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Prove that 30° is a constructible angle.

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian ISBN: 9781133599708 52

Solution for problem 8E Chapter 23

Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

Contemporary Abstract Algebra | 8th Edition

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Problem 8E

Problem 8E

Prove that 30° is a constructible angle.

Step-by-Step Solution:
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WWII: Nationalist Nightmares First U.S. Troops Land at Sicily (1943)  Use that location to push through Italy o Want to oppose Mussolini Teheran Conference (1943)  Meeting of Stalin (USSR, Roosevelt (US), and Great Britain (Churchill) o Big Three  Big three agree to open western front to relieve USSR  USSR promises to join US in war against Japan after defeat of Germany  Last show of good faith between US an USSR o Stalin says they have been holding down Eastern front and he wants control of the east = Roosevelt doesn’t like that o Underlying tensions D-Day (6 June 1944)  Immense operation in Normandy, France  Trying to force Germany to fight a war on multiple fronts  Preparations o Strategic air campaign paved way o French and Belgian railways crippled o Bridges demolished in NW France o Enemy airfields within 30-mile radius attacked  Establish beachhead = Allied troops land 5 assault divisions  3 months = 2 million troops and ½ million vehicles  Largest ship borne assault ever staged Hitler Moves into a Bunker Under Berlin (January 1945)  Direct final testament underground  Commits suicide eventually  Himmler his right hand man in concentration camps commits suicide  Mussolini executed by communist VE Day (May 1945)  Death of these Fascist leader  Celebration in Europe  Victory in Europe day Atomic Weapons  Hiroshima (6 August 1945) o 135000 initial casualties o Eventually more  Nagasaki (9 August 1945) o 60,000 initial casualties Antisemitism  Evolves overtime to focus more on race rather than economics  False understanding of race o Jewish Identity is based on culture, tradition, common ancestry, and religion of Judaism  Wants German blood to be purged from Jewish blood o Taking social Darwinism to the extreme Defining Exclusion  Nuremberg Laws (1935) o Legislation to exclude Jews politically o Defines citizenship in Germany along racial lines  Racial/Citizenship Categories: o German = 4 grandparents “German blood” o Crossbreed = 2 grandparents “Jewish blood” o Jew = 3-4 grandparents “Jewish blood” o Jews and crossbreeds excluded o Marriages forbidden between Jews and Germans Kristallnacht: Night of Shattered Glass (1938)  Act of violence against German official from a Jew o Assassination of the Third Secretary in German Embassy o Hitler capitalizes off of event o Causes fear and hatred  Synagogues burned  7,000 Jewish businesses destroyed  100 Jews killed  30,000 Jews sent to concentration camps  Jews barred from all public buildings  Jews prohibited from owning, managing, or working in retail stores  Jews encouraged to “emigrate from Germany” Inscribing Exclusion (1939-1945)  Use the yellow star of David and the letter J o Make visible who the Jews are o Want them to be seen as outsiders The Final Solution  Creation concentration camps o Those marked for exclusion eventually exterminated  Camps in Poland o Belzec, Chelmno, Majdanek, Sobibor, Treblinka, and Auschwitz Study Guide Part II Nationalist Nightmares  Teheran Conference (1943) o Meeting of the Big Three where they agree to open the western front to relieve USSR; USSR promises to join US in war against Japan after defeat of Germany  “Big Three” o Stalin of USSR, Roosevelt of U.S., and Churchill of Great Britain  D Day (6 June 1944) o Immense operation to make Germany fight a war on multiple fronts; established a beachhead in Normandy, France; considered the largest ship borne assault ever staged  VE-Day (May 1945) o The end of Fascist Dictatorship in Europe; Mussolini, Hitler, and Himmler all dead from suicide or execution; Victory in Europe  Hiroshima (6 August 1945) o First atomic bomb dropped here in Japan by the US; had initial 135000 casualties  Nagasaki (9 August 1945) o Second atomic bomb dropped in Japan by the US; 60000 initial casualties  Anti-Semitism o Hatred of Jewish race even though Jewish identity is based on ancestry, tradition, culture, and religion of Judaism  Nuremberg Laws (1935) o Laws that defined people as German (4 grandparents “German blood”), crossbreed (2 parents “Jewish blood”), or Jew (3-4 grandparents “Jewish blood); if a Crossbreed or Jew then excluded; marriage between Jews and German citizens is now forbidden  Kristallnacht (1938) o Night of Shattered Glass; there was an act of violence against a German official from a Jew and Hitler capitalizes of that act; huge destruction of Jewish homes, synagogues, and businesses; many put in concentration camps or killed; encouraged to emigrate  “Final Solution” o The creation of concentration camps to exterminate Jews, those marked with the yellow star or a J Extra things to Remember  1932 1. The height of German employment and important date in Hitler’s rise to power  Hitler’s Rise to Power 1. Formation of Nazi Party 2. Chancellor of Germany 3. Reich Stag Fire 4. Enabling Act 5. Death of Hindenburg  Assembling Lebensraum 1. Rhineland 2. Austria 3. Sudetenland 4. Poland

Step 2 of 3

Chapter 23, Problem 8E is Solved
Step 3 of 3

Textbook: Contemporary Abstract Algebra
Edition: 8
Author: Joseph Gallian
ISBN: 9781133599708

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Prove that 30° is a constructible angle.