• Introduction to course organization.
• Student Information sheets.
• Web Materials
• Portfolios and grading
• Some topics we will study.
• Measurement and the Pythagorean Theorem [1.1]
• Measuring angles, lengths and areas.
• Squares, rectangles, parallelograms and triangles.
• dissections, cut and paste methods of measurement.
• Discuss Pythagorean Theorem (PT) and proofs.
• Distribute Tangram sheets.
• Assignment for Tuesday.
• Read 1.1 and 1.2
• 1.1:  5-8, 11, 12, *13

• Measurement and the Pythagorean Theorem [1.1] Review in part.
• Measuring angles, lengths and areas.
• Squares, rectangles, parallelograms and triangles. Circles.
• dissections, cut and paste methods of measurement.
• Discuss Pythagorean Theorem (PT) and proofs.
• Do Pythagorean Activity Sheet
• Show video on PT
• Puzzles and Polygons [1.2]
• Flatland and the plane
• The triangle, quadrilateral, pentagon, and hexagon.
• More on measurements of angles and areas of polyons.
• Activity: 1.2 Ex. 4, 5, 6
• Miscellaneous:
• The film lists as a guide to the course topics.
• The color problem.
• The sphere  and the Torus.
• Flatland as social commentary/satire.
• Assignment for Wednesday:
• 1.2: 1-3, 8, 9

Tangrams.

• Do Tangram Activity

Cutting and reassembling polygons.

The Square Me Puzzle.
Making puzzles.

More on Dissection Puzzles:  Dissections (Junkyard) and equidecomposable polygons (mef)

• Scissors congruence: A sc= B means figure A can be cut into pieces that can be reassembled to form figure B.

This is also described using the word "equidecomposable".  "A and B are equdecomposable to B."
• SC=  is a reflexive, symmetric, and transitive relation. [like congruence and similarity in geometry and equality in arithmetic]
• Discussion: What kind of motions are used in reassembling pieces in a puzzle?
• A sc= B implies Area(A) = Area(B)
• Area(A) = Area(B)  implies A sc= B !!
• Simple cases:
• Parallelograms with common base.
• Parallelograms with common parallels and same area.
• Parallalograms with same area.
• Triangles and parallelograms with same area.
• Adding parallelograms.
• Adding triangles.

Triangulation.

Rigid Motions in (or about) the plane.

Orientation preserving

Translations

Rotations

Orientation reversing

Reflections

Glide reflections

Tilings Chapter 4

Regular

Activity in class: 4.1  Ex. 3, 4, 5

Semiregular

One polygonal Tile

4.1: 7, 8, 9

Tilings Chapter 4

Regular

Semiregular

Classification using vetex congruence.

How many polygons meet at a vertex?

What types can meet at a vertex?

How do the polygons fit around a triangle?

Read the "Rules" p86-88

One polygonal Tile - Non-regular:

Card tilings

4.1: 14 (based on 7)

More on Planar Tilings.

Polygonal

Quadrilateral Activity

Symmetry Chapter 5.

Reflectional symmetry

Rotational Symmetry

Translation Symmetry

Glide reflection symmetry

4.1: 10, 24
5.1: 6 (g,h,i)
5.2: 1,2
Plus symmetry of alphabet assignment.

Tilings video (FAPP)

Two tiles

Friezes

Wallpaper

Symmetry Chapter 5.

Symmetry Video (FAPP)  in different contexts

Polygonal

Planar

Tilings

Modifying tilings

In class activity: Modifying tilings

Symmetry groups of of the equilateral triangle and the square.

Activity: Miras for reflection- one and two reflections

Video : Isometries

Every plane isometry is the product of at most three reflections.

Two reflections = rotation or translation. 

---

Three reflections = reflection or glide reflection

 

	Preserve  Orientation	Reverse  Orientation
No Fixed points	Translation	Glide reflection
Fixed Point(s)	Rotation	Reflection

 

• Symmetry in tilings activity.
• Platonic (regular convex polyhedra) Solids
• Why are there only 5?
• Regular polygons around a vertex.
• All vertices are "the same".
• Symmetries in the plane compared to those in space- an intorduction:
• Translations
• Rotations: Center point - central axis
• Reflection :  across line - across plane
• Symmetries of the cube:
• Rotations
• reflections
• rotation- reflection

• products of reflections in space:
• Rotations and translations
• Applications to dance

• In the plane: dual tiling
• Vertex - Region
• edge-edge
• In space: Dual polyhedron. Connected by counting and constructions.
• Vertex - Face
• edge-edge

Cube- octahedron; Dodecahedron, icosahedron; tetrahedron.

Similarity.[ FAPP Similarity Video ]
    Similarity and Editing- font size applications.
Begin: Seeing the infinite... small and large.
The fourth dimension. Connection to coordinates.
Tower of Hanoi Activity
Assignment for Tuesday, July 29th.:
7/29 See assignment on 4th dimension.
6.2: 14
Make two tori: one from two annuli, one from a single "rectangle."

Assignment for Wednesday, July 30th:
See assignment on the torus and maps and surfaces.
See assignment on Zeno. 

Chromadepth
Assignment for Thursday, July 31st:
Symmetry Day.
See assignment on Projection (accepted on Thursday)
13.4 : 2-6 

Assignment for Monday, August 4
10.1: 4,5
13.3: 1,2