history-page26 - If the n(n + 3)/2 points determining an...

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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 3-dimensional objects using 2-dimensional 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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