Geographic Centre
 What is the Geographic Centre? Different  Methods The Geographic Centre of Germany Geographical Centres on the Internet References .
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What is the Geographic Centre?
It  is the centre of a country.
The country can be a municipality, a district, a state, or a confederation of states.

There are different methods to find a centre because there is no official definition. Giving a geographical centre is a game and you shouldn't take it too seriously (1). Anyway it has a certain meaning: Small towns can leave their anonymity and can build a monument.
Obviously the physical centre of gravity is seen as the geographical centre.
You find it, if you transfer the shape of a country on cardboard, cut it out and look for the centre of gravity of this slice. You can also simulate this process by a computer.

Different  Methods   top
 The „Kreis Lippe“ is chosen as a country on this page. I live there.  Lippe is situated in the north-eastern corner of the state North Rhine-Westphalia.

Some tiny local patriotism:
 ...... ...... Lippe is so important that its coat of arms, the „Lippische Rose“, appears in that of the state NRW ;-).

Different methods of finding a centre
1st aspect
 ...... The „Kreis Lippe“ and the former principality Lippe that existed up to1945 are nearly the same. So it is clear that you declare the home of the duke, Detmold castle, to be the centre of Lippe.

2nd aspect
 ...... You mark the three biggest towns and look for the centre of gravity of the triangle they form. You find it as the intersection of the medians.  So you get Hörstmar.  You can still take into account the number of the inhabitants of the town, when you look for the centre. More: You can take all towns of Lippe.

3rd aspect
You lay a rectangle around Lippe that touches the border in four points. The intersection of the diagonals can be seen as the  centre of Lippe.  There are many possibilities to choose a rectangle. Here are only two of them.

4th aspect
The next centre is that of a circle.
 ...... You find the centre by this: >Choose three clear-cut points A,B, C on the border. >Draw the triangle ABC. >Draw the normals from the midpoints of the sides of the triangle. >Take the point of intersection. The centre of the circumscribed circle is the centre of Lippe.  There is the village of Cappel

You can change this method:
You choose as many points as possible, give their coordinates, and determine by an algorithm and by a computer the smallest enclosing circle.
It is definitely fixed [(2), page 77].

This method is explained on Rashid Bin Muhammad's  homepage of (URL below) and illustrated by a Java applet you can nicely play with.

You find more web sites with google.com and the string smallest.enclosing.circle.

I don't know, whether the centre of a country  is determined this way. This is not the search for the centre of gravity.

5th aspect
 ...... This centre can be found in an experiment.  You transfer the shape of Lippe on cardboard and cut it out.  Then you hang up the slice on two points A and B one after the other and determine the vertical lines (red) going through the respective point.  The intersection is the centre of gravity and so the geographic centre. There is Wiembeck. This method is explained more precisely below.

Summery
 ...... Summary This picture shows the position of all mentioned centres.  The geographic centre of Lippe is in Point 6. ...... Lippische Rose

The Geographic Centre of Germany    top
I describe here how you can determine the geographic centre in a simple experiment.
 ...... 1 ...... 2 >Copy the shape of Germany from a map. >Cut out the silhouette. >(Picture 1) Fasten the slice near the border with a needle on the wall and let it hang freely. Hang a thread with a hanger on the same needle and fasten below a clothes-pin. >Mark the way of the “plumbline“ by a straight line >(Picture 2) Repeat this process on another point near the border.  >The intersection is the centre of gravity.
Result:
 ...... The centre is about 10  km north east of Eisenach and the Wartburg. The position of Eisenach is marked by a full circle.

It is understandable that this method of finding the centre of gravity is very rough.
>The border of Germany has many corners. It is already „straightened“ in the map.
>It  isn’t possible to cut it out exactly.
>What about the islands? Here the islands of Usedom, Rügen, Pellworm are taken into account, the islands in the North Sea are left out.
By the way, Americans solved this problem with Alaska and Hawai in this way: They only determined the centre of the mainland. In spite of that there are more problems. How do you take into account the Great Lakes, the curvature of the earth, and the projection of the earth surface?

 ...... You find villages like Flinsberg, Silberhausen and Niederorla as centres of Germany at de.wikipedia.  The villages lie north of my place x.

Geographic Centre of Bad Salzuflen

In front of the bakery Wiebusch  Heldmanstraße 12, 32108 Bad Salzuflen

Geographical Centres on the Internet    top

German

Berliner Morgenpost
Der Mittelpunkt der DDR liegt tief im dunklen Wald

Gerd Lamprecht
Geometrischer Schwerpunkt

Landesvermessungsamt NRW
Der geographische Mittelpunkt von Nordrhein-Westfalen    (Dortmund-Aplerbeck)

Torsten Städtler & Sven Heinemann
Die Reise zum geografischen Mittelpunkt Deutschlands

English

Algorithmic Solutions Software GmbH
Extremal Circles

David Austin (Grand Valley State University)
The Center of Population of the United States

Dale Sanderson
Geographic Center of the 48 States

Smallest Enclosing Circle Problem

References   top
(1) Andreas Engel: Emsige Suche nach der deutschen Mitte, Darmstädter Echo vom 14.2.1984.
Nachdruck in Mathematiklehren Heft 8, 8.2.1985
 ............ If the slice is of thick cardboard or wood, you can lay it at the top of a vertical standing needle. The slice stays horizontally.  A statement of the article:  The geographic centre of the German Republic" (before 1990) "is  near Herbstein near Lauterbach in Hessen."

(2) Rademacher, Toelplitz: Von Zahlen und Figuren, Berlin-Heidelberg-New York, 1930, Nachdruck 1968

This page has hints by Torsten Sillke.

Gail from Oregon Coast, thank you for supporting me in my translation.

Feedback: Email address on my main page

This page is also available in German.

URL of my Homepage: http://www.mathematische-basteleien.de/

©  2001 Jürgen Köller

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