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M4005 Geometry |
March 6, 2006 |
Lecture on Coordinates (30 minutes).
How are they treated in schoolbooks?
- A page from the Singapore 6th grade text
- Pages from Glencoe Algebra I (2006 Louisiana Edition).
Coordinates from an advanced perspective.
- Coordiante systems on a line. Naked lines. Imposing a coordiante system. Coordiantes are functions. Relationships between coordiate systems.
- Coordinate systems on the plane. Naked planes. Systems with perpendicular axesand other systems. Changing coordinates.
Coordinates from an historical perspective.
- Coordinates in Descartes' Geometry. Device on p. 318. Device on p. 320.
- Coordinates in Newton's work
Student discussion. (25 minutes).
Student groups will prepare answers to the question, "Why the graph of a linear equation is a line?" We will compare proposals.
Work on homework. (25 minutes).