What is a Convex Hull and How Does it Relate to Positive Definite Objects?

  • Context: Undergrad 
  • Thread starter Thread starter Tenshou
  • Start date Start date
  • Tags Tags
    Convex
Click For Summary

Discussion Overview

The discussion revolves around the concept of a convex hull, its definition, and its relationship to convex sets and positive definite objects. Participants explore the geometric interpretation of convex hulls and seek clarification on the properties that define convex sets.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks for an explanation of what a convex hull is and its purpose.
  • Another participant defines the convex hull as the smallest convex set containing a given set of points and encourages experimentation with drawing points to visualize the concept.
  • A participant expresses understanding of the geometric shapes formed by two, three, and four points but questions why these shapes are considered convex sets, specifically asking about the relationship between dimensions.
  • The same participant inquires why shapes like circles or squares are not considered convex hulls or convex sets.
  • Another participant speculates that convex sets may relate to positive definite objects but admits uncertainty about this connection.

Areas of Agreement / Disagreement

There is no consensus on the definition of convex sets or the relationship between convex hulls and positive definite objects. Multiple viewpoints and questions remain unresolved.

Contextual Notes

Participants express uncertainty about the definitions and properties of convex sets, indicating a need for clarification on these concepts. The discussion does not resolve the questions posed regarding the nature of convexity in various shapes.

Tenshou
Messages
153
Reaction score
1
I don't understand what a convex hull is and what it does. does anyone think they can explain what exactly it is?
 
Physics news on Phys.org
The convex hull of A is the smallest convex set that contains A.

If you want to see what it is, then you should experiment. Draw 2 points on a sheet of paper. What do you think that the convex hull is?
What about 3 points?
What about 4 points?
 
Thank you micromass, I think I get it... I think I understand that the two points should be a line segment, 3 points a triangle and 4 a tetrahedron. I just don't get why those are convex sets, is it because the dimension of the line segment(or the other stuff) is equal to the dimension of the plane that it sits in? Why isn't a circle a convex hull or a square? are they convex sets?
 
Tenshou said:
Thank you micromass, I think I get it... I think I understand that the two points should be a line segment, 3 points a triangle and 4 a tetrahedron. I just don't get why those are convex sets, is it because the dimension of the line segment(or the other stuff) is equal to the dimension of the plane that it sits in? Why isn't a circle a convex hull or a square? are they convex sets?

what is the definition od a convex set?
 
I do not know, but I think it talks about some set which is Positive Definite "object", but I am not sure :/ I mean just thinking about convex things that is what I think it could be.
 

Similar threads

Graduate Question regarding proof of convex body theorem
  • · Replies 21 ·
Replies
21
Views
2K
Undergrad How can I test for positive semi-definiteness in matrices?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Image construction with concave and convex mirrors
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Open interval or Closed interval in defining convex function
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Spherical aberration in Biconvex and Plano Convex lenses
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Assumptions about the convex hull of a closed path in a 4D space
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Different norms and how L1 leads to the sparsest solution
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How to practically perform first-principles calculations on Li-ion batteries?
  • · Replies 0 ·
Replies
0
Views
2K
Graduate What are the equality conditions for proving strict convexity?
  • · Replies 1 ·
Replies
1
Views
2K
How do I show that a subset is closed and convex?
  • · Replies 8 ·
Replies
8
Views
3K