way I understood the concept in math lecture: You are in dimension D. You have the outer sphere-equivalents of your dimension, arranged in an orthogonal manner, so that there's two of them in the direction of each axis. The radius of the outer sphere-equivalents is 1. The centres of these sphere-equivalents are connected with lines; this forms a cube-equivalent of the same dimension. The distance between corner and centre of this cube-equivalent is sqrt(D). The inner sphere-equivalent has the same centre as the cube-equivalent. Its radius is the centre-corner distance of the cube-equivalent, minus the radius of the outer sphere-equivalent: sqrt(D)-1. As a result, the inner sphere-equivalent gets larger as you go into higher dimensions. If you're in four dimensions, the inner and outer sphere-equivalents are the exact same size. Therefore, two orthogonal arrangements of sphere-equivalents fit perfectly into each other.

@Dayanto Ай бұрын

This is also directly related to the other tiling they mention. If you inflate the spheres until they touch (Voronoi tesselation), then you get two interleaving grids of equivalent shapes offset diagonally from each other That's the pattern you see on the floor in the Mezzanine.