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

[YoshiMoshi]

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

 

[Dick]

Well, there's Hausdorff dimension. But it doesn't mean much in terms of number of coordinates. Is that what you are talking about?

 

[HallsofIvy]

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)?

 

[haruspex]

Fractional dimensions arise in chaos theory (fractals) but that's not in the same sense as you describe.