What is the geographical center of Polk County, Florida?

June 16, 2007 8:24 PM

What is the geographical center of Polk County, Florida?

I'm defining geographical center as a the center of gravity of a "cut-out 2D map of the country, of uniform thickness and density" (Thanks, justkevin.)

Of course, I'd appreciate the answer, but I'm willing to do the work if someone could point out a link to software that could help figure this out for me, or a formula I could use (and by "I" I mean someone who hasn't had a math class in over 30 years.)

Baring those, an email from a kind professor whose class would do this as an extra credit question on a Friday pop quiz would make my Father's Day.

posted by ?! to science & nature (7 comments total)

I'm trying to think of a simple way to calculate this, given a map or something else that you would have access to. Nothing comes to mind immediately.

Anyway, the low-tech way to find center of mass would be to get a map of the county -- a USGS survey one would be great -- and then use some spray-glue to attach it to a foam-core project board. Those are pretty uniform in terms of thickness and weight, usually. Then, you very carefully cut out along the county border, through the map and the board, with an X-Acto knife.

You find the geographic center by hanging the cutout board from a pin placed in the corners, with a plumb line falling from it. You mark the plumb line, and where they intersect is the CoM. See this page for a diagram. If you're careful when drawing the lines, you should be able to find the CoM with reasonable accuracy (depending, obviously, on the size of the county -- with a small county you'll be able to fit a bigger map projection onto the foamboard, hence more accuracy).
posted by Kadin2048 at 8:37 PM on June 16, 2007

Even lower tech- print out a map of the county, cut out with scissors, balance on a pin/needle.
posted by MtDewd at 9:13 PM on June 16, 2007

This website gives lat/long (google: "geographical center" "polk county, fl")
posted by one_bean at 9:19 PM on June 16, 2007

Using the link above, here it is on Google maps.
posted by daninnj at 9:52 PM on June 16, 2007

The coordinates from one_bean's link
(27.992436, -81.758303) match the numbers from the 2000 Census. However, the 1990 Census puts the centroid at (27.95978, -81.70007). If you have google earth you can plug in the coordinates and look at the county lines, which I assume are up to date.

I think the 1990 Census coordinates are more reliable, unless the county's borders changed in the 90s. The posted year 2000 data may just be an first approximation.

For example, the 2000 census puts the geographic center of nice, rectangular Hardee county at
(27.538231, -81.809106), but the 1990 coordinates of (27.49362, -81.80927) look more reasonable to me, just eyeballing it.
posted by thrako at 10:14 PM on June 16, 2007

As others have mentioned, you're looking for the centroid of a polygon, which can be determined if you know the precise coordinates of the boundaries of the polygon -- which you do, thanks to the Census Bureau. You can download county coordinate files for each state here. Download the Florida file, and open up the archive. The "d00a" file lists all of the counties and their county number (49 for Polk).

Now open the "d00" file, and scroll down to to the first line of the county #49 coordinates (line 17,259). That line through 17,884 are the (fairly precise) lat/long coordinates of the boundaries of Polk County. Run those through the formula in my first link, and that will give you the geometric centroid of the county.
posted by Doofus Magoo at 6:04 AM on June 17, 2007

I grew up in Winter Haven, Fl.

I can definitively tell you that Cypress Gardens is the geographical center of both Polk County and the entire state of Florida.
posted by matty at 8:47 AM on June 17, 2007