Flexagons and the Math Behind Twisted Paper

Most FutureLearn courses run multiple times. Every run of a course has a set start date but you can join it and work through it after it starts. Find out more 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. You can use the hashtag #FLflexagon to talk about this course on social media.

Topics Covered

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

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Reviews summary

Fun flexagons and accessible math

Learners say this is a wonderful course that offers a perfect blend of hands-on paper folding and intriguing mathematical concepts. Many highlight the clear and easy-to-follow instructions, particularly praising the engaging and informative videos which make creating the flexagons accessible even for beginners. Students find the math explanations accessible and not intimidating, appreciating how the course makes math feel tangible and fun. It's frequently recommended as a fantastic resource for teachers and parents looking for educational activities for kids and students. However, some note that while the math is well-integrated, the depth is introductory and might feel lighter than expected for those seeking rigorous proofs or deep mathematical theory.

Videos are engaging and helpful.

"the videos were engaging and informative."

"The videos demonstrating the folding techniques were excellent."

"The video quality was good and the instructors explained things well."

"The videos were easy to pause and follow."

Fun, hands-on activity course.

"Perfect blend of hands-on activity and intriguing math."

"Great as a hands-on activity course."

"Engaging, unique, and surprisingly deep."

"Enjoyable course."

"A creative way to learn about mathematical concepts through paper folding."

"Loved the hands-on approach."

Great resource for parents and teachers.

"I especially appreciated the suggestions for activities to do with children."

"I've already used what I learned to create activities for my students."

"This is a fantastic resource for teachers and parents."

"Perfect for doing with older children or students."

Mathematical concepts explained simply.

"The mathematical concepts were explained in a way that was accessible without being overly simplistic."

"The math explanations, while introductory, were fascinating and well-integrated with the physical models."

"The math felt approachable and not intimidating at all."

"This course is brilliant for anyone who thinks they don't like math, it shows how fun and visual it can be."

Instructions for making flexagons are clear.

"The instructions for making the flexagons were clear and easy to follow..."

"The making process is well explained, though it took a couple of tries to get it right."

"The instructions were incredibly clear, making it easy to follow along with the folding."

"Simple materials, clear instructions, and a wonderful blend of craft and mathematics."

"Making the flexagons step-by-step with the videos was great."

Math section is introductory, not rigorous.

"The math side was a bit lighter than I expected, but still interesting."

"The math felt a bit disconnected from the folding at times, and didn't go into as much depth as I hoped based on the title."

"If you're looking for rigorous mathematical exploration, this might not be it."

"The 'math behind' felt superficial. I was hoping for more rigorous explanations or proofs."

"It's fun as a craft project, but the title might be slightly misleading for those seeking deep mathematical insight."

"The mathematical concepts were interesting, but I felt they could have been explored a bit further."

"It felt more like 'math appreciation' than 'math behind'."

Activities

Coming soon We're preparing activities for Flexagons and the Math Behind Twisted Paper. These are activities you can do either before, during, or after a course.