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Dr. Sarah's Math 3610 Web Page - Spring 1999
our mascot (as well
as one of my two cats), is very possessive about math textbooks!
Writing, Geometer's Sketchpad Projects, and Problem Sets
Writing Project Wile E. Coyote Needs your help Due
Wed Jan 20th at 5pm, Revisions Due Wed, Feb 3rd at 5pm
Geometer's Sketchpad - Draw anything you like - turn in the sketch, a script for it, and comments within the sketch. Due Mon, Feb 1 at 5pm.
Problem Set 1 (Minesweeper and 4-line/4-point geometry proofs). Due Fri, Feb 5 at 5pm, Revision due Mon, Feb 15th at 5pm
Writing Project Wile E. Coyote and Axioms.
Due Wed, Feb 10th at 5pm, Revisions due Fri, Feb 19th at 5pm.
Problem Set 2 (Statements and their negations). Due Wed, Feb 24th at 5pm.
Revisions due Fri, March 12th at 5pm
Geometer's Sketchpad 2: In class, we went thru the creation
of an upper half plane model in geometer's sketchpad, the creation
of a line(arc) thru 2 points, and answered the question: If you have
an arc AB, and a point C in the half--plane not on arc AB, how many
lines are parallel to AB through C?
We also discussed how to measure angles in this space. HW:
Turn in a sketch, script and comments about what we did in class,
and on a separate sketch, disprove: Every triangle has angle
measurement 180 degrees, by producing a sketch, script and comments.
DUE Mon 15th of March.
Oral/Blackboard Test 1 -
Monday and Wednesday, March 8th and 10th in class. On the test day,
right before each presentation, a student
will be randomly assigned a problem from among PS 1, p. 35's Thm
we did on geometer's sketchpad (The sum of the measures of the interior
angles of a triangle is 180 degrees proo
f assuming Euclid's axioms and p. 34 1,3, 4, 5, and 6 (NOT 2)), and one other
problem to be determined.
Notes will not be allowed during the presentation.
(The set of axioms will be provided).
Mathematics of proof,
Clarity of proof,
oral presentation (do you say anything you have written),
etc will be important.
PS 3. From Section 3.2, rigorously fill in the books proofs
for everything but the first Theorem(we did that in class).
DUE Monday, March 21st.
PS 4. Spherical Geometry.
1) Create a model of the sphere - suggestions - half of an orange peel,
half of a tennis ball, geometer's sketchpad...
In your model, draw lines (longitutes).
2) Can a triangle on the sphere have angle measure sum less than or equal to
Hint: Draw a triangle on your model. Use string or something else to draw
straight Euclidean lines (which will end up on the "inside" of the sphere).
Argue from there.
Geometer Sketchpad 3.
Prove that the following are Equivalent in
a) Euclid's 5th postulate p.30
b) Playfair's postulate p. 38
c)Converse of the alternate interior angle thm section 3.4
d) Hilbert's parallel postulate Axiom IV-I p. 44
e)SMSG parallel postulate 16
(See class highlights for full assignment).
Sarah J. Greenwald
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