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...
... middle of paper ...
...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.
Works Cited
Białynicki-Birula, Iwo. The bridges of Königsberg: Graph Theory. Oxford University Press,
2004. Print.
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
2014.
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.
The Jericho Covered Bridge in Kingsville, Maryland was built in 1865 and restored in 1982. The bridge is 100 feet long and cased in cedar planks and timber beams. Legend has it that after the Civil War many lynchings occurred on the bridge. Passersby were supposedly captured on the bridge and hung from the upper rafters. The bridge is very close to my house and I have driven over it several times. The storyteller, age 19, also lives a couple minutes away from the bridge. He has lived in Kingsville, Maryland his entire life. He recalled a dramatic story he had heard from his older brother involving the haunted bridge.
The Victoria Bridge, constructed in the mid-19th-Century in British North America, is a famous Canadian landmark that set the stage for the beginning of the industrialization phase of Canada and more specifically, Montreal. It would eventually “play a vital role in the growth of the city and the country”.
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.
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 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...
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
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...
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 Tacoma Narrows Bridge is perhaps the most notorious failure in the world of engineering. It collapsed on November 7, 1940 just months after its opening on July 1, 1940. It was designed by Leon Moisseiff and at its time it was the third largest suspension bridge in the world with a center span of over half a mile long. The bridge was very narrow and sleek giving it a look of grace, but this design made it very flexible in the wind. Nicknamed the "Galloping Gertie," because of its undulating behavior, the Tacoma Narrows Bridge drew the attention of motorists seeking a cheap thrill. Drivers felt that they were driving on a roller coaster, as they would disappear from sight in the trough of the wave. On the last day of the bridge's existence it gave fair warning that its destruction was eminent. Not only did it oscillate up and down, but twisted side to side in a cork screw motion. After hours of this violent motion with wind speeds reaching forty and fifty miles per hour, the bridge collapsed. With such a catastrophic failure, many people ask why such an apparently well thought out plan could have failed so badly?(This rhetorical question clearly sets up a position of inquiry-which iniates all research.) The reason for the collapse of the Tacoma Narrows Bridge is still controversial, but three theories reveal the basis of an engineering explanation. (Jason then directly asserts what he found to be a possible answer to his question.)
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.
In 1872, Charles Crocker, a railroad entrepreneur, called for a bridge that connected the Golden Gate Strait. The strait, approximately 3 miles long and 1 mile wide, is the entrance to San Francisco Bay, which is in California, from the Pacific Ocean. By 1916, Michael M. O'Shaughnessy, a San Francisco City Engineer, was asked by city officials to see if it was possible to build a bridge that crossed the strait. While most engineers claimed that a bridge was not able to be built and that it would cost about $100 million, Joseph Baermann Strauss claimed that a bridge would be easily built and would only cost about $25 to $30 million. After the long process of having the bridge design approved for constructing, on January 5, 1933, the construction of the Golden Gate Bridge had begun (“Golden Gate Bridge Research Library”). The main constructors included Joseph Baermann Strauss, Irving Morrow and Charles Ellis. Strauss had hired Irving Morrow to design small features for the bridge like pedestrian walkways and streetlamps. Morrow also made the bridge look luxurious by using a style called art deco (“Irving Morrow” and “Art Deco”). Since Morrow was to design the Bridge, he knew that it would play a significant role on its display in regards to its surroundings. As of today, “the color blends perfectly with the changing season tints of the spans’ natural setting against the San Francisco skyline and the Marin hills” (“Golden Gate Bridge Research Library”). Meanwhile, Charles Ellis was the engineering expert. He was later accused by Strauss of wasting money and time by working on equations of forces at the Golden Gate Bridge. Ellis was then told not to go back to construct the bridge. Ellis could not drop out of the project because he w...
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.