Results 1 to 5 of 5

Math Help - Mathematical Dimensions

  1. #1
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Mathematical Dimensions

    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)?

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Sep 2008
    Posts
    28
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,
    Quote Originally Posted by magentarita View Post
    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).
    Last edited by Moo; September 13th 2008 at 05:07 AM. Reason: grammar ! o.O
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Smile wow!!

    Quote Originally Posted by bnay View Post
    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.

    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Smile Moo

    Quote Originally Posted by Moo View Post
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. What is the value of the dimensions?
    Posted in the Algebra Forum
    Replies: 6
    Last Post: March 2nd 2011, 02:45 AM
  2. Dimensions
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 19th 2010, 08:08 AM
  3. Dimensions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 5th 2009, 11:25 AM
  4. Dimensions
    Posted in the Geometry Forum
    Replies: 4
    Last Post: November 29th 2008, 08:27 AM
  5. Dimensions
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: October 3rd 2008, 09:24 AM

Search Tags


/mathhelpforum @mathhelpforum