This Month's Feature Column

The Mathematics of Surveying: Part I

Introduction: Surveying and geometry

Tradition has it that geometry (literally, earth-measurement) began when the ancient Egyptians had to re-establish boundary lines between fields after the annual floods of the Nile; the United Nations Food and Agriculture Organization still recommends using a (3, 4, 5) triangle to set out right angles in survey work, a procedure that may well go back to the pharaohs. Today, surveyors continue to make explicit use of plane geometry and trigonometry on a day-to-day basis. Along with their seafaring cousins, the navigators, they may be the most geometrical of all professions. My plan in this column is to sample some of the more elementary current surveying procedures from a mathematical point of view, using The Surveying Handbook (edited by Russel Brinker and Roy Minnick, Van Nostrand Reinhold, New York, 1987) as my source.

It must be noted that at least one mathematician was a world-class surveyor. Laplace had advised the Académie des Sciences in 1791 on a new survey of the Paris meridian from Dunkerque to Barcelona (in order to establish the exact size of the earth and hence the length of the meter; the French Revolution had washed away, along with the traditional divisions of land, the units that had measured them). But Gauss himself conducted a survey of the state of Hanover between 1821 and 1825, and continued to direct work on refinements of the grid. One of the nine volumes of his collected works is entirely devoted to geodesy.

Tony Phillips
Stony Brook University
tony at math.sunysb.edu