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

  • Thread starter Thread starter YoshiMoshi
  • Start date Start date
  • Tags Tags
    Dimension Space
Click For Summary

Homework Help Overview

The discussion revolves around the concept of half-dimensional spaces, specifically R^(3/2), and its meaning or representation in mathematical terms. Participants explore the implications of fractional dimensions in relation to traditional dimensional spaces like R, R^2, and R^3.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the meaning and visualization of R^(3/2) as a half-dimensional space. Some reference the concept of Hausdorff dimension and its relevance to fractional dimensions. Others inquire about the context in which R^(3/2) is mentioned.

Discussion Status

The discussion is ongoing, with participants providing insights into fractional dimensions and their applications, such as in chaos theory and fractals. There is no explicit consensus, but various interpretations and avenues for exploration are being considered.

Contextual Notes

Participants are navigating the complexities of dimensionality, particularly in relation to mathematical definitions and visualizations. The original poster expresses uncertainty about the terminology and seeks clarification on half dimensions.

YoshiMoshi
Messages
233
Reaction score
10

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

 
Physics news on Phys.org
Well, there's Hausdorff dimension. But it doesn't mean much in terms of number of coordinates. Is that what you are talking about?
 
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)?
 
Fractional dimensions arise in chaos theory (fractals) but that's not in the same sense as you describe.
 

Similar threads

Undergrad Round 3-sphere symmetries as subspace of 4D Euclidean space
  • · Replies 6 ·
Replies
6
Views
2K
Where Did ##(n−r+1)^{th}## Come From in Binomial Expansion?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Chunks of action smaller than Planck's constant
  • · Replies 2 ·
Replies
2
Views
1K
Number of ways of arranging 7 characters in 7 spaces
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Unit vectors -- How can they be dimensionless?
  • · Replies 2 ·
Replies
2
Views
2K
Find largest number of linearly dependent vectors among these 6 vectors
  • · Replies 14 ·
Replies
14
Views
7K
Is (y + z)x1 = (y1 + z1)x the equation of a straight line in 3D space?
  • · Replies 17 ·
Replies
17
Views
3K
Questions about linear independent and spanning set and basi
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad What does the equation dΩ32 = dr2 + r2dΩ22 mean in terms of flat space?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate What does the metric of a 6D space with 3 compactified dimensions look like?
  • · Replies 20 ·
Replies
20
Views
3K