Berlin

Berlin (/bərˈlɪn/, German: [bɛɐ̯ˈliːn]) is the capital of Germany and one of the 16 states of Germany. With a population of 3.5 million people, it is the second most populous city proper and the seventh most populous urban area in the European Union. Located in northeastern Germany on the banks of Rivers Spree and Havel, it is the centre of the Berlin-Brandenburg Metropolitan Region, which has about six million residents from over 180 nations. Due to its location in the European Plain, Berlin is influenced by a temperate seasonal climate. Around one-third of the city's area is composed of forests, parks, gardens, rivers and lakes.

First documented in the 13th century and situated at the crossing of two important historic trade routes, Berlin became the capital of the Margraviate of Brandenburg (1417–1701), the Kingdom of Prussia (1701–1918), the German Empire (1871–1918), the Weimar Republic (1919–1933) and the Third Reich (1933–1945).Berlin in the 1920s was the third largest municipality in the world. After World War II, the city was divided; East Berlin became the capital of East Germany while West Berlin became a de facto West German exclave, surrounded by the Berlin Wall (1961–1989) and East Germany territory. Following German reunification in 1990, Berlin was once again designated as the capital of united Germany.

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100 (number)

100 or one hundred (Roman numeral: Ⅽ) is the natural number following 99 and preceding 101.

In medieval contexts, it may be described as the short hundred or five score in order to differentiate the English and Germanic use of "hundred" to describe the long hundred of six score or 120.

In mathematics

100 is the square of 10 (in scientific notation it is written as 10²). The standard SI prefix for a hundred is "hecto-".

100 is the basis of percentages (per cent meaning "per hundred" in Latin), with 100% being a full amount.

100 is the sum of the first nine prime numbers, as well as the sum of some pairs of prime numbers e.g., 3 + 97, 11 + 89, 17 + 83, 29 + 71, 41 + 59, and 47 + 53.

100 is the sum of the cubes of the first four integers (100 = 1³ + 2³ + 3³ + 4³). This is related by Nicomachus's theorem to the fact that 100 also equals the square of the sum of the first four integers: 100 = 10² = (1 + 2 + 3 + 4)².

2⁶ + 6² = 100, thus 100 is a Leyland number.

100 is an 18-gonal number. It is divisible by the number of primes below it, 25 in this case. It can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient. It can be expressed as a sum of some of its divisors, making it a semiperfect number.

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