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⬣ ABOUT ⬣
Despite being easy to state, the problem of constructing regular polygons confounded the Ancient Greeks. It took over 2000 years to make progress, and in this video we’ll trace a path through history to learn what innovations allowed more polygons to be constructed.

⬣ TIMESTAMPS ⬣
00:00 - Introduction
01:47 - Ancient Constructions
08:14 - What the Ancient Greeks Lacked
11:20 - From Geometry to Numbers
16:28 - From Numbers to Equations
21:58 - From Equations to the Complex Plane
31:48 - Gaussian Periods
36:10 - Final Construction

⬣ INVESTIGATORS ⬣
Nothing for you here. Sorry!

⬣ REFERENCES ⬣
Euclid's constructions mentioned at 3:50:
Perpendicular lines: http://aleph0.clarku.edu/~djoyce/elem...
Duplicate angles: http://aleph0.clarku.edu/~djoyce/elem...
Alternate angles: http://aleph0.clarku.edu/~djoyce/java...
Parallel lines: http://aleph0.clarku.edu/~djoyce/elem...
Parallelogram properties: http://aleph0.clarku.edu/~djoyce/elem...

The Thirteen Books of Euclid’s Elements. T. L. Heath (1908)

J. Derbyshire: "Unknown Quantity: A Real and Imaginary History of Algebra" Joseph Henry Press (2006)

Al-Kamil treats irrational quantities as numbers in their own right
H. Selin, U. D'Ambrosio: "Mathematics Across Cultures: The History of Non-Western Mathematics" Springer (2000)

Al-Mahani’s definition of rational and irrational
M. Galina: "The theory of quadratic irrationals in medieval Oriental mathematics" Annals of the New York Academy of Sciences 500 (1987) 253-277.

Al-Khwaizmi quadratic equations
Al-Jabr - Al Khwarizmi

Sridhara’s method
D. E. Smith: “History of Mathematics” Vol 2 Dover (1925)

Tombstone story
C. W. Dunnington: "Carl Friedrich Gauss: Titan of Science" Hafner Publishing (1955)

⬣ CREDITS ⬣
Intro music by Tobias Voigt. Other music by Danijel Zambo and Apex Music.

Image Credits
Euclid
https://cdn.britannica.com/46/8446-05...
Arithmetica
https://upload.wikimedia.org/wikipedi...
Al-Jabr
https://upload.wikimedia.org/wikipedi...
Gauss
https://upload.wikimedia.org/wikipedi...
Heptadecagon Construction
https://upload.wikimedia.org/wikipedi...
Gauss Tombstone
https://upload.wikimedia.org/wikipedi...