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Unit of Four Dimensional Space Measurement?

  1. Feb 7, 2013 #1
    I have been wondering what type of measurement is used to measure the space inside of a four dimensional (space, not time) object. For example, a one dimensional line's distance gets measured, a two dimensional object's area gets measured, and a three dimensional object's volume gets measured, but what type of unit do four dimensional objects get? I am not looking for a specific measurement, such as inches, liters, or square centimeters. What is the category that four dimensional measurements fall under? I have looked all over the internet, but could not find an answer, so I decided Physics Forums looked like a good place to ask.
  2. jcsd
  3. Feb 8, 2013 #2
    Four dimensional Lebesgue measure.

    It might also be called hypervolume.
  4. Feb 8, 2013 #3

    Simon Bridge

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    Welcome to PF;
    I was going to go with "hypervolume".
    You gotta realize that at some point you will run out of special words for the measure - what if you have 23 space dimensions? Now what do you call it?

    Technically the dimensions can have any units though ... so the area of the 2D shape on a v-t graph is a displacement. The meaning of the object, in physics, depends on what it is modelling.
  5. Feb 8, 2013 #4


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    the notion of volume generalizes to higher dimensions in exactly the same way that area extends length and 3 dimensional volume extends area.

    I found it instructive to realize that the Pythagorean theorem works in three dimensions exactly as in two. The same applies in four or more.
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