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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
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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 ;-). |
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Different methods
of finding a centre
1st aspect
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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.
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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
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Summary
This picture shows the position of all mentioned centres.
The geographic centre of Lippe is in Point 6. |
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Lippische Rose
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The Geographic Centre
of Germany top
I describe here how you can determine the geographic centre in a simple
experiment.
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1
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... ...
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:
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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. |
Geographical Centres
on the Internet top
German
Landesvermessungsamt NRW
Der geographische
Mittelpunkt von Nordrhein-Westfalen (Dortmund-Aplerbeck)
Stadt Belzig
Mittelpunkt
der DDR
Torsten Städtler & Sven Heinemann
Die Reise zum geografischen
Mittelpunkt Deutschlands
Wikipedia
Mittelpunkt
Europas, Mittelpunkt
Deutschlands
English
Algorithmic Solutions Software GmbH
Extremal
Circles
BBC
In pictures: The
centre of Great Britain
David Austin (Grand Valley State University)
The
Center of Population of the United States
NN
Geographic
Center of the 48 States
Rashid Bin Muhammad
Smallest
Enclosing Circle Problem
Wikipedia
Bounding sphere,
Geographical
centre of Europe
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
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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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