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

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

#Geometry #Topology #MobiusStrip

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered 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"

Math	Appears 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

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 - 7 years, 4 months ago

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 Staff - 7 years, 4 months ago

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 - 7 years, 4 months ago

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 - 7 years, 4 months ago

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 - 7 years, 4 months ago

@Narges Gholinejad – What browser are you using?

Taehyung Kim - 7 years, 4 months ago

@Taehyung Kim – internet explorer

Narges Gholinejad - 7 years, 4 months ago

@Narges Gholinejad – No wonder it doesn't work.

Ryan Soedjak - 7 years, 4 months ago

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

Narges Gholinejad - 7 years, 4 months ago

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 - 7 years, 4 months ago

Hello there

Thomas Godwin - 7 years, 4 months ago

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

Pranjit Handique - 7 years, 4 months ago

Math	Appears 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}`	$\boxed{123}$