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CurvesSurfaces1: Affine and Projective Geometry, and the Problem of Lines

N J Wildberger from UNSW introduces a new series on Curves and Surfaces, aiming for a concrete and more geometrical approach to Algebraic Geometry. This introductory lecture introduces basic notation and terminology for affine and projective points, and associated vector spaces, using projective coordinates to solve standard problems in 2D geometry. Some of H. Grassmann's thinking is introduced in the context of products of projective row and column points. We want to understand lines, first in 2D geometry, and then later in 3D geometry, where things get considerably more complicated. We also introduce the idea of projective representation of curves. Many thanks to Joshua Capel for help in camera set-up, and to Joshua Ho for videoing. Video Content 00:00 Intro to affine and projective terminology for curves 7:29 Column K-vector 11:10 A picture (affine grid plane) 17:43 Projective points 22:54 When are two projective k points equal? 28:20 Products of projective 2 points 32:15 The projective plane 38:01 Solving 2-D problems 44:40 Projective Curves ************************ 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. 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   ************************ 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   м