• Weizmann Institute of Science logo

Flexagons and the Math Behind Twisted Paper

Learn how to make flexagons - beautiful and unique paper constructions - and explore the math behind them.

7,244 enrolled on this course

Flexagons and the Math Behind Twisted Paper
  • Duration

    3 weeks
  • Weekly study

    2 hours
  • 100% online

    Learn at your own paceHow it works
  • Unlimited

    $23.33/monthLearn more

Discover the unusual math of twisted strips of paper

Flexagons are twisted strips of folded paper, which reveal their properties when flexed.

This online course will explain what flexagons are, their history and their naming conventions. You’ll find out how to create your own flexagons and be able to share them with our global community of learners.

You’ll also explore mathematical fields that provide tools to analyze flexagons, including topology and graph theory and learn about Möbius strips, Tuckermann diagrams and more.

Download video: standard or HD

Skip to 0 minutes and 5 seconds A mathematician is an adventurer, an explorer in an imaginary world full of secrets, equipped only with an inquisitive mind and a twinkle in his eye. Hello, I’m Dr. Yossi Elran and in this course we’re going to study some amazing objects - Flexagons! Flexagons are twisted strips of paper, assembled in such a way, that they have more than two sides, creating the most unusual properties! Throughout the course, we’re going to make and explore some of these fascinating, paper constructions, and by the end of the course, you’ll be able to create your own flexagons and understand some of the fun math behind them. We’re in for a real treat! Click on ‘Join’ to join.

What topics will you cover?

  • The invention of flexagons
  • How to make flexagons
  • Cyclic and non-cyclic flexagons
  • Advanced flexagons
  • Möbius strips and their surprising properties
  • The math behind flexagons, Möbius strips and knotted paper bands

When would you like to start?

Start straight away and learn at your own pace. If the course hasn’t started yet you’ll see the future date listed below.

  • Available now

Learning on this course

You can take this self-guided course and learn at your own pace. On every step of the course you can meet other learners, share your ideas and join in with active discussions in the comments.

What will you achieve?

By the end of the course, you‘ll be able to...

  • Produce, create and fold Flexagons and Mobius Strips
  • Explore flexagons and discover some of their unique properties
  • Synthesize your knowledge and discover links between different mathematical tools

Who is the course for?

This course is aimed at learners who enjoy being creative, solving puzzles, folding paper and revealing hidden mathematics. It will be especially useful for parents or teachers looking to inspire a love of math and do fun math activities with young people.

Who will you learn with?

I'm a recreational mathematician and metagrobologist and head our institute's technology in education unit. I have a Ph.D. in theoretical quantum chemistry, and think math and science are really cool!

Who developed the course?

Davidson Institute of Science Education at the Weizmann Institute of Science

The Weizmann Institute of Science is one of the world’s leading multidisciplinary basic research institutions in the natural and exact sciences. The Davidson Institute of Science Education is the educational arm of the Weizmann Institute.

Recommended

Ways to learn

Upgrade this course

Unlimited

Basic access

Choose the best way to learn for you!

$49

$23.33/month

Billed at $279.99 for a year

Free

Unlock your expertiseEndless possibilities!Try before you upgrade
Access to this courseticktickLimited to 3 weeks
Access to ALL eligible short courses with additional benefits, for a yearcrosstickcross
Discuss your learning in commentstickticktick
Tests to check your learningticktickcross
Certificate when you're eligiblePrinted and digitalDigital onlycross
Join and Upgrade

Ways to learn

Buy Unlimited to access this course and hundreds of other short courses for a year or Upgrade just this course for extra benefits. Or, join with basic access.

Unlimited

$23.33/month

Billed at $279.99 for a year

Endless possibilities!

  • Access to this course
  • Access to ALL eligible short courses with additional benefits, for a year
  • Discuss your learning in comments
  • Tests to boost your learning
  • Digital certificate when you're eligible

Upgrade this course

$49

Unlock your expertise

  • All of the above* for this course only, plus a printed certificate when you’re eligible

*Excludes access to all eligible short courses with additional benefits for a year

Basic access

Free

Try before you buy

  • Limited access to course content for 3 weeks

Find out more about certificates, Upgrades or Unlimited.

Find out more about certificates, Upgrades or Unlimited.

Learning on FutureLearn

Your learning, your rules

  • Courses are split into weeks, activities, and steps, but you can complete them as quickly or slowly as you like
  • Learn through a mix of bite-sized videos, long- and short-form articles, audio, and practical activities
  • Stay motivated by using the Progress page to keep track of your step completion and assessment scores

Join a global classroom

  • Experience the power of social learning, and get inspired by an international network of learners
  • Share ideas with your peers and course educators on every step of the course
  • Join the conversation by reading, @ing, liking, bookmarking, and replying to comments from others

Map your progress

  • As you work through the course, use notifications and the Progress page to guide your learning
  • Whenever you’re ready, mark each step as complete, you’re in control
  • Complete 90% of course steps and all of the assessments to earn your certificate

Want to know more about learning on FutureLearn? Using FutureLearn

Learner reviews

Learner reviews cannot be loaded due to your cookie settings. Please and refresh the page to view this content.

Do you know someone who'd love this course? Tell them about it...

You can use the hashtag #FLflexagon to talk about this course on social media.