West Berlin

West Berlin was a political enclave which comprised the western part of Berlin during the years of the Cold War. There was no specific date on which the sectors of Berlin occupied by the Western Allies became "West Berlin", but 1949 is accepted as the year in which the name was adopted. West Berlin aligned itself politically with the Federal Republic of Germany and was directly or indirectly represented in its federal institutions. West Berlin was formally controlled by the Western Allies and was surrounded by the Soviet-controlled East Berlin and East Germany. West Berlin had great symbolic significance during the Cold War, as it was considered by westerners as an "island of freedom", it was subsidised by West Germany as a "showcase of the West". A wealthy city, West Berlin was noted for its distinctly cosmopolitan character, as a centre of education and culture. With about two million inhabitants, West Berlin had the largest population of any city in Germany during the Cold War era. West Berlin was 100 miles east and north of the Inner German border and only accessible by land from West Germany by narrow rail and highway corridors.

It consisted of the American and French occupation sectors established in 1945. The Berlin Wall, built in 1961, physically separated West Berlin from its East Berlin and East German surroundings until it fell in 1989. On 3 October 1990, the day Germany was reunified and West Berlin formally reunited as the city of Berlin; the Potsdam Agreement established the legal framework for the occupation of Germany in the wake of World War II. According to this agreement, Germany would be formally under the administration of four Allies until a German government "acceptable to all parties" could be established; the territory of Germany, as it existed in 1937, would be reduced by most of Eastern Germany thus creating the former eastern territories of Germany. The remaining territory would be divided into four zones, each administered by one of the four allied countries. Berlin, surrounded by the Soviet zone of occupation—newly established in most of Middle Germany—would be divided, with the Western Allies occupying an enclave consisting of the western parts of the city.

According to the agreement, the occupation of Berlin could end only as a result of a quadripartite agreement. The Western Allies were guaranteed three air corridors to their sectors of Berlin, the Soviets informally allowed road and rail access between West Berlin and the western parts of Germany. At first, this arrangement was intended to be of a temporary administrative nature, with all parties declaring that Germany and Berlin would soon be reunited. However, as the relations between the Western Allies and the Soviet Union soured and the Cold War began, the joint administration of Germany and Berlin broke down. Soon, Soviet-occupied Berlin and western-occupied Berlin had separate city administrations. In 1948, the Soviets tried to force the Western Allies out of Berlin by imposing a land blockade on the western sectors—the Berlin Blockade; the West responded by using its air corridors for supplying their part of the city with food and other goods through the Berlin Airlift. In May 1949, the Soviets lifted the blockade, West Berlin as a separate city with its own jurisdiction was maintained.

Following the Berlin Blockade, normal contacts between East and West Berlin resumed. This was temporary. In 1952, the East German government began further isolating West Berlin; as a direct result, electrical grids were separated and phone lines were cut. The Volkspolizei and Soviet military personnel continued the process of blocking all the roads leading away from the city, resulting in several armed standoffs and at least one skirmish with the French Gendarmerie and the Bundesgrenzschutz that June. However, the culmination of the schism did not occur until 1961 with the construction of the Berlin Wall. From the legal theory followed by the Western Allies, the occupation of most of Germany ended in 1949 with the establishment of the Federal Republic of Germany on 23 May and of the German Democratic Republic on 7 October. Under Article 127 of the Basic Law of the Federal Republic, provision was made for federal laws to be extended to Greater Berlin as well as Baden, Rhineland-Palatinate and Württemberg-Hohenzollern within one year of its promulgation.

However, because the occupation of Berlin could only be ended by a quadripartite agreement, Berlin remained an occupied territory under the formal sovereignty of the allies. Hence, the Basic Law was not applicable to West Berlin. On 4 August 1950 the House of Representatives passed a new constitution, declaring Berlin to be a state of the Federal Republic and the provisions of the Basic Law as binding law superior to Berlin state law. However, this became statutory law only on 1 September and only with the inclusion of the western Allied provision according to which Art. 1, clauses 2 and 3, were deferred for the time being. It stated that: Article 87 is interpreted as meaning that during the transitional period Berlin shall possess none of the attributes of a twelfth Land; the provision of this Article concerning the Basic Law will only apply to the extent necessary to prevent a conflict between this Law and the Berlin Constitution... Thus civic liberties and personal rights (except f

Stern–Brocot tree

In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree. The Stern–Brocot tree was discovered independently by Moritz Stern and Achille Brocot. Stern was a German number theorist; the root of the Stern–Brocot tree corresponds to the number 1. The parent-child relation between numbers in the Stern–Brocot tree may be defined in terms of continued fractions or mediants, a path in the tree from the root to any other number q provides a sequence of approximations to q with smaller denominators than q; because the tree contains each positive rational number once, a breadth first search of the tree provides a method of listing all positive rationals, related to Farey sequences. Every positive rational number q may be expressed as a continued fraction of the form q = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1 ⋱ + 1 a k = where k and a0 are non-negative integers, each subsequent coefficient ai is a positive integer.

This representation is not unique because one has = for every sequence of coefficients a0... ak−1. Using this identity to rewrite any representation of the former form into the latter form, one may obtain that the final coefficient satisfies ak ≥ 2. Unless q = 1, the number q has a parent in the Stern–Brocot tree given by the continued fraction expression, which in case ak = 2 one can rewrite as. For instance, the rational number ​23⁄16 has the continued fraction representation 23 16 = 1 + 1 2 + 1 3 + 1 2 =, so its parent in the Stern–Brocot tree is the number = = 1 + 1 2 + 1 4 = 13 9; this parent is formed by decreasing the denominator in the innermost term of the continued fraction by 1, contracting with the previous term if the fraction becomes 1 1. Conversely each number q in the Stern–Brocot tree has two children: if q = = one child is the number represented by the continued fraction [

Helene Madison

Helene Emma Madison was an American competition swimmer, Olympic champion, former world record-holder. Madison won three gold medals in freestyle event at the 1932 Summer Olympics in Los Angeles, along with Romeo Neri of Italy, the most successful athlete at the 1932 Olympics: women's 100-meter freestyle, 400-meter freestyle, 4×100-meter freestyle relay. In sixteen months in 1930 and 1931, she broke sixteen world records in various distances. Following the 1932 Olympics she appeared in the films The Human Fish and The Warrior's Husband and hence, as a professional, was not allowed to participate in the 1936 Summer Olympics in Berlin. After her swimming career, she had odd jobs as a swimming instructor, department store clerk and a nurse. Madison had Helene Madison Ware, who at one time lived in Marysville, Washington. Divorced three times and living alone, she died of throat cancer in 1970 in Washington, she was inducted into the International Swimming Hall of Fame in 1966, the U. S. Olympic Hall of Fame in 1992.

List of members of the International Swimming Hall of Fame List of multiple Olympic gold medalists List of Olympic medalists in swimming World record progression 100 metres freestyle World record progression 200 metres freestyle World record progression 400 metres freestyle World record progression 800 metres freestyle World record progression 1500 metres freestyle World record progression 4 × 100 metres freestyle relay Helene Madison – Honor Swimmer profile at International Swimming Hall of Fame Helene Madison at the International Olympic Committee Helene Madison on IMDb