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Currently Playing: The Samurai-Toilet Paper Problem

If a samurai cuts a rolled-up mat and you found it unrolled, what angle did he cut? The answer is in the Archimedean Spiral. Become a Patreon member: https://www.patreon.com/PhysicsfortheBirds 0:00 Introduction 1:25 Samurai Problem 3:48 Three ways to find Length 7:59 Samurai Problem Answer 8:38 Experiment 10:01 Papyrus Problem Joan's Paper Roll Problem: https://web.archive.org/web/20131103150639/http://mtl.math.uiuc.edu/special_presentations/JoansPaperRollProblem.pdf Archimedean spiral: https://mathworld.wolfram.com/ArchimedesSpiral.html Using Archimedean spirals on scrolls: https://archiv.ub.uni-heidelberg.de/propylaeumdok/1713/1/Hoffmann_Die_Laenge_des_P.Spiegelberg_1994.pdf Using Autocorrelation on scrolls: https://www.dialoguejournal.com/wp-content/uploads/sbi/articles/Dialogue_V43N04_413.pdf Accuracy of length prediction: https://pmc.ncbi.nlm.nih.gov/articles/PMC7577460/