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⋆
If the
n(n
+
3
)/
2 points determining an
n
th degree curve are chosen to be among the
n
2
points that two
n
th degree curves share, there seems to be a lack of determinacy.
⋆
Resolution: The equations aren’t independent.
Descriptive Geometry
•
What is it?
◦
The study of the representation of 3dimensional objects using 2dimensional Fgures.
◦
think of mechanical drawings, drafting, etc.
•
Essentially invented by Monge in the late 1700s. (Much geometry done in revolutionary
±rance. Monge’s motivation: To “pull the ±rench nation out of its hitherto dependence on
foreign industry”.)
•
Uses parallel projection.
•
Monge went on to do nontrivial mathematics with such representations.
Projective Geometry
•
What is it?
◦
The study of geometric properties of and classes of geometric objects that are un
changed by projections, or changes of perspective.
◦
Original motivation was a desire to help painters: A painting should be a section of the
projection of the lines of light from the thing being painted to the eye.
◦
Projection preserves neither congruence, nor similarity, nor angle, nor length, nor area.
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 Fall '10
 wen
 Geometry, Equations

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