Convergence of Area
To get a better approximation of the area of Minnesota, we need to use a
finer grid. Rather than count squares ourselves, we will have the computer
decide that a square is within the boundary if its lower left corner is within
the state boundaries. The approximate area will be the sum of the areas of
the squares contained within the state.
- Use the Maple command
to compute an approximate are of MN. Can you explain why this answer
is different from your answer to Question #1?
- Increase your grid size to 15 by 15 and then 20 by 20 and recompute
approximate areas. Use the data you've collected to estimate
the area of the model. (Explain how you arrived at your conclusion.)
Answer this question at home.
- The Southern border of Minnesota is about 250 miles
long and the distance from the southern border to Canada is
approximately 375 miles.
Use these facts to determine the horizontal and vertical scale of the
model that we are using.
- Use your data to approximate the actual total land area
(in square miles) of Minnesota. Consult an atlas, almanac, or encyclopedia
to find the actual land area of Minnesota. Based on these facts,
do you think the model of Minnesota that we are using is a good model?
Next: Integrating Density Distributions
Previous: The Area of Minnesota
Frederick J. Wicklin <firstname.lastname@example.org>
Document Created: Fri Jan 27 CST
Last modified: Fri Feb 3 11:43:54 1995