Friday, November 5, 2010

On the Problems with Surveys of Farm Land

For those of you who like me own a farm you might be surprised to know that the survey of your farm in Rappahannock County is incorrect. I am wondering how to get an accurate survey.

Every high school math student knows that the area of square is the length times the width. A surveyor calculates the surface area of your farm by dividing it up into lots of little squares until they more or less fill up the picture of your farm drawn on a piece of paper. This mechanical way of calculating area works and is how Archimedes calculated the area of a circle. When the difference between the area of all those little squares that encompass your survey and the actual area enclosed by your survey is zero then they are the same. This is the basic principle of calculus which was deducted from the geometry of Euclid. But Euclidean geometry only works on flat surfaces. What, for example, is the surface area of a soccer ball? Certainly its more than the area of the circle made by the shadow of the soccer ball which is cast on the ground.

The same can be said of the surface area of your farm. Here in Rappahannock County it's not flat. There's hills and hollows. So to calculate the actual surface area of your farm you would need to know something of the contour of your land--that is, you would need a topographical map. To calculate the surface area over the surface of what mathematicians would call the resulting "manifold" would be quite complex. This is called "topology". Does anyone know how to do this? Can a surveyor do this?

Shoot me the answer if you know. Otherwise be happy that your 65 acre farm is probably much larger than that. Exactly how much larger is what I would like to know. If I can add 4 acres to my farm I could get a conservation easement, but since lawyers cannot think abstractly no title attorney would be convinced. What do you think? This could turn the who land use, zoning, easement discussion upside down.-

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