R^(1/2) Question, half dimension space meaning?

In summary, the conversation is about the different dimensions represented by R, with R^2 being two-dimensional, R^3 being three-dimensional, and so on. The concept of R^(3/2) or other half dimensions is mentioned, with the question of whether there is any meaning or visualization for this type of space. The only reference to R^(3/2) is in relation to being halfway between R^1 and R^2. The speaker also mentions Hausdorff dimension, but it is noted that it doesn't have a direct connection to the number of coordinates. Chaos theory is also briefly mentioned as a possible source of fractional dimensions.
  • #1
YoshiMoshi
226
8

Homework Statement


I know some people use R to mean all numbers in only one dimension which span a line. R^2 meaning numbers with two dimensions that span a plane. R^3 meaning three dimensional numbers that span three dimensional space. I'm not really sure if I worded that correctly but I think you know what I'm saying. So what's the meaning/representation of R^(3/2) or other half dimensions? Where R^(3/2) is half way between R^1 and R^2. I was just wondering if this currently has any meaning or visualization of half a dimensional space.

Homework Equations

The Attempt at a Solution

 
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  • #2
Well, there's Hausdorff dimension. But it doesn't mean much in terms of number of coordinates. Is that what you are talking about?
 
  • #3
YoshiMoshi said:

Homework Statement


I know some people use R to mean all numbers in only one dimension which span a line. R^2 meaning numbers with two dimensions that span a plane. R^3 meaning three dimensional numbers that span three dimensional space. I'm not really sure if I worded that correctly but I think you know what I'm saying. So what's the meaning/representation of R^(3/2) or other half dimensions? Where R^(3/2) is half way between R^1 and R^2. I was just wondering if this currently has any meaning or visualization of half a dimensional space.

Homework Equations

The Attempt at a Solution

Where did you see reference to R^(3/2)?
 
  • #4
Fractional dimensions arise in chaos theory (fractals) but that's not in the same sense as you describe.
 

1. What does R^(1/2) represent in mathematics?

R^(1/2) represents the square root of the set of real numbers (R). It is a way to denote a half-dimension space.

2. How do you interpret a half-dimension space?

A half-dimension space is a mathematical concept that represents a space with only half of the usual dimensions. In the case of R^(1/2), it represents a space with only one-half dimension, which is essentially a one-dimensional space.

3. What is the significance of R^(1/2) in scientific applications?

R^(1/2) is often used in scientific applications to represent a space that is restricted in some way, such as only allowing one type of motion or having a limited number of dimensions. It can also be used to simplify complex mathematical models.

4. How is a half-dimension space different from a regular dimension space?

A half-dimension space is different from a regular dimension space in that it has fewer dimensions, making it simpler to work with mathematically. It is often used to represent physical systems that are restricted in some way, such as having limited motion or interactions.

5. Can R^(1/2) be extended to other dimensions?

Yes, R^(1/2) can be extended to other dimensions by using different fractional exponents. For example, R^(1/3) represents a one-third dimension space, and R^(1/4) represents a one-fourth dimension space. However, these fractional dimensions can be difficult to visualize and may not have practical applications.

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