Scholar Sauce | What's the Deal with Euclid's Vth Postulate? (Part 1) 500 Subscribers Special! @scholarsauce | Uploaded December 2023 | Updated October 2024, 4 hours ago.
Thank you to our first 500 subscribers! Your support makes this channel possible. Please share this video with your friends and help us get to 1000!
In his book, the Elements written in 300 BCE, Euclid described planar geometry using five postulates or axioms. One of these axioms was considerably more complicated than the others and seemed to some to be likely provable as a theorem from the other four more natural postulates. But no ancient Greek was ever able to prove Euclid's fifth postulate and this question persisted for over 2000 years until it was finally resolved in the 19th century CE. It took 2000 years to confirm that indeed you cannot prove Euclid's fifth postulate from the other four, but this proof resulted in us learning of another type of plane geometry that is completely consistent and satisfies the first four of Euclid's postulates but not the fifth. This type of geometry is called hyperbolic geometry and weird stuff happens there: triangles have less than 180 degrees, similar triangles are congruent, and rectangles are nowhere to be found. This discovery inspired further advancements in geometry including Riemannian and semi-Riemannian geometry which is the mathematical framework that Albert Einstein used to develop general relativity and advance our understanding of gravity and the universe.
*Books*
_Foundations of Geometry_
Author: Gerard Venema
Link: pearson.com/en-us/subject-catalog/p/foundations-of-geometry/P200000006404/9780136845188
*Images*
_The Acropolis at Athens_
Artist: Leo von Klenze
License: Public Domain
Acquired: commons.wikimedia.org/wiki/File:Akropolis_by_Leo_von_Klenze.jpg
_Papyrus Fragment of Euclid's Elements_
Artist: Euclid
License: Public Domain
Acquired: math.ubc.ca/~cass/Euclid/papyrus/tha.jpg
_Euclid of Megara_
Artist: Justus van Gent
License: Public Domain
Acquired: commons.wikimedia.org/wiki/File:Euklid2.jpg
_Bronze Age Dwelling at Flag Fen_
Artist: Ian and Viv Hamilton
License: Public Domain
Acquired: en.m.wikipedia.org/wiki/File:Bronze_age_dwelling_at_Flag_Fen.JPG
_Modern Building_
Artist: Sharee Basinger
License: Public Domain
Acquired: publicdomainfiles.com/show_file.php?id=13969228218118
_1910 Ford-T_
Artist: Harry Shipler
License: Public Domain
Acquired: en.m.wikipedia.org/wiki/File:1910Ford-T.jpg
_Mercedes Benz Sports Car_
Artist: Alex Borland
License: Public Domain
Acquired: publicdomainpictures.net/en/view-image.php?image=256545&picture=mercedes-benz-sports-car
*Music*
Various Tracks from the YouTube Audio Library
Thank you to our first 500 subscribers! Your support makes this channel possible. Please share this video with your friends and help us get to 1000!
In his book, the Elements written in 300 BCE, Euclid described planar geometry using five postulates or axioms. One of these axioms was considerably more complicated than the others and seemed to some to be likely provable as a theorem from the other four more natural postulates. But no ancient Greek was ever able to prove Euclid's fifth postulate and this question persisted for over 2000 years until it was finally resolved in the 19th century CE. It took 2000 years to confirm that indeed you cannot prove Euclid's fifth postulate from the other four, but this proof resulted in us learning of another type of plane geometry that is completely consistent and satisfies the first four of Euclid's postulates but not the fifth. This type of geometry is called hyperbolic geometry and weird stuff happens there: triangles have less than 180 degrees, similar triangles are congruent, and rectangles are nowhere to be found. This discovery inspired further advancements in geometry including Riemannian and semi-Riemannian geometry which is the mathematical framework that Albert Einstein used to develop general relativity and advance our understanding of gravity and the universe.
*Books*
_Foundations of Geometry_
Author: Gerard Venema
Link: pearson.com/en-us/subject-catalog/p/foundations-of-geometry/P200000006404/9780136845188
*Images*
_The Acropolis at Athens_
Artist: Leo von Klenze
License: Public Domain
Acquired: commons.wikimedia.org/wiki/File:Akropolis_by_Leo_von_Klenze.jpg
_Papyrus Fragment of Euclid's Elements_
Artist: Euclid
License: Public Domain
Acquired: math.ubc.ca/~cass/Euclid/papyrus/tha.jpg
_Euclid of Megara_
Artist: Justus van Gent
License: Public Domain
Acquired: commons.wikimedia.org/wiki/File:Euklid2.jpg
_Bronze Age Dwelling at Flag Fen_
Artist: Ian and Viv Hamilton
License: Public Domain
Acquired: en.m.wikipedia.org/wiki/File:Bronze_age_dwelling_at_Flag_Fen.JPG
_Modern Building_
Artist: Sharee Basinger
License: Public Domain
Acquired: publicdomainfiles.com/show_file.php?id=13969228218118
_1910 Ford-T_
Artist: Harry Shipler
License: Public Domain
Acquired: en.m.wikipedia.org/wiki/File:1910Ford-T.jpg
_Mercedes Benz Sports Car_
Artist: Alex Borland
License: Public Domain
Acquired: publicdomainpictures.net/en/view-image.php?image=256545&picture=mercedes-benz-sports-car
*Music*
Various Tracks from the YouTube Audio Library
