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)