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

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