CARTOGRAPHY

Problem

The outline of the state of Delaware is approximated by the polygon with vertices, given in consecutive order, in the file delaware.data. The scale here is 1 map unit = ?? miles. Our goal is to determine the length of the border, the geographical center, and the area of the state of Delaware.

1. Using Maple's polygonplot command draw the outline of the state of Delaware.
2. Find the length (in miles) of the border of state of Delaware.
3. Using Green's theorem, one may show that the region in the x,y plane bounded by the simple closed curve
   
   has area
   
   Using this find the formula for the area of a polygon with vertices (in consecutive order) .
4. Using the formula obtained above compute the area of Delaware in square miles.
5. Let D be a region enclosed by the simple closed curve C x=x(t), y=y(t), . We know that its centroid is given by
   
   So to obtain the centroid of a polygonal region we need a clever way to compute and . Using Green's Theorem convert these integrals to an integral over the boundary C of the region.
6. Using the above result, compute the centroid of the polygonal region in (3).
7. Using Maple compute the geographical center of Delaware

Suggestions

• You will need to learn how to read data from a file from within Maple.
• For (3) and (6), first calculate the integrals over a line segment joining the points to .

 
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