Cartography is the art of representing the world around us in the form of maps, but how do cartographers create accurate and detailed maps? One of the fundamental methods used in cartography is triangulation. This ingenious technique has a fascinating history and has been the basis of many major cartographic projects throughout the ages. In this article, we will explore the history of triangulation, understand how it works in practice, discover some examples of large cartographic projects carried out using this method, and explore its current uses.
The history and invention of triangulation
Triangulation has a history dating back to ancient times , but it was in the 17th century that the modern method was developed. One of the first users of triangulation was the Danish geographer, astronomer and mathematician Tycho Brahe, in the 16th century. However, it is the Dutch mathematician Willebrord Snell von Royen or Snellius (1580-1626) who is often credited as the father of modern triangulation. Snellius used triangulation to precisely measure the length of one degree of meridian, which allowed the circumference of the Earth to be calculated with a precision never before achieved.
Quadrant created by Tycho Brahe
Concretely, how does triangulation work in cartography?
Triangulation is based on the simple principle of Euclidean geometry. Using three reference points, called stations, mapmakers can measure the angles between these stations and calculate the distances between them. These stations are often located on mountain peaks, tall buildings, or purpose-built structures so as to be visible from afar.
Once angles and distances are measured accurately, mapmakers can begin to construct a series of interconnected triangles, creating a reference network on the Earth's surface. This network is essential for establishing accurate maps, because it allows distances to be measured and calculated between points that are not directly accessible.
Do you want to carry out a triangulation yourself? For this you will need three things:
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A theodolite or angle measuring instrument for measuring the angles of triangles.
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A meter stick or tape measure to determine distances between points.
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A map or plan to record measurements and draw triangles.
Here is a simple method to perform triangulation:
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Choose three clearly visible and accessible reference points or stations on your property.
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Measure two of the angles using the theodolite or other measuring instrument
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Measure the distance between the two angles you measured using the tape measure or tape.
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Get your calculators on! By knowing that the sum of the angles of a triangle is 180°, you can calculate the unmeasured angle and thanks to the law of Sinus, you can calculate the two still unknown distances. And there you have it, you have just achieved a triangulation!
Two examples of large cartographic projects carried out using triangulation
Triangulation has been used in many major cartographic projects throughout history. Among the most notable, we can cite the United States Coast Expedition led by Ferdinand Hassler in the 19th century. This expedition mapped the Atlantic coast of the United States with incredible precision using triangulation to establish reference points and measure distances.
Another emblematic example is the creation of the map of France by the Cassini family in the 18th century. The Cassini family carried out a complex geodesic triangulation covering the entire French territory. The result was Cassini's famous map, which is considered one of the first accurate and detailed maps of France .
Conclusion
Triangulation is a revolutionary method in cartography that has made it possible to create precise and detailed maps throughout the centuries. From Snellius to Cassini, this method has been used to carry out major cartographic projects that have shaped our understanding of the world. Today, although measurement technologies have evolved considerably, triangulation remains a fundamental method used in modern cartography. Using this ingenious technique, cartographers can continue to create detailed and accurate maps that help us explore and understand our geographic environment.