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Week 7 Syllabus
Reading
- Review Sved, Ogilvy and Bix on orthogonal circles, the models, and the
hyperbolic plane. Also review Bix and An Eye for Similarity Transformations
on dilations.
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445 Monday, February 15
HOLIDAY
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445 Wednesday, February 17
Introduction to Projective Geometry. Definition of parallel and central
projection. Example of projection of two intersecting roads leads
to method for finding projection of midpoint. (This is harmonic division
in disguise.)
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487 Computer Lab 7, Wednesday, February 17
A first lab exercise was to draw the projection of the intersecting
roads to see that the image of the midpoint of AB is unchanged if the
images of A, B and the point at infinity on line AB are fixed.
The rest of the lab was devoted to exploring spherical geometry with Sketchpad
using stereographic projection to map the sphere to the plane. Sketchpad
scripts for this, along with sketches explaining this, are on the server.
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445 Friday, February 19
Desargues Theorem. Class exercise on converse of Desargues by beginning
with points P, Q, R on a line (the fold of a manila folder) and drawing
two triangles P1 Q1 R1 and P2 A2 R2 perspective from the line (e.g.,
lines P1Q1 and P2 Q2 pass through R, ...). In this case the lines P1P2,
Q1 Q2 and R1 R2 are concurrent.
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Assignment 7 Part A is due on Wednesday,
2/26
Assignment 7 Parts B and C are due
on Friday, 2/28
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