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This content is taken from the Davidson Institute of Science Education at the Weizmann Institute of Science's online course, Flexagons and the Math Behind Twisted Paper. Join the course to learn more.

Skip to 0 minutes and 0 seconds Hello and welcome to our course on flexagons, brought to you by the Davidson Institute of Science Education, the educational wing of the Weizmann Institute of Science in Israel. It’s our job to bring math and science to the public, and that’s what I hope to do together with you in this Future Learn course. So, join me on a fantastic journey into one of the most curious, mathematical objects there is. This is a flexagon. A flexible, two-dimensional sheet of paper, that has more than two sides. This flexagon is called a tri-hexa-flexagon. It is shaped like a hexagon, and has three sides.

Skip to 0 minutes and 35 seconds What I’m doing here with my fingers is called “flexing” the flexagon, exposing the different sides, or as we shall call them, faces, one by one. This tri-hexa-flexagon is cyclic and goes on forever, but not all flexagons are like this. This is a tetra-tetra-flexagon, shaped like a quadrilateral with four faces, and not cyclic. The family of flexagons is huge. Here are some from my collection. We’re going to spend the next three weeks together, studying these flexagons, and there is still lots to discover, properties that even mathematicians haven’t found yet, so maybe you’ll make a real contribution to the field. The way we’re going to do this course is just by going step by step through the 3 weeks of our course.

Skip to 1 minute and 16 seconds The first week we’ll dedicate to finding out just what are flexagons, and learn about some of the problems we run into, when trying to define them. We will also meet the most basic flexagons. In the second week we’ll make and study some of the advanced flexagons, and in the third week we’ll delve into Möbius strips, their connection with flexagons, and a bit more about the math behind both. The course is full of activities, videos, articles and quizzes. Even more important though are your comments, and the discussions throughout the course, so please don’t be shy and post a lot! I’ll be there to help along the way, but what makes me really excited is when you help each other.

Skip to 1 minute and 55 seconds That kind of social interaction within the course really mimics a proper classroom and benefits everyone. Throughout the course there will be templates that you can download and print out, so that you can make your own flexagons. Are you ready? Then, let’s go!

Meet lead educator Dr Yossi Elran

Welcome from Dr Yossi Elran

This course is all about flexagons and the math behind twisted strips of paper. Each week will have a theme, and we’ll learn about it through videos, articles and discussion. There will also be other optional tasks and exercises you can try to enhance your learning. Each week builds on the last, so we strongly recommend you work through each week in order. Each week should take you 2 to 3 hours to complete if you do all the tasks. There are quizzes in Weeks 1 & 2 and a test in Week 3 for learners who upgrade.

Before we start - print the templates we will be using!

Unlike other online courses, this is a “hands-on” course. You will be making flexagons from paper templates throughout the course. The templates can be downloaded and printed on a colour printer at the relevant step, or, you can print out all the templates in advance from the link below (‘related files’).

Using FutureLearn

If this is your first FutureLearn course, you may find it useful to watch this ‘how it works’ video guide. Even if you’re an old hand, you may still like to read this FutureLearn blog post which explains all the recent changes to the in-course navigation. We also recommend reading six tips and tools for social learning on FutureLearn to get the most out of the interactive and social learning features of this course.

Follow Yossi

To see Yossi’s comments in your activity feed or when using the ‘following’ filter in discussions, visit his FutureLearn profile and click “follow”.

You can also follow us on other social media, Facebook and Twitter, by using the hashtag #FLflexagon. In fact, you will be using social media quite extensively during the course to post images of your work, so please, don’t forget the Hashtag! When posting or sharing, make sure your posts are set to ‘public’, but please review your privacy settings to make sure you are only allowing access to what you want.

I will also be following you, reading your comments and actively participating in the discussions - for the first three weeks of the course. After that, unfortunately, I’m unable to monitor the course - because I’ll be running others, but you are still encouraged to continue discussions with other course members!

Get extra benefits, upgrade your course

You can now get extra benefits by upgrading this course, including:

Unlimited access to the course: Go at your own pace with unlimited access to the course for as long as it exists on FutureLearn.
Access to tests: Ensure you’ve mastered the material with access to tests on the course.
A Certificate of Achievement: To help you demonstrate your learning we’ll send you a Certificate of Achievement when you become eligible.

Find out more

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This video is from the free online course:

Flexagons and the Math Behind Twisted Paper

Davidson Institute of Science Education at the Weizmann Institute of Science