**Hint:** Think string and hanging pictures.

**Solution Commentary:** The following e-mail discussion reveals solutions to the problem:

From: Millie Johnson [WWU Mathematics Professor]

Sent: Friday, January 19, 2007

To: Dean Kahn [Editor]

If you have a decent map, you could numerically estimate the centroid and get as close as you want to the center depending on how finely
you cut the grid lines.

That is, you need the geographic region on a piece of flat paper and you need a straightedge and ruler. Establish a grid over the entire
region. The finer the grid, the closer the estimate of the centroid (center of mass-in this case geographic center) will be.

The centroid is the point on planar region that if placed on the tip of a sharpened pencil lead, would theoretically balance the region. Since you are only considering the geography, then the assumption is that the region is homogeneous. The balancing problem uses an adjusted formula if you consider, say, density of population. Yup,
there are formulas for these computations.

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From: Millie Johnson

Sent: Friday, January 19, 2007

To: Dean Kahn [Editor]

Subject: Part II

Part II and a lot less trouble:

1. Cut out a map of Bellingham on stiff material, cardboard, tagboard.

2. Hang the map by a string.

3. Draw a vertical line across the map from the point of suspension.

4. Remove the string and rotate the map a little (a few degrees), hang it by a newly attached string, and draw another vertical line. The lines drawn should intersect at approx the centroid.

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From: Dean Kahn [Editor]

Sent: Friday, January 19, 2007

To: Millie Johnson

Subject: Part II

A fellow at the USGS suggested cutting out a map of the city, gluing it to firm paper, cutting the paper to fit the map outline, then using a pen or other pointed object to find the balance point, and that, more or less, is the center of the city. Would that approximate the "string"
approach?

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From: Millie Johnson

Sent: Friday, January 19, 2007

To: Dean Kahn [Editor]

Subject: RE: Part II

Same thing. The string method is usually a bit easier, since the balance point is rather tricky to find on unusual shapes.

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From: Dean Kahn [Editor]

Sent: Friday, January 19, 2007

To: Millie Johnson

Subject: Part II

With the string method, and with such an irregular shape as the city of Bham, how many string reattachments are necessary? Is just two
sufficient? Also, it sounds like it doesn't matter where on the perimeter to attach the string initially. Is that correct?

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Date: Sat, 20 Jan 2007

From: Millie Johnson

To: Dean Kahn [Editor]

Subject: RE: FW: Part II

Irregularity is irrelevant. The centroid (see my first message) is the balance point. Since there is one centroid for Bham, then theoretically regardless of where you attach the string, the vertical line will cross the centroid (balance point). Since two lines intersect in a point and theoretically there should be ONE point, then two string attachments should do. However, since there will be experimental error, you could try a bunch of string attachments and sort of take an average of the intersection locations.

The first method that I sent to you (cutting up the region into a fine grid might be more accurate, but would take a lot more time.

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**Additional Note:** From the March 23, 2007, issue of the *USA Today* newspaper: "The 1959 site (i.e. geographic center) was determined, according to David Doyle, chief geodetic surveyor for the National Geodetic Survey, by using a map of the USA, pasted onto a hard surface like cardboard, and then balancing it on an object such as a pencil. Some rudimentary math was applied to allow for Hawaii and Alaska, he said."