# Unit of Four Dimensional Space Measurement?

1. Feb 7, 2013

### Joshuame13

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. Feb 8, 2013

### micromass

Four dimensional Lebesgue measure.

It might also be called hypervolume.

3. Feb 8, 2013

### Simon Bridge

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.

4. Feb 8, 2013

### lavinia

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.