How Many Ways Can You Fold a Map?
Physics for the Birds
@physicsforthebirdsAbout
I share things that I get excited about: math, physics, electronics, programming, music -- anything that requires taking things apart. My goal is to explain it simply enough that any 4th grader will be inspired and rigorously enough that any professor will be convinced. Patreon: https://patreon.com/PhysicsfortheBirds
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How many ways can you fold a map? The problem is pretty hard, even for computers. Become a Patreon member: https://www.patreon.com/PhysicsfortheBirds 0:00 Intro 2:07 Wrong ways of counting folds 3:54 How to fold a paper into thirds 4:44 An algorithm for counting 6:35 I rant about code 10:19 Map folds in robotics 12:47 Conclusion Overview of Folding Math: Geometric Folding Algorithms, Erik Demaine and Joseph O'Rourke Map Folding Intro: https://www.ams.org/journals/mcom/1968-22-101/S0025-5718-1968-0221957-8/S0025-5718-1968-0221957-8.pdf Multi-Dimensional Map-Folding: https://academic.oup.com/comjnl/article/14/1/75/356368 Sequences involving Map Folds: https://oeis.org/A001418 Modern Fold-Counting Code: https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a001/A001415.java Map Folding in Robotics: https://www.semanticscholar.org/paper/A-Geometric-Folding-Pattern-for-Robot-Coverage-Path-Zhu-Yao/670031bc76fecf4172e1c367de3259750a0323f9
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