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2025 34 min
What role were ruler and compass constructions really serving? Check out Ben's channel: @bensyversen Interview with the author of this video: https://youtu.be/VohYM99j8e0 Supporters get early views of new videos: https://3b1b.co/support Written, produced, edited, and animated by Ben Syversen Additional editing: Jack Saxon 3d Blender model: Jan-Hendrik Müller Additional Blender help: Thibaut Modrzyk (@Deepia) Illustrations: Alex Zepherin/DonDada Studio Camera: Giacomo Belletti Drums: Jeremy Gustin Additional music from Epidemic Sound Special thanks to Viktor Blåsjö: https://intellectualmathematics.com/opinionated-history-of-mathematics/ Lean footage is borrowed from Alex Kontorovich’s lecture series on formal Euclidean geometry: https://www.youtube.com/playlist?list=PLs6rMe3K87LEkc2nd2VZVyLfgJH0Rgage References/Recommended reading: Euclid’s Elements: Visual edition of Book 1: https://intellectualmathematics.com/dl/Elements.pdf Euclid’s Elements in full: https://farside.ph.utexas.edu/books/Euclid/Elements.pdf The Thirteen Books of The Elements, translated with introduction and commentary by Sir Thomas L. Heath Commentary and academic papers: A Commentary on the First Book of Euclid’s Elements, Proclus, translated by Glenn R. Morrow Operationalism: An Interpretation of the Philosophy of Ancient Greek Geometry, Viktor Blåsjö: https://link.springer.com/article/10.1007/s10699-021-09791-4 The Euclidean Diagram, Kenneth Manders A New Look at Euclid’s Second Proposition, Godfried Toussaint https://www-cgrl.cs.mcgill.ca/~godfried/teaching/dm-reading-assignments/Euclid-Second-Proposition-Math-Intell.pdf Logic of Ruler and Compass Constructions, M. Beeson https://www.michaelbeeson.com/research/papers/Cambridge.pdf Euclid’s Fourth Postulate, Vincenzo De Risi https://www.cambridge.org/core/journals/science-in-context/article/abs/euclids-fourth-postulate-its-authenticity-and-significance-for-the-foundations-of-greek-mathematics/DD7EB8AFEDD350A0A8B0BE714D74D2EE Some related books: Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace, Leonard Mlodinow The Geometry of Rene Descartes, Rene Descartes Timestamps: 0:00 - About guest videos 0:54 - Why ruler and compass? 2:38 - Diagrams as part of the proof 8:08 - Geometry as philosophy 15:21 - Mistakes in diagrammatic reasoning 19:07 - The parallel postulate 28:34 - Letting go of the ruler and compass ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly. Mailing list: https://3blue1brown.substack.com Twitter: https://twitter.com/3blue1brown Bluesky: https://bsky.app/profile/3blue1brown.com Instagram: https://www.instagram.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Facebook: https://www.facebook.com/3blue1brown Patreon: https://patreon.com/3blue1brown Website: https://www.3blue1brown.com
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