Seeing the infinite... small and large.

How many points are there on a line segment? Can you count them all?

Any list (possibly infinite) of points in a given segment of a euclidean line will not have every point in that segment on the list.

Note that we can make a list of points corresponding to the rational numbers once a unit length had been established.

1/1,2/1,3/1,4/1,...

1/2,2/2,3/2,...

1/3,2/3,...

1/4, ....

What is a curve?

Curves and approximations of curves by line segments and polygons.

Regular Polygons and the circle.

The length of a curve.

Infinite curves: The snowflake.

Activity on snowflakes.

Space filling curves.

Projective Geometry- Calculus Beginnings

The conics.

- Lines - Ratios, Rates, Proportions-Measurement.

Parabolas

Coordinates and Functions.

Static vs. Dynamic visualizations