Waste less time on Facebook — follow Brilliant.
×

Choose Your Own Möbius Adventure

I thought it might be fun to share a set of problems on Möbius strips. These interesting objects have several surprising and wonderful properties, and best of all, they're very easy to make.

To make it more fun, try making your own Möbius strip and experiment with it.

Instructions for making a Möbius strip

  1. Cut a long strip of paper. You'll want it to be several cm across, and it should be much longer than its width.
  2. Bring the ends together to make a simple loop.
  3. Before attaching them together, add a single half-twist to one side of the strip (as in the image above).
  4. Enjoy your Möbius strip!

Note by Arron Kau
3 years, 9 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

I have always seen this performed as a magic trick from my childhood. I was amazed. Later, I came to know about the secret from a children's magic book. In my college I have only learnt mathematics which is limited to electrical engineering. I want to know exactly which branch of mathematics deals with this types of shapes and twists. is it topology. I have never been formally introduced to this subject. an u suggest a good book.

Pranjit Handique - 3 years, 9 months ago

Log in to reply

I don't know about topology beyond a lay understanding, but as a kid I read a book called One Two Three... Infinity and enjoyed it.

It talks about the Möbius strip, but then moves onto the topology twisting spaces in 4 dimensions. It also talks about other various subjects like infinite series, and the different types of infinity (\(\aleph _{0}, \aleph _{1}\), etc). It's written from a lay perspective though, you may be looking for a more serious exploration.

Dan Krol - 3 years, 9 months ago

Log in to reply

I think it would be interesting too.but i have kind of problem with the questions which i should choose the correct answer(I mean i prefer to write the answer...)

Narges Gholinejad - 3 years, 9 months ago

Log in to reply

Narges, for some of these problems (especially 3 and 4), multiple choice was the only way to really make the questions work.

If I could ask, why do you like the other kind of questions more? Is it because you get multiple tries?

Arron Kau Staff - 3 years, 9 months ago

Log in to reply

oh,i feel ashame to say what is my problem.....but let me say;when i choose,it doesn't work!i click on the answer but nothing happen :- (

Narges Gholinejad - 3 years, 9 months ago

Log in to reply

@Narges Gholinejad What browser are you using?

Taehyung Kim - 3 years, 9 months ago

Log in to reply

@Taehyung Kim internet explorer

Narges Gholinejad - 3 years, 9 months ago

Log in to reply

@Narges Gholinejad No wonder it doesn't work.

Ryan Soedjak - 3 years, 9 months ago

Log in to reply

@Ryan Soedjak i solved my problem with that......... anyway;thank you!

Narges Gholinejad - 3 years, 9 months ago

Log in to reply

Thanx, Dan. I will order for one right away.

Pranjit Handique - 3 years, 9 months ago

Log in to reply

Hello there

Thomas Godwin - 3 years, 9 months ago

Log in to reply

It's amazing shape in 3-D... one can iterate in single line without crossing. if cut in half, we get 2 mobius strips...

Anubhav Balodhi - 3 years, 9 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...