2D Structures in 3D Space

Dimensions, an interesting while intimidating subject to talk about. There are rumors which scientists are trying to prove about dimensions like “is there a higher dimension” and “what is the highest dimension”. If I recall correctly, in one science fiction aliens have the means to change dimensions, and the universe started with 13 dimensions. By changing dimensions unlimited possibilities occur. But first we need to start with the basics, the dimensions we can see.

Imagine a piece of paper. You hold it in the air. It looks like a 2D rectangle in the 3D space you see. It is hopefully vertical to the ground because of gravity. Taking the gravity out, we are able to move onto abstract graphs that the paper stays in the air sideways. It is possible to imagine it in our head that in front of us, there is a piece of paper floating in the sky in a certain direction.

It also comes to the mind of mathematicians that it is no longer visible by human eyes as we expand into further dimensions. There are all kinds of properties for the shapes while it is hard for it to be presented simply by “triangle, sphere, …” Mathematicians move on from that and decide the space they are living in first, called a subspace. For example, a piece of paper(2D) lives in the 3D plane of a subspace xy-plane. There is a fixed area for the paper, and now we know where it is.

It is interesting to try to think about higher dimensions and what it looks like. Is someone among us the projection of a higher dimension? Just like we see the paper is flat on the ground, the paper can only see a 2D figure of us. That has always been an imaginary question to think about.