4th dimension & Non-euclidean geometry (Part 1)

I'm currently interested in the concept of high dimensions and stuff, I did many types of research, mostly games Devlogs which gave great assumption of the higher dimensions. I'll share what I learned in a series of notes.

First, of course, what is the 4th dimension? Some believed that the 4th dimension is the axis of time, but I'm going to talk about another concept here. Let's take a look at some lower dimensions: 0D: 0d objects have no axis to exist on, almost equals to nothing, but there is an existing object. (We can't see)

1D: Objects can exist on the x-axis, but no others, space took up by the object is called length. (We can't see)

2D: Objects can exist on the x and y-axis, a plane! Y-axis is perpendicular to the x-axis, space took up is called the area.

3D: Objects can exist on the x, y and z-axis. Z-axis is perpendicular to both x and y-axis, space took up is called the volume.

Now, some brainstorms?

(Concept) 4D: Objects can exist on the x, y, z and w-axis. W-axis is perpendicular to all x, y and z-axis ( Can you imagine? ) We don't have a proper name for an area taken up by a 4d object, but let's say if all 4 axis is measured in centimetres, then our unit for the object will be...

In the next part, we'll discuss how will 4d object look like.

And feel free to comment if you have any ideas!

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

BTW this is an illustration of a 4d cube which I don't quite agree on:

Half pass3 - 1 month, 2 weeks ago

What about an animation? Check Wikipedia's animation of a $4$ D cube.

Yajat Shamji - 1 month, 2 weeks ago

yeah, This concept doesn't quite fit that gif too, but I'll definitely add some animations in the next part!

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$