The Simplest Unsolvable* Ancient Problem

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Ancient Greek mathematicians wrestled for centuries with a seemingly pointless problem that led them to rich mathematical discoveries.
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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, and @twoswap for help with some LaTeX animations.
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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

3d print your own conic compass! https://www.instructables.com/The-Lost-Art-of-the-Conic-Section-Compass/

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