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North Rhine-Westphalia

North Rhine-Westphalia is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand North Rhine-Westphalia rather than just read about it. In short: North Rhine-Westphalia or North-Rhine/Westphalia (German: Nordrhein-Westfalen [ˌnɔɐtʁaɪn vɛstˈfaːlən] ), commonly shortened to NRW, is a landlocked state (Land) in Western Germany. With more than 18 million inhabitants, it is the most populous state in Germany.

North Rhine-Westphalia — main illustration
North Rhine-Westphalia — illustration

Key takeaways

  • North Rhine-Westphalia belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect North Rhine-Westphalia to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of North Rhine-Westphalia from memory before moving on to harder problems.

Reference excerpt

North Rhine-Westphalia or North-Rhine/Westphalia (German: Nordrhein-Westfalen [ˌnɔɐtʁaɪn vɛstˈfaːlən] ), commonly shortened to NRW, is a landlocked state (Land) in Western Germany. With more than 18 million inhabitants, it is the most populous state in Germany. Apart from the city-states (Berlin, Hamburg and Bremen), it is also the most densely populated state in Germany. Covering an area of 34,084 km2 (13,160 sq mi), it is the fourth-largest German state by size. North Rhine-Westphalia features 30 of the 81 German municipalities with over 100,000 inhabitants, including Cologne (over 1 million), the state capital Düsseldorf (630,000), Dortmund and Essen (about 590,000 inhabitants each) and other cities predominantly located in the Rhine-Ruhr metropolitan area, the largest urban area in Germany and the fourth-largest on the European continent. The location of the Rhine-Ruhr at the heart of the European Blue Banana makes it well connected to other major European cities and metropolitan areas like the Randstad, the Flemish Diamond and the Frankfurt Rhine-Main Region. North Rhine-Westphalia was established in 1946 after World War II from the Prussian provinces of Westphalia and the northern part of Rhine Province (North Rhine), and the Free State of Lippe by the British military administration in Allied-occupied Germany and became a state of the Federal Republic of Germany in 1949. The city of Bonn served as the federal capital until the reunification of Germany in 1990 and as the seat of government until 1999. Culturally, North Rhine-Westphalia is not a uniform area; there are significant differences, especially in traditional customs, between the Rhineland region on the one hand and the regions of Westphalia and Lippe on the other. Its economy is the largest among German states by GRDP, but the state ranks below the national average in GRDP per capita.

History

Creation The state of North Rhine-Westphalia was established by the British military administration's "Operation Marriage" on 23 August 1946 by merging the province of Westphalia and the northern parts of the Rhine Province, both being political divisions of the former state of Prussia within the German Reich. On 21 January 1947, the former state of Lippe was merged with North Rhine-Westphalia. The constitution of North Rhine-Westphalia was then ratified through a referendum.

Rhineland

The first written account of the area was by its conqueror, Julius Caesar, the territories west of the Rhine were occupied by the Eburones and east of the Rhine he reported the Ubii (across from Cologne) and the Sugambri to their north. The Ubii and some other Germanic tribes such as the Cugerni were later settled on the west side of the Rhine in the Roman province of Germania Inferior. Julius Caesar conquered the tribes on the left bank, and Augustus established numerous fortified posts on the Rhine, but the Romans never succeeded in gaining a firm footing on the right bank, where the Sugambri neighboured several other tribes including the Tencteri and Usipetes. North of the Sigambri and the Rhine region were the Bructeri. As the power of the Roman Empire declined, many of these tribes came to be seen collectively as Ripuarian Franks and they pushed forward along both banks of the Rhine, and by the end of the fifth century had conquered all the lands that had formerly been under Roman influence. By the eighth century, the Frankish dominion was firmly established in western Germany and northern Gaul, but at the same time, to the north, Westphalia was being taken over by Saxons pushing south. The Merovingian and Carolingian Franks eventually built an empire which controlled first their Ripuarian kin, and then the Saxons. On the division of the Carolingian Empire at the Treaty of Verdun, the part of the province to the east of the river fell to East Francia, while that to the west remained with the kingdom of Lotharingia. By the time of Otto I (d. 973), both banks of the Rhine had become part of the Holy Roman Empire, and the Rhenish territory was divided between the duchies of Upper Lorraine on the Moselle and Lower Lorraine on the Meuse. The Ottonian dynasty had both Saxon and Frankish ancestry.

As the central power of the Holy Roman Emperor weakened, the Rhineland split into numerous small, independent, separate vicissitudes and special chronicles. The old Lotharingian divisions became obsolete, although the name survives for example in Lorraine in France, and throughout the Middle Ages and even into modern times, the nobility of these areas often sought to preserve the idea of a preeminent duke within Lotharingia, something claimed by the Dukes of Limburg, and the Dukes of Brabant. Such struggles as the War of the Limburg Succession therefore continued to create military and political links between what is now Rhineland-Westphalia and neighbouring Belgium and the Netherlands. In spite of its dismembered condition and the sufferings it underwent at the hands of its French neighbours in various periods of warfare, the Rhenish territory prospered greatly and stood in the foremost rank of German culture and progress. Aachen was the place of coronation of the German emperors, and the ecclesiastical principalities of the Rhine bulked largely in German history. Prussia first set foot on the Rhine in 1609 by the occupation of the Duchy of Cleves and about a century later Upper Guelders and Moers also became Prussian. At the Peace of Basel in 1795, the whole of the left bank of the Rhine was resigned to France, and in 1806, the Rhenish princes all joined the Confederation of the Rhine. After the Congress of Vienna, Prussia was awarded the entire Rhineland, which included the Grand Duchy of Berg, the ecclesiastic electorates of Trier and Cologne, the free cities of Aachen and Cologne, and nearly a hundred small lordships and abbeys. The Prussian Rhine province was formed in 1822 and Prussia had the tact to leave the lower Rhenish districts in undisturbed possession of the liberal institutions to which they had become accustomed under the republican rule of the French. In 1920, the districts of Eupen and Malmedy were transferred to Belgium (see German-speaking Community of Belgium).

Westphalia

… excerpt ends here. Continue reading the full article.

Illustrations

North Rhine-Westphalia illustration
North Rhine-Westphalia illustration
North Rhine-Westphalia illustration
North Rhine-Westphalia: Map of the Lower Rhenish–Westphalian Circle in 1799 by John Cary
Map of the Lower Rhenish–Westphalian Circle in 1799 by John Cary
North Rhine-Westphalia: Ratification of the Peace of Westphalia of 1648 in Münster by Gerard Terborch
Ratification of the Peace of Westphalia of 1648 in Münster by Gerard Terborch

Worked examples

Example 1 — a first encounter with North Rhine-Westphalia

Start with the simplest possible case. Write down what North Rhine-Westphalia claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to North Rhine-Westphalia before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about North Rhine-Westphalia ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of North Rhine-Westphalia

In research
North Rhine-Westphalia appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses North Rhine-Westphalia in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
North Rhine-Westphalia is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1946 establishments in Germany, NUTS 1 statistical regions of the European Union, North Rhine-Westphalia, so understanding it makes those chapters shorter.
In everyday life
Look for North Rhine-Westphalia outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study North Rhine-Westphalia in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what North Rhine-Westphalia means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain North Rhine-Westphalia out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is North Rhine-Westphalia in simple terms?

North Rhine-Westphalia or North-Rhine/Westphalia (German: Nordrhein-Westfalen [ˌnɔɐtʁaɪn vɛstˈfaːlən] ), commonly shortened to NRW, is a landlocked state (Land) in Western Germany. With more than 18 million inhabitants, it is the most populous state in Germany.

Why does North Rhine-Westphalia matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study North Rhine-Westphalia?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on North Rhine-Westphalia.

Tags

  • 1946 establishments in Germany
  • NUTS 1 statistical regions of the European Union
  • North Rhine-Westphalia
  • States and territories in Europe established in 1946
  • States of Germany

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