What was Euclid really doing? | Guest video by Ben Syversen

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