Thursday,  October 16

Begin: Seeing the infinite... small and large with similarities.
The Snowflake curve.
Recall the written Snowflake Activity.

Make a BIG snowflake!

What is a curve?  How long is a curve?
Can a curve cover an entire region of the plane? We watched  (
Space Filling Curves) the "Space filling curves" video.

Other Fractals: we watched the FAPP video section on fractals - "fractional dimensions".

The  Hypercube and coordinates:
What do we measure?  How does this determine "dimension?"
For a Line segment we can use one number to indicate distance and direction from a single point:  0 .... 1

For a Square we use two "coordinates" and we can identify the vertices of the square: (0,0), (1,0), (0,1),(1,1)

For a Cube
we use three "coordinates" and we can identify the vertices of the cube with qualities such as "left..right", "up... down", and "front ... back":
(0,0,0) , (1,0,0), (0,1,0),(1,1,0)

(0,0,1), (1,0,1), (0,1,1), (1,1,1)

For a Hypercube
....
we use four "coordinates" and we can identify the vertices of the hypercube with qualities such as "left..right", "up... down", and "front ... back" and "inside... outside": (0,0,0,0) , (1,0,0,0), (0,1,0,0),(1,1,0,0)

(0,0,1,0), (1,0,1,0), (0,1,1,0), (1,1,1,0)

(0,0,0,1) , (1,0,0,1), (0,1,0,1),(1,1,0,1)

(0,0,1,1), (1,0,1,1), (0,1,1,1), (1,1,1,1)