Around the date 1763, a problem arose in Königsberg, Germany (Diestel). This problem began with a few curious citizens but soon spread to scientists and other intellects, and eventually became known as the Königsberg Bridge Problem. The town of Königsberg was cut into four separate land masses by the river Pregel (Green). At the time, Königsberg was a large trading city, valuable because of its position on the river. The prosperity of the city allowed the people to build seven bridges so citizens could traverse through these four separate land masses with ease. Each bridge had a name, which included Connecting Bridge, Honey Bridge, High Bridge, Blacksmith’s Bridge, Merchant’s Bridge, Wooden Bridge, and Green Bridge. As the story goes, citizens would often make bets among themselves to see who could pick a route that crossed each of the seven bridges only once, not yet knowing that this was an impossible feat (Paoletti). This was the beginning of the Königsberg Bridge Problem, which would soon attract the attention of many, including a man by the name of Leonard Euler. Not only would the solution to this problem set the grounds for what would become known as the graph theory, but it would also be forever remembered in the world of mathematics (Green, Paoletti, and Diestel 19).
The bridges of Königsberg posed a problem not many, if any, had ever considered before. At first, their question was, could all seven bridges be crossed once and only once in order to reach each land mass? But soon it became, could all bridges such a path take place in any network of bridges anywhere? The answer was unsure, though none could succeed in the task, until Leonard Euler, a genius of the eighteenth-century, proposed his solution to the problem...
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...00’s when curious citizens began to wonder if a path could be made across seven bridges without crossing them more than once. Many great things come from humble beginnings, and the bridges of Königsberg were definitely a humble beginning for such a thing as the graph theory.
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Diestel, Reinhard. Graph Theory. New York: Springer, 2000. eBook.
Green, Thomas M. “Euler’s Königsberg’s Bridges Problem”. Contra Costa College:
Mathematics Department. Contra Costa College, 2014. Web. 12 February 2014.
Paoletti, Teo. “Leonard Euler's Solution to the Konigsberg Bridge Problem”.
Mathematical Association of America (2011): n.pag. Web. 13 February 2014.
Yamaguchi, Jun-ichi. “Introduction of Graph Theory”. EMAT 6690. N.p. Web. 13 February
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Steven Hermosillo Professor Wallace Fire Tech 105 15 November 2015 Silver Bridge Collapse According to Wikipedia, Forty-six people were killed in the silver-bridge collapse and another nine people were injured. “The Silver Bridge was an eye-bar-chain suspension bridge built in 1928 and named for the color of its aluminum paint. The bridge connected Point Pleasant, West Virginia, and Gallipolis, Ohio, over the Ohio River” (Wikipedia). This was a highly used bridge serving thousands of cars a day before the collapse.
OWLCREEK BRIDGE" ." ABP Journal. 1.1 (2005): n. page. Web. 23 Mar. 2014. Bierce, Ambrose “An Occurrence at Owl Creek Bridge”. The Norton Introduction to
The Golden Gate bridge, standing as an icon of roadway innovations, took multiple engineers years to design and complete. They could not just simply build an ordinary bridge. They had to take into consideration the physics behind it, as well as, what kind of effect the environment would have upon the bridge. The bridge sits along one of the most active fault lines in the world, so engineers had to make sure their bridge could withstand a little movement. Today the Golden Gate bridge still stands tried and true, as does many other innovations that 20th century engineers came up with.
The concept for the Holland Tunnel was developed in 1906.1 In 1906, a coalition of the New York State and New Jersey Interstate Bridge and Tunnel Commission began studies for a bridge connecting lower Manhattan to Jersey City, New Jersey.2 By the end of World War I (1918), the number of cars and trucks on U.S. roads had skyrocketed. This trend did not differ in the streets of New York City.3 At this time the Hudson River ferries were carrying about 30 million vehicles each year (24,000 vehicles a day3) from New York to New Jersey. This had become a major problem for commuters and a solution was needed.2
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How important are Miller's language choices and use of stage directions in aiming the audience to view Eddie as a tragic hero in the play ‘A View from the Bridge’?
The first and most challenging problem associated with building the Mackinac Bridge arrived long before the bridge was even designed. Financing such an enormous project was no easy feat. In 1928, the idea of connecting the upper and lower peninsulas was proposed to Congress for the first time (Brown 4). At the time, the suspected bridge project was very much under government scrutiny and control. In fact, the initial boost in interest in pursuing the construction of a bridge came about due to the depression. The Public Works Administration (PWA) had been created under President Franklin D. Roosevelt’s New Deal economic plan which would fund certain construction projects with th...
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The Berlin Crisis reached its height in the fall of 1961. Between August and October of that year, the world watched as the United States and the Soviet Union faced off across a new Cold War barrier, the Berlin Wall. In some ways, the Wall was Khrushchev’s response to Kennedy’s conventional buildup at the end of July, and there were some in the West who saw it that way. However, as Hope Harrison has clearly shown, Khrushchev was not the dominant actor in the decision to raise the Wall, but rather acquiesced to pressure from East German leader Walter Ulbricht, who regarded the Wall as the first step to resolving East Germany’s political and economic difficulties. The most pressing of these difficulties was the refugee problem, which was at its height in the summer of 1961 as thousands of East Germans reacted to the increased tensions by fleeing westward. But Ulbricht also saw the Wall as a way to assert East German primacy in Berlin, and thus as a way to increase the pressure on the West to accept East German sovereignty over all of Berlin.
The mayor of Cologne, Konrad Adenauer, dedicated the first completed length of the system, stretching roughly 18 miles from Cologne to Bonn in 1932. When the Nazis took over, they built a further 2,400 miles to move military personnel and goods; with an additional 1,550 miles under construction before World War...
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Quinn, R. (2008). Building the Bridge As You Walk On It. In J.L. Pierce, & J.W. Newstrom (Eds). The Manager’s Bookshelf (pp 233-236). Upper Saddle River, NJ: Pearson
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.