The Area of Minnesota
In Lab 12 we numerically
approximated the area of planar regions defined by some equations or set
of equations. This section asks the question: what do we do if we do not
have a formula for the region of interest?
The basic geometric idea is the same as it was in the previous lab: impose
a grid on the region and count the number of boxes falling within the region.
As the grid becomes finer and finer, the area of the boxes within the region
will typically approach the actual area of the region.
We illustrate this geometric picture by formulating a model for the state
of Minnesota. First, you must read in some Maple commands:
read `/u/calcIII/MVCalc.define`;
We model the state of Minnesota as the region enclosed by it's east and
west borders (approximated by a set of data points connected by linear
segments) and it's north and south borders (approximated by straight lines).
Question #1
- Issue the maple command:
MNgridplot(10,10);
to see the model that we are using. Compare this model to the
actual map that you were given. How is
the model different from reality? Do you think our model is a
reasonable approximation of reality? Why or why not?
- Estimate the area of our model by using the 10x10 grid. What method
do you use to decide which boxes are inside Minnesota?
Next: Convergence of Area
Previous: Introduction
Frederick J. Wicklin <fjw@geom.umn.edu>
Brian Burt
Document Created: Fri Jan 27 CST
Last modified: Tue Sep 26 13:29:35 1995