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III. THE SEVEN BRIDGES OF KOENIGSBERG: Đề thi thật IELTS READING (IELTS Reading Recent Actual Test)
THE SEVEN BRIDGES OF KOENIGSBERG
Where the Pregolya river meets the Baltic sea, the Russian enclave of Kaliningrad looks out across the Vistula lagoon towards Gdansk in Poland. In past times these two cities formed part of a vast network of trading cities stretching from Estonia to England, flourishing through the later Medieval period thanks to a commercial and defensive confederation of merchant guilds. Reaching the height of its prosperity in the late sixteenth century, thanks to its export of wheat, timber, hemp and furs, Kaliningrad was originally called Koenigsberg and was visited by more than one hundred ships annually. The resulting wealth allowed the people of the city to construct seven bridges connecting the banks of the river and two large central islands together.
As a result of this construction, the townsfolk were able to travel between these formerly distinct regions of the city more easily. According to local legend, this pastime of city centre strolling became so popular that curiosity began to emerge among the inhabitants about the different routes they could take. At some point, this evolved into a type of Sunday afternoon game, with the goal of devising a route by which all seven of the bridges would be crossed once and once only. However, despite all their efforts, it did not seem possible to complete the route following these rules. The puzzle remained unsolved for so long that the riddle was elevated up through the academic classes and ultimately to one of the greatest mathematical minds of the time, Leonhard Euler.
Although Swiss, this prolific mathematician, physicist, astronomer, logician and engineer was at that time a resident of St Petersburg, further north along the Baltic coast in Russia. Euler was a tremendously industrious academic, publishing around 500 books and papers over the course of his life, so to many it seemed odd that his interest would be piqued by such a trivial logical problem. In fact, when the mayor of Gdansk originally contacted him to probe his mind for a solution to the problem in a letter of 1736, Euler's response indicated his initial reluctance due to the problem "bearing little relationship to mathematics", suggesting that the solution would be "based on reason alone" and that its discovery "does not depend on any mathematical principle." However, it seems that Euler's inclination towards certainty and understanding was too strong to resist, as a letter written soon after to a friend, Giovanni Marinoni, explains that in Euler's view the Koenigsberg problem "...is so banal, but seemed to me worthy of attention in that neither geometry, nor algebra, nor even the art of counting...">> Form đăng kí giải đề thi thật IELTS 4 kĩ năng kèm bài giải bộ đề 100 đề PART 2 IELTS SPEAKING quý đang thi (update hàng tuần) từ IELTS TUTOR
On August 26, 1736, the mathematician shared a paper presenting a systematic explanation of his thoughts and interpretation of the problem, and ending by concluding that the citizens of Koenigsberg were not mistaken, there was indeed no route that could achieve the desired goal. The analysis began by stating that the nature of this problem certainly concerns geometry, but not of the familiar kind involving measurements and calculations, before making the connection to a topic recently discussed by the German polymath, Gottfried Leibniz - that of an innovative field of study called 'geometry of position', but of which little record exists. Euler then explained the need for abstraction in order to solve the problem, taking us to the crucial and groundbreaking part of his analysis.
It was clear to him that the barrier preventing the people of Koenigsberg from understanding the puzzle came about as a result of their unrefined perception of it. He thus started his analysis by removing all extraneous features of the map, leaving us with the 'land masses' (islands and river banks) and the bridges connecting them. This may seem extraordinarily simple to us - as we interact with abstracted diagrams and schematics everyday, in the form of transit maps and appliance manuals - but, at the time, equivalent documents were largely decorative and not created with efficient practicality in mind. Euler then described the land masses as dots and the bridges as lines and gave each of the former a letter A, B, C and D and the latter a number one through seven.
THE SEVEN BRIDGES OF KOENIGSBERG REVISUALISED
Although a piece of paper, a pen and a keen mathematical mind would be needed to understand the following fifteen paragraphs of analysis, they are not necessary to understand the significance of his method. The method Euler employed could be adapted as a framework to solve any problem that involved networks and routes through the analysis of all permutations. This was crucial to the later development of logistical analysis, in which the goal is to find the most efficient path or paths in complex systems, and its application can be seen in activities as diverse as the arrangement of postal routes, electrical circuits, DNA sequencing and chemical compounds.
Euler's endurance thus paid off and the brain-teaser that had perplexed the citizens of Koenigsberg was no more. Sadly, though, the inhabitants of Kaliningrad can no longer enjoy the pursuit that first put Koenigsberg on the intellectual map. Although in 1875 a new bridge was constructed - meaning that the route was at last achievable - two of the original constructions fell to bombing in World War II, while a further two were demolished and replaced by a modern highway.
Questions 14-17
Do the statements agree with the information given in Reading Passage 2: The Seven Bridges of Koenigsberg?
In answer boxes 14-17, write:
TRUE if the statement agrees with the information
FALSE if the statement contradicts the information
NOT GIVEN if there is no information on this in the reading passage
Koenigsberg was a successful Medieval port.
Prior to the construction of the bridges, the people of Koenigsberg did not often visit other parts of the city.
Interest in the logic problem first arose at the city's university.
Leonhard Euler was immediately interested in the problem.
IV. Dịch bài đọc THE SEVEN BRIDGES OF KOENIGSBERG
V. Giải thích từ vựng THE SEVEN BRIDGES OF KOENIGSBERG
VI. Giải thích cấu trúc ngữ pháp khó THE SEVEN BRIDGES OF KOENIGSBERG
VII. Đáp án THE SEVEN BRIDGES OF KOENIGSBERG
14 → TRUE
15 → FALSE
16 → FALSE
17 → FALSE
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