Complex numbers and curves | Math History | NJ Wildberger

In the 19th century, the study of algebraic curves entered a new era with the introduction of homogeneous coordinates and ideas from projective geometry, the use of complex numbers both on the curve and at infinity, and the discovery by the great German mathematician B. Riemann that topological aspects of complex curves were intimately connected with the arithmetic of the curves.

In this lecture we look at the use of homogeneous coordinates, stereographic projection and the Riemann sphere, circular points at infinity, Laguerre's projective description of angle, curves over the complex numbers and the genus of Riemann surfaces.

This meeting of projective geometry, algebra and topology led the way to modern algebraic geometry.

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Screenshot PDFs for my videos are available at the website http://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 https://www.researchgate.net/profile/...

My blog is at http://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 https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated.

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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 Mathematics  
Old Babylonian Mathematics (with Daniel Mansfield):    / playlist  
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History:    • MathHistory: A course in the History ...  
Wild Trig: Intro to Rational Trigonometry:    • WildTrig: Intro to Rational Trigonometry  
MathFoundations:    • Math Foundations  
Wild Linear Algebra:    • Wild Linear Algebra  
Famous Math Problems:    • Famous Math Problems  
Probability and Statistics: An Introduction:    • Probability and Statistics: an introd...  
Boole's Logic and Circuit Analysis:    • Boole's Logic and Circuit Analysis  
Universal Hyperbolic Geometry:    • Universal Hyperbolic Geometry  
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 TRIANGLE CENTERS  
Six: An elementary course in pure mathematics:    • Six: An elementary course in Pure Mat...  
Algebraic Calculus One:    • Algebraic Calculus One  
Algebraic Calculus Two:    • Algebraic Calculus Two  
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