This is the ninth lecture of this course on Linear Algebra by N J Wildberger. Here we give a gentle introduction to three dimensional space, starting with the analog of a grid plane built from a packing of parallelopipeds in space.We discuss two different ways of drawing 3D objects in 2D, emphasizing the importance of parallel projection. Some discussion of the nature of space and modern physics, then an introduction of affine space via coordinates. The distinctions between points and vectors is important, and we talk also about lines and planes.CONTENT SUMMARY: Introduction: @00:073 dimensional? geometry; gaining intuition; expect models and pictures and some philosophy; parallelpipeds; pattern generated by 3 basic vectors; arithmetizing space; affine situation; no notion of length;pg 1: @04:15 Perspective projection; Parallel projection @06:29;pg 2: @09:42 example of parallel projection; suggested exercises @14:00pg 3: @15:36 coordinate axes; right handed configuration;pg 4: @20:05 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 @28:20 ;pg 6: @29:09 A vector; remark on importance of distinction between points and vectors;pg 7: @31:58 points, lines, planes;pg 8: @33:25 relations between 2 lines in space; identical, parallel, intersecting, skew;pg 9: @34:27 determination of plane; relations between 2 planes; identical, parallel, intersecting; pg 10: @35:35 Affine space; Vector space; vector space has structure that an? affine space has not; pg 11: @39:51 exercises 9.(1:2) ; pg 12: @41:12 exercise 9.3 (THANKS to EmptySpaceEnterprise)
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