Mathematics 4270
Fall, 1999


Topic list for the exam on November 17. This is a closed-book
exam. No calculators. It takes place during the usual class period,
in the usual room.


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3.4.3 Envelopes. Know equations (3.32) and (3.33) on page 222. (Envelope
	is found by eliminating t_0 from these two equations.) Derivation
	not required; just know the facts.

3.4.4 Cardioids. All the geometric arguments on page 224; their application
	to parametric equations on page 225 (Theorem 3.26).

3.4.5 Clairaut's Equation -- know formula (3.40) on page 236 and how it
	relates to Equation (3.38) on page 234. Derivation not required.
	Just know Equation (3.40) and be able to apply it in simple cases.

3.4.6 Evolutes not included. (They are included in one of the projects.)

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4.1.1 Formulas for the perspective drawing (pages 264-266), and how
	we derive them.

4.2.3 Equation (4.1) -- for a line in homogeneous coordinates.

4.5   Representing plane motions as collineations. Really, you already
	know the matrices in this section.

4.6   Representing perspectivities as collineations. One matrix to know.

4.7   Projections from a plane to a line. Not included on exam.

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5.1.3 Homogeneous coordinates -- a knowledge of how to use them.

5.2   Collineations of projective space. Know the meaning of Theorem
	5.7, and how to apply it.

5.3   Know all the matrix formulas in 5.3.2 (translations), 5.3.3
	(reflections), 5.3.4 (rotations), 5.3.6 (magnifications), 5.3.9
	(projections). Be able to use them appropriately.

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6.1   Projections of a globe. Know the algorithm (page 332), and how to
	explain it.