The Simplest Unsolvable* Ancient Problem

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Go to https://cyberghostvpn.com/BenSyversen to get 84% off from this video's sponsor, CyberGhost VPN, with 4 months free! Tell me more about yourself and join my mailing list! https://forms.gle/r8fKCGtDTt2KbftA8 Ancient Greek mathematicians wrestled for centuries with a seemingly pointless problem that led them to rich mathematical discoveries. ____ Join my Patreon for early previews, ad free versions of the videos, and to support the channel! https://patreon.com/BenSyversen Sign up for my mailing list! https://ben-syversen.kit.com Or, support me on Ko-Fi with a one-time donation: https://ko-fi.com/bensyversen ______ Credits: Written, recorded, edited, animated by Ben Syversen Illustrations by Alex Zepherin/Don Dada Studios Additional illustrations by Kendall Eddy Special thanks to Viktor Blåsjö for his feedback and for answering my many questions about this topic. Thanks to @Aleph0 for letting use a few clips from his wonderful recent video about the Twin Prime Conjecture: https://youtu.be/egA9K_R5pkg?si=5clrcZDR0CZkn2bs Additional thank you to @SimonUbsdell and @Deepia-ls2fo for helping me with Blender! ______ Sources and recommended reading: Operationalism: An Interpretation of the Philosophy of Ancient Greek Geometry, Viktor Blåsjö: https://link.springer.com/article/10.1007/s10699-021-09791-4 “Science Awakening,” B.L. Van der Waerden “A History of Greek Mathematics,” Thomas Heath “The Ancient Tradition of Geometric Problems” Wilbur Knorr For a good summary of the conics of Apollonius, which my parabola explanation is based on, read: “A History of Mathematics, An Introduction” by Victor J Katz Music from Epidemic Sound Except where indicated on screen, additional images are public domain or licensed via Envato Elements Time stamps: 00:00 Intro 01:30 History of Numbers 05:03 Straightedge and Compass Constructions 07:35 Doubling the Cube 10:22 Archytas' Solution 15:18 Eudoxus' Solution 15:37 Menaechmus' Solution 20:26 Conic Sections and Conic Compasses 22:15 Other Solutions and Other Problems 23:59 The Delians 24:32 Modern Analogies 26:48 A Request