Kuinka kolmiot mittasivat Maan // How triangles measured the Earth

High above the waves of lake Päijänne and most treetops, on the top of 192 meters high Oravivuori in Jyväskylä, stands this small, simple concrete block. This modest-looking cube, however, has played a part in both calculating the size of the Earth and creating the first accurate map of Finland. How? With triangles. Before satellites and GPS devices triangulation was the most accurate method of calculating the shapes and distances of the planet. After the Earth’s flattening on the poles had been proven by measurements done in the Tornio river valley, the head of the Tartu observatory Friedrich Georg Wilhelm von Struve developed an idea to calculate the true size of the Earth by measuring the full length of one longitudinal line. By coincide he decided that the line to be measured was the one running through Tartu. Struve planned and organised a chain known as Struve Geodetic Arc, starting from Norwegian Lapland and running through 10 modern states, all the way to the Black Sea. Back then, however, it only ran on Swedish and Russian lands. The measurements were done between 1816 and 1855, taking almost 40 years. To better understand why the party organised by Struve had to climb this remote hill in the Finnish Lake country I have to explain some maths. Sorry. The sum of the angles of a triangles is famously 180 degrees. This means that if the size of two angles is known it is easy to calculated the the third. The laws of trigonometry also guarantee that no matter of the shape of the triangle if the length one side and sizes of all the angles are known, the lengths of the other two sides can be calculated with a sin formula. If multiple triangles form a chain with the triangles sharing points every single side from every triangle can be calculated if only one side from one triangle is known. This allows easy and accurate measurements of very long distances. The measurements themselves for Struves project were done by climbing to predetermined high places, possibly to towers purpose built for this project, which had a direct line of sight to two other points of the triangle. With the help of various devices the angle or angles between other points was measured with the help of lights shown from those places, after which the precise coordinates of the measurement spot were calculated by the location and movement of stars. These methods were so accurate that partly the same methods were used up until the 1980’s. In total the Struve Geodetic Arc was 2820 kilometers long and included 265 measurement points. Unesco has also recognised the value of the Arc and added it to the World Heritage list in 2005. There were originally many more of these measuring points in Finland, but only six of those are now protected. You see, these points were marked in to the ground with metal plaques and lead screws but local people thought them to be a little too valuable for this so the only remaining clues left are a few holes in the rock and a cross here and there. The last measurements here in Oravivuori were made in the 1980’s after which the satellite and GPS technology largely replaced triangulation in land surveying. This cube here then is standing as a memorial from the times when the best way to measure long distances and shapes of the World was a few high spots and a lot of triangles.

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