Mathematical Dimensions

**magentarita** · September 12th 2008, 06:14 PM

I know that plane geometry as taught is high school is 2D or two dimensional.

I know that there is something called 3D math. For example, points in space (x,y,z) are different than points in the form (x,y).

How many dimensions are there in the world of mathematics?

Is there such a thing as 4D math?

In other words, is there such a thing as a point having 4 letters like (w,x,y,z)?

**bnay** · September 12th 2008, 10:59 PM

In math, anything above three dimensions is called hyperspace. It's pretty difficult if not downright impossible to picture any more than 4 dimensions (space and time) in your mind, but scientists are discovering new dimensions trapped within particles. So yes, there are more than three dimensions in mathematics. You can actually find distances between points (w,x,y,z) and (w',x',y',z') by taking the square root of (w-w')^2 + (x-x')^2 + (y-y')^2 + (z-z')^2. This works for any number of dimensions.
Hopefully that answered the question alright

**Moo** · September 12th 2008, 11:00 PM

Hello,

Originally Posted by magentarita

I know that plane geometry as taught is high school is 2D or two dimensional.

I know that there is something called 3D math. For example, points in space (x,y,z) are different than points in the form (x,y).

In my country, we learn 3D spaces in the final year of high school

How many dimensions are there in the world of mathematics?

Is there such a thing as 4D math?

In other words, is there such a thing as a point having 4 letters like (w,x,y,z)?

The four dimension space is mostly use by physicists, I guess it is in relativity

As for mathematics, there is an infinity of possible dimensions. For example, matrices illustrate this, since their dimension can be any nonnegative integer n.
There are applications in analysis, algebra or calculus... where you use $\mathbb{R}^n$ . An element of it is in the form $x=(x_1,x_2,\dots,x_n)$ where n is arbitrary.
And there are quite a lot of uses, but we don't quite use it for graphic representations.

Example :
The distance from a point $x=(x_1, x_2, \dots, x_n)$ to another point $y=(y_1, y_2, \dots, y_n)$ in $\mathbb{R}^n$ is defined as being :

$\left(|x_1-y_1|^n+|x_2-y_2|^n+\dots+|x_n-y_n|^n \right)^{\frac 1n}=\left(\sum_{i=1}^n |x_i-y_i|^n\right)^{\frac 1n}$
(you can check that this works for p=2 and gives the formula you know).

**magentarita** · September 13th 2008, 04:30 AM

Originally Posted by bnay

In math, anything above three dimensions is called hyperspace. It's pretty difficult if not downright impossible to picture any more than 4 dimensions (space and time) in your mind, but scientists are discovering new dimensions trapped within particles. So yes, there are more than three dimensions in mathematics. You can actually find distances between points (w,x,y,z) and (w',x',y',z') by taking the square root of (w-w')^2 + (x-x')^2 + (y-y')^2 + (z-z')^2. This works for any number of dimensions.
Hopefully that answered the question alright

Great information. I had no idea that I can take the square root of such points beyond 3D and find the distances between them by applying basic algebra.

**magentarita** · September 13th 2008, 04:35 AM

Originally Posted by Moo

Hello,

In my country, we learn 3D spaces in the final year of high school

The four dimension space is mostly use by physicists, I guess it is in relativity

As for mathematics, there is an infinity of dimensions. For example, matrices illustrate this, since their dimension can be any nonnegative integer n.
There are a lot of applications (in analysis, algebra or calculus...) where you use $\mathbb{R}^n$ . An element of it is in the form $x=(x_1,x_2,\dots,x_n)$ where n is arbitrary.
And there are quite a lot of applications, but we don't quite use it for graphic representations.

Example :
The distance from a point $x=(x_1, x_2, \dots, x_n)$ to another point $y=(y_1, y_2, \dots, y_n)$ in $\mathbb{R}^n$ is defined as being :

$\left(|x_1-y_1|^n+|x_2-y_2|^n+\dots+|x_n-y_n|^n \right)^{\frac 1n}=\left(\sum_{i=1}^n |x_i-y_i|^n\right)^{\frac 1n}$
(you can check that this works for p=2 and gives the formula you know).

I thank you for the information provided. Of course, I am not going to step into deeper water right now. I am still a precalculus student and so, it wouldn't make sense to undertake such advanced math material. It is very fascinating, nonetheless.

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wow!!

Moo

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