Thursday, September 4
Puzzles and Polygons [1.2]

Dissections, cut and paste methods of measurement.

Cutting and reassembling polygons.

Tangrams.

Tangram Activities last class
Tangoes: a commercial game based on tangrams
Tapestry Project from previous Math 103 students.
Cutting and reassembling polygons.
Convex: Any two points in the figure
have a line segment connecting them. If that line segment is always
inside the figure, then the figure is called "convex".
Making Dissection Puzzles:

Dissections
(Junkyard)

Equidecomposable
polygons (translation from Portugese)
Where we are going:
* 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]

Theorem I : A sc= B implies Area(A) = Area(B)

Theorem II [The converse of Theoerm I!]: Area(A) = Area(B) implies
A sc= B !!

Simple cases as evidence and a foundation for building toward the proof
of Theorem II.:

A triangle is SC to a rectangle.

A rectangle is SC to a square.

Two squares are SC to a single square.

A polygon is SC to a square.

Triangulation
.: Any polygom can be decomposed into triangles!

If two polygons have equal area, then they are SC to the
same square!

Discussed the presidential puzzles: Washington, ..., Jefferson,...,Lincoln,
... ,Clinton, Bush II.