1

This is a question from a tutorial for topology manifold. It is stated as: How many charts do you need to cover the Moebius strip that has a river printed on it?

The chart was defined as"Chart: -The (chosen) subset of the d-dimensional reals that a topological manifold maps to"

I really want to put images here to help clarify but I don't have enough reputation to add images.

this question shows up from 9:40 to 13:42 in this tutorial: https://www.youtube.com/watch?v=ghfEQ3u_B6g&t=766s&ab_channel=TheWE-HeraeusInternationalWinterSchoolonGravityandLight

The answer is two but it didn't explain why.

Thanks!

Alex Ravsky
  • 90,434
Nicole
  • 11
  • 1
    Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos Sep 10 '20 at 06:57
  • 1
    Please give us some more context. In particular, it would be ideal if potential answerers didn't have to sit through a video tutorial. Could you please state the problem in detail, summarize the answer given (i.e. list the steps of the proof if one is provided), and make explicit exactly what it was that you found confusing? – Ben Grossmann Sep 10 '20 at 07:07
  • I answered a similar question in https://math.stackexchange.com/questions/2103593/how-can-we-prove-that-no-single-chart-can-cover-the-moebius-strip-but-that-two-s/4780868#4780868 – Azilu Oct 04 '23 at 17:41

1 Answers1

2

You can easily cover the Möbius strip with two (overlapping) rectangles. Those are your charts.

Ted Shifrin
  • 115,160