Dr. Sarah's Math 3610 Web Page - Spring 1999

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  • Class Highlights-Day by day.
  • Class Assignments-Writing Projects, Problem Sets and Geometer's Sketchpad
  • Geometer's Sketchpad
  • Dr. Sarah's Schedule
  • Teaching High School Geometry 1 hour credit seminar
  • Syllabus and Grading Policies
  • 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, blackboard technique, oral presentation (do you say anything you have written), eye contact 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 180 degrees?
    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 Euclidean Geometry:
    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 Due Fri. (See class highlights for full assignment).

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