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The listings below for classes near in the future is solid, but as you look further into the future, changes become more likely!
Class 1, Wed, Jan 30. Course goals and methods of operation, geometry & art, folding a tray, and Lab 1, a geometry walk to make verbal and visual note of geometric objects and symmetry
Class 2, Fri, Feb 1.
a. Defining and refining categories constructed from the shapes/objects and symmetries found in the geometry walk
b. Equilateral triangle folded in half
Due: Homework 1
Class 3, Mon, Feb 4.
a. Lab 2: paper folding from scratch, folding a "curve"
b. The 1/6 - 1/3 - 1/2 straight angle triangle and dollar bill folding
Due: Homework 2
Class 4, Wed, Feb 6.
a. Discussion of pages xi-xii, xv, and 3-7 through the 4 definitions of Euclid at the top of page 7
b. Discussion of properties of the 30-60 right triangle and dollar bill folding
Due: Homework 3
Class 5, Fri, Feb 8. Lab 3: Introduction to The Geometer's Sketchpad
Due: Homework 4
Class 6, Mon, Feb 11. Origami: A unit to make cubes - Observations and Questions
Due: Homework 5
Wed, Feb 13. Class Cancelled
Due: Homework 6
Class 7, Fri, Feb 15. Lab 5: Transformations and Script Tools on The Geometer's Sketchpad
Due: Homework 7
Class 8, Mon, Feb 18. Bisection of segment and angle, trisection of a segment, and origami: A unit to make triangle stars (See Lab 4.)
Due: Homework 8, Revision of category work from groups whose work was not accepted, & Submission of Portfolios (from students whose names are in A-D)
Class 9, Wed, Feb 20.
a. Workshop with options to do origami, reflections, question writing, or problem solving
b. Trisection of a line segment by folding: the mathematics
c. Trisection of an angle: A method
Due: Submission of Portfolios (from students whose names are in F-M)
Class 10, Fri, Feb 22.
Revision of categories: Going beyond the geometry walk
Due: Submission of Portfolios (from students whose names are in P-Z)
Class11, Mon, Feb 25.
Lab 6: Creating "elementary folding moves"
Due: Homework 11
Class 12, Wed, Feb 27.
a. Discussion of pages 7-10 and page 13 of Journey
b. Discussion and work to improve "elementary folding moves"
Due: Homework 12
Class 13, Fri, Feb 29. Lab 7, using Sketchpad in an "unmess-upable" way and sketching folding processes
Due: Homework 13
Class 14, Mon, Mar 3. Developing more "elementary folding moves"
Due: Homework 14
Class 15, Wed, Mar 5. Euclid's definitions and common notions, the five Euclidean postulates, and Lab 9, Euclid's 5th Postulate
Due: Homework 15
Class 16, Fri, Mar 7. Time to complete Lab 7 and Lab 9 and to work on problems.
Due: Homework 16
Class 17, Mon, Mar 10. Notes on pp 14-15 in Journey: The power of a point w.r.t. a circle, a Discussion: Do we need additional elementary folding moves? and a Start on: Lab 10, constructions by ruler and compass
Due: Homework 17
Class 18, Wed, Mar 12. A comparison of the constructions by ruler & compass and by elementary folding moves, continued work on Lab 10.
Due: Homework 18
Class 19, Fri, Mar 14.
a. Q&A session
b. Building a hypercube
Due: Homework 19
Class 20, Mon, Mar 24. Lab 10 constructions by elementary folding moves? Which are possible?
Due Tues, Mar 25: Homework 20
Class 21, Wed, Mar 12. Investigation: What makes a line a straight line? Elliptic and hyperbolic families of circles in Journey, pages 16-23
Due: Homework 21
Class 22, Fri, Mar 28. Dramatic reading of Journey, with dynamic geometry illustrations of orthogonal circles
Due: Homework 22
Class 23, Mon, Mar 31. Continued dramatic reading of Journey, with dynamic geometry illustrations of orthogonal circles, plus background geometry of angles "in" circles
Due: Homework 23
Class 24, Wed, Apr 2. Applying the Elementary Folding Moves and applying the Euclidean Postulates
Due: Homework 24
Class 25, Fri, Apr 4.
a. Revision of the proposed EFM in draft 3 of Elementary Folding Moves
b. Mapping a sphere onto a plane, stereographic projections in crystallography
Due: Homework 25
Class 26, Mon, Apr 7.
a. Experimenting with the proposed EFM 5
b. Lab 16, stereographic projection and geometric inversion
Due: Homework 26
Class 27, Wed, Apr 9.
a. Inversion
b. Rigid motions in the plane
Due: Homework 27
Class 28, Fri, Apr 11.
a. Establishing inversion properties
b. Defining orthogonal circles
Due: Homework 28
Class 29, Mon, Apr 14.
a. Questions about the 5th Postulate story
b. Finding orthogonal circles to fit specified conditions
c. The Poincare disk model of the hyperbolic plane
Due: Homework 29
Class 30, Wed, Apr 16. Proofs that the Poincare disk model of the hyperbolic plane satisfies the properties of Euclid's first four postulates
Due: Homework 30
Class 31, Fri, Apr 18. Constructing a hyperbolic circle for the hyperbolic plane. Q&A - Other investigations: Interior angle sums, rectangles?
Due: Homework 31
Class 32, Mon, Apr 21. Lab 18, investigating the hyperbolic plane with Sketchpad script tools (postponed to Wednesday, when we'll have computers) What can you do without a 5th Postulate? + Time to fix up prior lab work and problems
Due: Homework 32
Class 33, Wed, Apr 23. Lab 18, investigating the hyperbolic plane with Sketchpad script tools
Class 34, Fri, Apr 24. TBA
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