Where is the Centroid of a Moebius Strip? [SOLVED]

  • Context: Graduate 
  • Thread starter Thread starter kureta
  • Start date Start date
  • Tags Tags
    Centroid
Click For Summary
SUMMARY

The centroid of a Moebius strip can be defined within a Euclidean 2D plane by considering its topological equivalence to a circle. By cutting a disk from the plane and replacing it with the Moebius strip, one can analyze its properties, including interior, exterior, border, area, and centroid. The centroid's location is determined by the strip's width and radius, providing a clear mathematical framework for understanding this unique geometric shape.

PREREQUISITES
  • Understanding of topology, specifically the properties of a Moebius strip
  • Familiarity with Euclidean geometry and 2D space concepts
  • Knowledge of geometric properties such as area and centroid calculations
  • Basic mathematical skills for manipulating geometric formulas
NEXT STEPS
  • Research the properties of topological surfaces, focusing on the Moebius strip
  • Study centroid calculation methods for complex shapes in 2D geometry
  • Explore the implications of cutting and sewing in topology
  • Investigate applications of Moebius strips in mathematical modeling and design
USEFUL FOR

Mathematicians, geometry enthusiasts, educators, and students interested in advanced geometric concepts and topological properties.

kureta
Messages
12
Reaction score
0
[SOLVED] centroid of a moebius strip

Since the edge of a moebius strip is topologically equivalent to a circle, we can cut a disk form an euclidean 2D plane and sew a moebius strip on its place. Now we have a 2D space with a circular-edged moebius strip added. And now this strip is a 2D region in 2D space and we can talk abut its interior, exterior, border, area, centroid, etc. Where is this moebius strip's centroid? (we should be able to define it with the strip's width and radius.
 
Physics news on Phys.org
I don't mean to be rude or arrogant (because maybe all my questions were stupid and not worth spending time on) but I've asked 4 questions in this forum and the best answer I got (if any) was "err... I knew this but i forgot". Of course this is not a Q&A forum. This is a discussion forum. But after a couple of tries people gave up discussing too. So I will mark this thread as "solved" and never ask a question again (like anyone would care). I wish all academicians here a successful academical career.
 

Similar threads

Graduate Handles and non-orientible 3D manifolds
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Find an explicit formula for this n-sum problem
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Electric and magnetic field lines in a plane wave of finite extent
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Continuation of Coordinates Across Black Hole Horizons
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Twistors and celestial holography
  • · Replies 21 ·
Replies
21
Views
6K
Graduate Differential Topology: Essential Concepts Explained
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Where is Laplace's Equation Valid in Different Domains?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Calculating the density of optimally packed spheres
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Real life engineering problem I or guidance
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Quantum Field theory vs. many-body Quantum Mechanics
  • · Replies 36 ·
2
Replies
36
Views
6K