{"id":427,"date":"2020-08-24T01:39:27","date_gmt":"2020-08-24T01:39:27","guid":{"rendered":"http:\/\/region12.herbzinser07.com\/dir\/science07\/?p=427"},"modified":"2020-08-24T01:39:27","modified_gmt":"2020-08-24T01:39:27","slug":"lincoln-douglas-7-bridges-math-problem","status":"publish","type":"post","link":"http:\/\/region12.herbzinser07.com\/dir\/science07-sideas\/2020\/08\/24\/lincoln-douglas-7-bridges-math-problem\/","title":{"rendered":"Lincoln-Douglas 7 Bridges math problem"},"content":{"rendered":"

RD-blog-number-2478 by Herb Zinser<\/span><\/h3>\n

<\/h3>\n

Lincoln-Douglas<\/span><\/h1>\n

7 Bridges math problem<\/span><\/h1>\n

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Seven Bridges<\/a><\/span>\u00a0of K\u00f6nigsberg – Wikipedia, the free encyclopedia<\/a><\/span><\/h3>\n

en.wikipedia.org\/wiki\/<\/span>Seven<\/span>_<\/span>Bridges<\/span>_of_K\u00f6nigsberg<\/span><\/p>\n

Jump to<\/span>\u00a0<\/span>Significance in the history of\u00a0<\/span>mathematics<\/span>\u200e:<\/span><\/p>\n

In the history of\u00a0<\/span>mathematics<\/span>, Euler’s solution of the K\u00f6nigsberg\u00a0<\/span>bridge problem<\/span>\u00a0is considered to be the\u00a0<\/span>…<\/span><\/p>\n

Euler’s analysis<\/a><\/span>\u00a0–<\/span>\u00a0<\/a><\/span>Significance in the history of …<\/a><\/span>\u00a0–<\/span>\u00a0<\/a><\/span>Variations<\/a><\/span><\/p>\n

Math<\/a><\/span>\u00a0Forum: Leonhard Euler and the\u00a0<\/a><\/span>Bridges<\/a><\/span>\u00a0of Konigsberg
\n<\/a><\/span>math<\/span>forum.org\/isaac\/<\/span>problems<\/span>\/<\/span>bridges<\/span>1.html
\nHis work in this field was inspired by the following\u00a0<\/span>problem<\/span>:\u00a0<\/span>…<\/span>\u00a0<\/span>Seven bridges<\/span>\u00a0were built so that the people of the city could get from one part to another. A crude\u00a0<\/span>…<\/span><\/p>\n

Konigsberg\u00a0<\/a><\/span>bridge
\n<\/a><\/span>math<\/span>.youngzones.org\/Konigsberg.html
\nHe explained why crossing all\u00a0<\/span>seven bridges<\/span>\u00a0without crossing a bridge twice was impossible. While solving this\u00a0<\/span>problem<\/span>, he developed a new\u00a0<\/span>mathematics<\/span>\u00a0field\u00a0<\/span>…<\/p>\n

<\/span>\u00a0crossing all\u00a0<\/span>seven bridges<\/span>\u00a0…..\u00a0<\/span>While solving this\u00a0<\/span>problem<\/span>, he developed a new\u00a0<\/span>mathematics<\/span>\u00a0field\u00a0<\/span>… BIO-MATH agents
\n<\/span><\/p>\n

\u00a0BIO-MATH agents<\/span><\/p>\n\n\n\n\n
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\"undefined\"<\/p>\n<\/td>\n

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\"undefined\"<\/p>\n<\/td>\n<\/tr>\n

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Lincoln in<\/span>\u00a0<\/a><\/span>New York City<\/a><\/span>\u00a0the day of his famous<\/span>\u00a0<\/a><\/span>Cooper Union speech<\/a><\/span><\/p>\n<\/td>\n

<\/td>\n\n

Stephen A. Douglas<\/a><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Lincoln<\/a><\/span>\u2013<\/a><\/span>Douglas debates<\/a><\/span>\u00a0– Wikipedia, the free encyclopedia<\/a><\/span><\/h3>\n

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<\/span>Lincoln<\/a><\/span>\u2013<\/a><\/span>Douglas debates<\/a><\/span>\u00a0– Wikipedia, the free encyclopedia
\n<\/a><\/span>en.wikipedia.org\/wiki\/<\/span>Lincoln<\/span>\u2013<\/span>Douglas<\/span>_<\/span>debates
\n<\/span>The\u00a0<\/span>Lincoln<\/span>\u2013<\/span>Douglas Debates<\/span>\u00a0of 1858 were series of seven debates between Abraham Lincoln, the Republican candidate for the Senate in Illinois, and the\u00a0<\/span>\u2026<\/span><\/p>\n

<\/p>\n

<\/span>Background<\/a><\/span>\u00a0–<\/span>\u00a0<\/a><\/span>The debates<\/a><\/span>\u00a0–<\/span>\u00a0<\/a><\/span>Results<\/a><\/span>\u00a0–<\/span>\u00a0<\/a><\/span>Notes<\/a><\/span><\/p>\n

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\n<\/a><\/span><\/p>\n

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<\/a><\/span>\u00a0<\/span>series of seven debates \u00a0–>\u00a0<\/span>crossing all\u00a0<\/span>seven\u00a0<\/span>(communications)<\/span>\u00a0bridges<\/span>\u00a0<\/span><\/p>\n

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<\/p>\n

<\/span>Seven Bridges of Lincoln-Douglas<\/span><\/p>\n

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Seven Bridges of K\u00f6nigsberg<\/span><\/p>\n

Seven Bridges of K\u00f6nigsberg<\/span><\/p>\n


\n<\/span>\"\"<\/p>\n

<\/span>The\u00a0<\/span>Seven Bridges of K\u00f6nigsberg<\/span>\u00a0is a historically notable problem in mathematics. Its negative resolution by<\/span>\u00a0<\/a><\/span>Leonhard Euler<\/a><\/span>\u00a0in 1735 laid the foundations of<\/span>\u00a0<\/a><\/span>graph theory<\/a><\/span>\u00a0and prefigured the idea of<\/span>\u00a0<\/a><\/span>topology<\/a><\/span>.<\/p>\n

The city of<\/span>\u00a0<\/a><\/span>K\u00f6nigsberg<\/a><\/span>\u00a0in<\/span>\u00a0<\/a><\/span>Prussia<\/a><\/span>\u00a0(now<\/span>\u00a0<\/a><\/span>Kaliningrad<\/a><\/span>,<\/span>\u00a0<\/a><\/span>Russia<\/a><\/span>) was set on both sides of the<\/span>\u00a0<\/a><\/span>Pregel River<\/a><\/span>, and included two large islands which were connected to each other and the mainland by seven bridges.<\/p>\n

The problem was to find a walk through the city that would cross each bridge once and only once. The islands could not be reached by any route other than the bridges, and every bridge must have been crossed completely every time; one could not walk halfway onto the bridge and then turn around and later cross the other half from the other side. The walk need not start and end at the same spot. Euler proved that the problem has\u00a0<\/span>no<\/span>\u00a0solution. There could be no non-retracing the bridges. The difficulty was the development of a technique of analysis and of subsequent tests that established this assertion with mathematical rigor.
\n<\/span>Seven Bridges of \u00a0Illinois
\nSeven Bridges of \u00a0University of Ill \/nois(e)
\nSeven Bridges of \u00a0University of Chic<\/p>\n

<\/span>Euler’s analysis
\n<\/span>The only important feature of a route is the sequence of bridges crossed. This allowed him to reformulate the problem in abstract terms (laying the foundations of<\/span>\u00a0<\/a><\/span>graph theory<\/a><\/span>), eliminating all features except the list of land masses and the bridges connecting them.<\/p>\n

The\u00a0<\/span>Lincoln\u2013Douglas Debates of 1858<\/span>\u00a0were series of seven debates between<\/span>\u00a0<\/a><\/span>Abraham Lincoln<\/a><\/span>, the<\/span>\u00a0<\/a><\/span>Republican<\/a><\/span>\u00a0candidate for the<\/span>\u00a0<\/a><\/span>Senate<\/a><\/span>\u00a0in<\/span>\u00a0<\/a><\/span>Illinois<\/a><\/span>, and the incumbent<\/span>\u00a0<\/a><\/span>Senator<\/a><\/span>\u00a0<\/a><\/span>Stephen Douglas<\/a><\/span>, the<\/span>\u00a0<\/a><\/span>Democratic Party<\/a><\/span>\u00a0candidate. The debates were held in seven towns in the state of<\/span>\u00a0<\/a><\/span>Illinois<\/a><\/span>:
\n<\/span>Ottawa<\/a><\/span>\u00a0on August 21,
\n<\/span>Freeport<\/a><\/span>\u00a0on August 27,
\n<\/span>\u00a0<\/a><\/span>Jonesboro<\/a><\/span>\u00a0on September 15,
\n<\/span>\u00a0<\/a><\/span>Charleston<\/a><\/span>\u00a0on September 18,
\n<\/span>\u00a0<\/a><\/span>Galesburg<\/a><\/span>\u00a0on October 7,
\n<\/span>\u00a0<\/a><\/span>Quincy<\/a><\/span>\u00a0on October 13,
\n<\/span>Alton<\/a><\/span>\u00a0on October 15<\/span>\u00a0(about John D<\/span>alton<\/span>)<\/span><\/p>\n

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\n<\/span><\/p>\n

the\u00a0<\/span>Pregel River<\/a><\/span>, and included two large islands which were connected to each other and the mainland by seven bridges.<\/span><\/p>\n

\"\"<\/p>\n


\nthe\u00a0<\/span>Pregel River<\/a><\/span>, and included
\n<\/span>two large INTELLECTUAL<\/span><\/p>\n

\u00a0islands<\/span>\u00a0<\/span>which were connected to each other and the mainland by seven (database city) bridges.<\/span><\/p>\n

The debates were held in seven small city \/towns<\/span><\/p>\n

in the geography state of Illinois \u2026..
\nregarding States of Mind and various<\/span><\/p>\n

Information cities and states:<\/span><\/p>\n

\"\"<\/p>\n