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  The American Surveyor     

Carl Friedrich Gauss Print E-mail
Written by Fred Roeder, LS   
Saturday, 11 April 2009

Every self-­respecting surveyor knows that our first, third, and sixteenth Presidents had for a brief period in their lives been surveyors. But not even the most chauvinistic of our peers would argue that Washington's picture appears on the dollar bill because of our country's desire to honor a surveyor. Surveyors are just not that famous, or are they?

Imagine my surprise when my nephew handed me a new German 10-­mark bill and my eyes fell on a triangulation diagram consisting of a chain of triangles connecting 17 named stations, alongside a picture of a sextant covering almost half of the entire bill. On the obverse was a portrait of Carl Friedrich Gauss and the equation of his famous error curve.

I doubt seriously that the average German knows more about Gauss than does the average American, who is in the top 10 percent if he knows that Gauss was one of the three greatest mathematicians of all time (the others being Archimedes and Newton), whose accomplishments fill pages in any encyclopedia of mathematics and science. It is therefore all the more remarkable that money designers chose to honor Gauss the geodetic surveyor, rather than Gauss the mathematician and astronomer. It helps to drive home an important truth: surveyors play a key role in the life of any civilized society.

Carl Friedrich Gauss was born in 1777 into a poor family (his father was a gardener) in the German city of Braunschweig (Brunswick). He was an extremely precocious child, astounding his parents and teachers with his mathematical abilities from the age of three years. There is a story that the child mentally added the numbers from one to 100 in a few minutes by reasoning that the order in which they are added doesn't matter, and he simply added 1 + 99+ 2 + 98 + 3 + 97…all the way to 49 + 51, reducing the whole problem to (49 x 100) + 100 + 50 = 5,050. While still a teenager he propounded the theory of least squares, demonstrated a solution to the age old problem of dividing a circle into 17 parts, and made important mathematical discoveries that he was too shy to publish and entrusted only to his diary.

His genius came to the attention of Ferdinand, Duke of Brunswick, who undertook to finance his education and in the process became his lifelong patron and friend. Gauss attended the University of Göttingen and in 1799 got a doctorate in mathematics from the University of Helmstedt. About this time he turned his attention to astronomy, making brilliant computations of orbits of asteroids. In 1807 he became director of the observatory in Göttingen, a post he held until his death in 1855.

Most of his contributions to mathematics and science he set down in about 155 meticulously written papers. He published papers only after the most thorough investigation and after he was sure it met his motto: Ut nihil amplius desiderandum relictum sit-that nothing further remains to be done. His mind was so full of numbers that when he was interrupted in solving a problem and told that his wife was dying, he reportedly replied: "Tell her to wait until I am done."

From about 1817 Gauss made studies in geodesy. His interest was aroused by a need for an accurate determination of the geographical position of his observatory. In 1828 he was commissioned by George IV of England to triangulate the entire kingdom of Hannover. Hannover is a hilly expanse of about 15,000 square miles in northern Germany between the Elbe river and the Dutch border, which in those days belonged to England, the English monarchs being of the House of Hannover.

Gauss was too much of a mathematician to fall in love with the mechanics of triangulation. "All the measurements in the world are not worth one theorem by which the science of eternal truth is genuinely advanced," he once wrote. The survey, which Gauss completed in 1847, did not produce a very accurate map of Hannover, there being more to making a map than establishing geodetic positions on a few triangulation stations. It resulted, however, in a number of important advances in the mathematics of curved surfaces, such as his development of curvilinear coordinates. To increase the accuracy of his observations he developed a new lens, the Gauss eyepiece, still used for auto­collimation in spectrometers. To improve pointing accuracy on distant targets, he invented the heliotrope. The most important result of his triangulation was a book on geodesy, which he published in two volumes between 1844 and 1847.

Gauss probably did not consider himself a surveyor anymore than George Washington did, but remember the saying: Tell me what you do and I will tell you who you are. I think our profession can claim him for his immense contribution to surveying and accept the honors on the German 10 mark bill.

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