Explore three-dimensional affine geometry in this 43-minute lecture from the Wild Linear Algebra series. Gain intuition about 3D space through parallel projections, coordinate systems, and the distinction between points and vectors. Examine the nature of space, the arithmetic basis of geometry, and the relationships between lines and planes. Delve into affine and vector spaces, with practical exercises to reinforce key concepts. Ideal for those seeking a comprehensive introduction to 3D geometry and its applications in modern physics and mathematics.
Three Dimensional Affine Geometry - Wild Linear Algebra A - NJ Wildberger
Insights into Mathematics via YouTube
Overview
Syllabus
CONTENT SUMMARY: Introduction: @
pg 1: @04:15 Perspective projection; Parallel projection @;
pg 2: @09:42 example of parallel projection; suggested exercises @
pg 3: @ coordinate axes; right handed configuration;
pg 4: @ The nature of space; remark to base our understanding of space on arithmetic;
pg 5: @23:43 A point in space - a triple of numbers; a point rather than a vector @ ;
pg 6: @ A vector; remark on importance of distinction between points and vectors;
pg 7: @ points, lines, planes;
pg 8: @ relations between 2 lines in space; identical, parallel, intersecting, skew;
pg 9: @ determination of plane; relations between 2 planes; identical, parallel, intersecting;
pg 10: @ Affine space; Vector space; vector space has structure that an affine space has not;
pg 11: @ exercises 9.1:2 ;
pg 12: @ exercise 9.3 THANKS to EmptySpaceEnterprise
Taught by
Insights into Mathematics
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