Numerical calculation of the true geographic midpoint of Germany by filling 68k boundary coordinates with one million squares and then determining the most central square.
This repository is the result of a 40 pages long course paper from the 10th class in high school. In order to summarize and publish the key findings of our paper I created a website (only available in German).
Have a look at: www.der-mittelpunkt-deutschlands-neu-berechnet.com/
Niederdorla, Silberhausen, Flinsberg, Krebeck, Landstreit, and many more. Currently there are officially 5 midpoints in Germany. All have been precisely calculated using a wide variety of methods. However, each method has its own shortcomings and inaccessibilities, and so each calculated midpoint is fraught with errors. Let's take a look at one of the most famous midpoints in Germany - Niederdorla. For this midpoint calculation, a rectangle was drawn around the German border from the degrees of latitude and longitude and then the midpoint in Niederdorla was determined by the intersections of the diagonals of the rectangle. But does this midpoint really represent the true geographic midpoint of Germany? In our eyes, this is an outdated, obsolete approximation to the midpoint of a geographical area. The midpoint calculated in this way only represents the midpoint of the spanned rectangle, but not the midpoint of the area to be calculated. Maybe you believe now that every area of a federal state somehow approximates a rectangle and so the diagonal intersection is approximately a representative result. Well, then imagine the calculation methods using the example of Japan. The midpoint of Japan would be in the sea. But shouldn't the midpoint of a surface be at least in the area!?
In our research project and simultaneous computer science course paper for the 10th grade, we show the disadvantages of all existing methods in detail. Furthermore, we have made it our goal to develop a method which determines the true midpoint of an area and dispenses with the shortcomings of the existing methods. Until now, the midpoint of an area has been defined by its inadequate calculation method. In contrast to that, we define the midpoint via its actual mathematical determination. In this context, we worked out and implemented the method of "squaring" (German: Quadrierung) and calculated the new midpoint of Germany, which is located in the center of Mihla. The method os squaring works as follows: First we divided the German geographical area into more than a million squares. Then we determine the square with the smallest sum of distances in relation to all other squares as the midpoint.
In this project, the advantages and the accuracy of the squaring method are compared with the previous methods. We also showed that the midpoint of a area is not equal to the center of gravity. Accordingly, we also recalculated center of gravity of Germany, with the result in east of Bischofroda. In addition to the midpoint of Germany, we also calculated the midpoint of Usedom and Japan. Furthermore, we also calculated the number of square kilometers of the German area and implemented the calculation method with the spanned rectangle. By doing so we confirmed the official midpoint in Niederdorla to check our reference systems and coordinate systems. We also extended the method of squaring to 3D space, which also allows us to calculate the midpoint and center of gravity of a 3D-body.
Below you can see the main result of our paper: An image of the squared geographical map of Germany with a total of 1,074,000 filled squares at a picture resolution of 475 megapixels. The midpoint is colored RED (Mihla) and the outermost point (outpoint) is green (Sylt - north west). The closer the square is to the midpoint (sum of distances per square), the blacker it is colored.
The official caluclation resuts of the coordinates of the midpoint are:
ETRS89/UTM (WGS84) Z: 32U E: 592769 W: 5659306
(Can be plotted on a map at https://www.koordinaten-umrechner.de/)
Converted Longitude: 51.077808 Latitude: 10.324368
(Can be plotted on a map at https://www.google.de/maps)
