What was Euclid really doing? | Guest video by ⁨@bensyversen

2025-09-18

[public] 123K views, 17.2K likes, dislikes audio only

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

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