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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
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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 ;-). |
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:
... ...
|
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
Landesvermessungsamt NRW
Der
geographische Mittelpunkt von Nordrhein-Westfalen
(Dortmund-Aplerbeck)
Wikipedia
Mittelpunkt
Deutschlands, Mittelpunkt
Europas, Liste
der geographischen Mittelpunkte,
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
Rashid Bin Muhammad
Smallest
Enclosing Circle Problem
Wikipedia
Bounding
sphere,
Geographical
centre of Europe, Geographical
centre
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: https://www.mathematische-basteleien.de/
©
2001 Jürgen Köller
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