Thursday,  October 6

Review of tilings and symmetry in plane with FAPP videos.
Do Activity on transforming tesselations.

Space: How do we understand objects in space?
(continued from last class)

New Assignment for Tuesday, October 18th : Make a torus with 2 and 1 piece!

Cross sections: Look at the tetrahedron with cross sections : triangles and what?

Shadows: Recall our previous class  when we considered how the tetrahedron might case shadows.

Analyze shadows and cross sections for a cube.

Fold downs- flattened figures: Consider how the cube can be assembled from folded down squares in two different configurations: a cross or a "zig-zag."

What does a folded down flattened torus look like?
A rectangle with opposite sides resulting from cutting the torus open making a cylinder and then cutting the cylinder along its length.

    A torus


analogue...  point... line.... polygon.... polyhedron......
What is the difference between Euclidean Geometry, Projective Geometry, and Topology

Euclid: congruence, similar... measurements, scale
Questions: Is a triangle congruent/similar to another triangle?
Is an circle congruent /similar to an ellipse?

Is a triangle congruent/similar to a square?

Projective: We will discuss this in greater detail later in the course. Projections preserve lines, points of intersection and contact (tangency).
Questions: Can a triangle project onto any other triangle?
Can a circle project onto to an ellipse?
Can a triangle
project onto a square?

Next class we will see how this formula can help solve some problems on the plane and elsewhere.