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Pencils and stacks
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Equations of Lines and Planes in 3D - Wild Linear Algebra A - NJ Wildberger
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- 1 CONTENT SUMMARY: pg 1: @
- 2 pg 2: @
- 3 pg 3: @
- 4 pg 4: @
- 5 pg 5: @ special lines in the 2dimensional case; the x and y axes, and lines parallelel to the x and y axes;
- 6 pg 6: @ pencils and stacks;
- 7 pg 7: @ question: What does the space of all lines look like?; topologically gluing a line to every point on a circle;
- 8 pg 8: @ cylinder; Mobius band;
- 9 pg 9: @ lines and planes in 3D; planes; cartesian equation of a plane;
- 10 pg 10: @ solving a system of equations in 3D; matrix of determinants of minors;
- 11 pg 11: @ lines in 3D; two points, point and vector, intersection of 2 planes; parametric equation;
- 12 pg 12: @ line in cartesian and parametric form; cartesian form describes 2 planes that meet in a line;
- 13 pg 13: @ examples;
- 14 pg 14: @ meet of two planes; method found in very few linear algebra texts; a way of introducing parameters; THANKS to EmptySpaceEnterprise
- 15 Introduction
- 16 Meet of lines
- 17 Special lines
- 18 Pencils and stacks
- 19 What does the spaces of all lines look like?
- 20 Two possibilities
- 21 The analog of a line in 2D is a plane in 3D
- 22 Two planes generally meet in a line
- 23 Lines are determined by: two points, point + vector, two planes
- 24 Lines also have Cartesian equations
- 25 Meet of two planes
- 26 Parametric equation for a plane
- 27 Parametric to Cartesian plane
- 28 Cartesian to parametric plane
