The development of non-Euclidean geometry is often presented as a high point of 19th century mathematics. The real story is more complicated, tinged with sadness, confusion and orthodoxy, that is reflected even the geometry studied today. The important insights of Gauss, Lobachevsky and Bolyai, along with later work of Beltrami, were the end result of a long and circuitous study of Euclid's parallel postulate. But an honest assessment must reveal that in fact non-Euclidean geometry had been well studied from two thousand years ago, since the geometry of the sphere had been a main concern for all astronomers.
This lecture gives a somewhat radical and new interpretation of the history, suggesting that there is in fact a much better way of thinking about this subject, as perceived already by Beltrami and Klein, but largely abandoned in the 20th century. This involves a three dimensional linear algebra with an unusual inner product, looked at in a projective fashion. This predates and anticipates the great work of Einstein on relativity and its space-time interpretation by Minkowski.
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Screenshot PDFs for my videos are available at the website wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at www.researchgate.net/profile/...
My blog is at njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!
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Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: / playlist
list=PL8403C2F0C89B1333
Year 9 Maths: • Year9Maths
Ancient Mathematics: • Ancient Mathematics
Wild West Banking: • Wild West Banking
Sociology and Pure Mathematics: • Sociology and Pure Mat...
Old Babylonian Mathematics (with Daniel Mansfield): / playlist
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: • MathHistory: A course ...
Wild Trig: Intro to Rational Trigonometry: • WildTrig: Intro to Rat...
MathFoundations: • Math Foundations
Wild Linear Algebra: • Wild Linear Algebra
Famous Math Problems: • Famous Math Problems
Probability and Statistics: An Introduction: • Probability and Statis...
Boole's Logic and Circuit Analysis: • Boole's Logic and Circ...
Universal Hyperbolic Geometry: • Universal Hyperbolic G...
Differential Geometry: • Differential Geometry
Algebraic Topology: • Algebraic Topology
Math Seminars: • MathSeminars
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And here are the Wild Egg Maths Playlists:
Triangle Centres: • ENCYCLOPEDIA OF TRIANG...
Six: An elementary course in pure mathematics: • Six: An elementary cou...
Algebraic Calculus One: • Algebraic Calculus One
Algebraic Calculus Two: • Algebraic Calculus Two
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