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United States home front during World War I
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Home Front
Weapons for Liberty – U.S.A. Bonds by J. C. Leyendecker, 1918
Location
United States
The United States homefront during World War I saw a systematic mobilization of the country's entire population and economy to produce the soldiers, food supplies, ammunitions and money necessary to win the war. Although the United States entered the war in April 1917, there had been very little planning, or even recognition of the problems that Great Britain and the other Allies had to solve on their own home fronts. As a result, the level of confusion was high in the first 12 months.
The war came in the midst of the Progressive Era, when efficiency and expertise were highly valued. Therefore, both individual states and the federal government established a multitude of temporary agencies to bring together the expertise necessary to redirect the economy and society into the production of munitions and food needed for the war, as well as the circulation of beliefs and ideals in order to motivate the people.
Contents
1 American entry into the war
2 US government
2.1 Temporary agencies
2.2 Government propaganda
3 Military draft
4 Civil liberties
5 Motion pictures
6 Economics
6.1 Munitions production before U.S. entry
6.2 Munitions production after U.S. entry
6.3 Farming and food
6.4 Economic confusion in 1917
6.5 Shipments to Europe
6.6 Labor
7 Women
7.1 Children
8 Americanization of ethnics
9 Alien internments
10 Anti-German activity
11 War bonds
12 Attacks on the USA
12.1 Sabotage
13 See also
14 Notes and references
15 Further reading
15.1 Economics and labor
15.2 Historiography
15.3 Primary sources and year books
16 External links
American entry into the war[edit]
Main article: American entry into World War I
Firmly maintaining neutrality when World War I began in Europe in 1914, the United States helped supply the Allies, but could not ship anything to Germany because of the British blockade. Sympathies among many politically and culturally influential Americans had favored the British cause from the start of the war, as typified by industrialist Samuel Insull, born in London, who helped young Americans enlist in British or Canadian forces. On the other hand, especially in the Midwest, many Irish Americans and German Americans opposed any American involvement and were anti-British. The suffragist movement included many pacifists, and most churches opposed the war.[1]
German efforts to use its submarines ("U-boats") to blockade Britain resulted in the deaths of American travelers and sailors, and attacks on passenger liners caused public outrage. Most notable was the torpedoing without warning the passenger liner Lusitania in 1915. Germany promised not to repeat, but it reversed its position in early 1917, believing that unrestricted U-boat warfare against all ships headed to Britain would win the war even at the cost of American entry. When Americans read the text of the German offer to Mexico, known as the Zimmermann Telegram, they saw an offer for Mexico to go to war with Germany against the United States, with German funding, with the promise of the return of the lost territories of Arizona, New Mexico, and Texas. On Apr 1, 1917, Wilson called for war, emphasizing that the U.S. had to fight to maintain its honor and to have a decisive voice in shaping the new postwar world.[2] Congress voted on April 6, 1917 to declare war, 82 to 6 in the Senate, and 373 to 50 in the House of Representatives.[3]
US government[edit]
Main article: Presidency of Woodrow Wilson
Temporary agencies[edit]
Congress authorized President Woodrow Wilson to create a bureaucracy of 500,000 to 1 million new jobs in five thousand new federal agencies.[4] To solve the labor crisis, the Employment Service of the Department of Labor attracted workers from the South and Midwest to war industries in the East.
Government propaganda[edit]
In April 1917, the Wilson Administration created the Committee on Public Information (CPI), known as the Creel Committee, to control war information and provide pro-war propaganda. Employing talented writers and scholars, it issued anti-German pamphlets and films. It organized thousands of "Four-Minute Men" to deliver brief speeches at movie theaters, schools and churches to promote patriotism and participation in the war effort.[5]
Military draft[edit]
Main article: Selective Service Act of 1917
A World War I era draft card.
In 1917 the administration decided to rely primarily on conscription, rather than voluntary enlistment, to raise military manpower for World War I. The Selective Service Act of 1917 was carefully drawn to remedy the defects in the Civil War system and—by allowing exemptions for dependency, essential occupations, and religious scruples—to place each man in his proper niche in a national war effort. The act established a "liability for military service of all male citizens"; authorized a selective draft of all those between twenty-one and thirty-one years of age (later from eighteen to forty-five); and prohibited all forms of bounties, substitutions, or purchase of exemptions. Administration was entrusted to local boards composed of leading civilians in each community. These boards issued draft calls in order of numbers drawn in a national lottery and determined exemptions. In 1917 and 1918 some 24 million men were registered and nearly 3 million inducted into the military services, with little of the resistance that characterized the Civil War.[6]
Secretary of War Newton Baker draws the first draft number on 20 July 1917.
Using questionnaires filled out by doughboys as they left the Army, Gutièrrez reports that they were not cynical or disillusioned. They fought "for honor, manhood, comrades, and adventure, but especially for duty."[7]
Civil liberties[edit]
The Espionage Act of 1917 and the Sedition Act of 1918 attempted to punish enemy activity and extended to the punishment expressions of doubt about America's role in the war. The Sedition Act criminalized any expression of opinion that used "disloyal, profane, scurrilous or abusive language" about the U.S. government, flag or armed forces. Government police action, private vigilante groups, and public war hysteria compromised the civil liberties of many Americans who disagreed with Wilson's policies.[8]
The private American Protective League, working with the Federal Bureau of Investigation, was one of many private patriotic associations that sprang up to support the war and at the same time identify slackers, spies, draft dodgers and anti-war organizations.[9]
In a July 1917 speech, Max Eastman complained that the government's aggressive prosecutions of dissent meant that "You can't even collect your thoughts without getting arrested for unlawful assemblage."[10]
Motion pictures[edit]
The nascent film industry produced a wide variety of propaganda films. The most successful was The Kaiser, the Beast of Berlin, a "sensational creation" designed to rouse the audience against the German ruler. Comedies included Mutt and Jeff at the Front. The greatest artistic success, considered by many a landmark of film history, was Charlie Chaplin's Shoulder Arms, which followed the star from his induction into the military, his accidental penetration of the German lines, and his eventual return having captured the Kaiser and Crown Prince and won himself a pretty French girl.[11] Other activities included film shorts supporting the sale of war bonds or for war relief such as Tom's Little Star.
Economics[edit]
Munitions production before U.S. entry[edit]
By 1916, Britain was funding most of the Empire's war expenditures, all of Italy's and two thirds of the war costs of France and Russia, plus smaller nations as well. The gold reserves, overseas investments and private credit then ran out, forcing Britain to borrow $4 billion from the U.S. Treasury in 1917–18.[12] Much of this money was spent paying United States industries to manufacture ammunition. United States Cartridge Company expanded its work force ten-fold in response to September 1914 contracts with British purchasing agents; and ultimately manufactured over two billion rifle and machine gun cartridges.[13] Baldwin Locomotive Works expanded their Eddystone, Pennsylvania, manufacturing facilities in 1915 to manufacture Russian artillery shells and British rifles.[14] The United States production of smokeless powder was equal to the combined production of the European Allies during the last 19 months of the war; and by the end of the war United States factories were producing smokeless powder at a rate 45 percent higher than the European Allies' combined production. Production rate of explosives by the United States was similarly 40 percent higher than Britain and nearly twice that of France.[15] Shipments of American raw materials and food allowed Britain to feed itself and its army while maintaining her productivity. The financing was generally successful.[16] Heavy investment in ammunition manufacturing machinery did not bring long term prosperity to some major American companies. The United States Cartridge Company Lowell, Massachusetts, factory which manufactured nearly two-thirds of the small arms cartridges produced in the United States during the war, closed eight years later.[17] After Baldwin manufactured over six million artillery shells, nearly two million rifles, and 5,551 military locomotives for Russia, France, Britain and the United States,[14] postwar production never used more than one-third the capacity of the Eddystone factory; and Baldwin declared bankruptcy in 1935.[18]
Munitions production after U.S. entry[edit]
The US effort to produce and ship war material to France was characterized by several factors. The US declared war on Germany on 6 April 1917 with only a small munitions industry, very few medium and heavy artillery pieces, and few machine guns. By June 1917 the US had decided that their forces would primarily operate alongside the French, and would acquire their artillery and machine guns by purchasing mostly French weapons in theater, along with some British weapons in the case of heavy artillery. Shipments from the US to France would primarily be of soldiers and ammunition; artillery equipment in particular occupied too much space and weight to be economical. These priorities combined with the short 19-month US participation in the war meant that few US-made weapons arrived in France, and the need for extensive training of artillery units once in France meant that fewer still saw action before the Armistice. A comparison with World War II would be that the US started preparing for that war in earnest shortly after the Germans invaded Poland in September 1939; by the time the US entered the war following the attack on Pearl Harbor in December 1941 there had already been 27 months of mobilization.[19]
Artillery
It was envisioned that US artillery production of French- and British-designed weapons, and a few US-designed weapons chambered for French ammunition, would be ramped up and that US-made artillery would eventually be delivered to the battlefields in quantity. However, major production snarls occurred with most of the artillery programs, and as mentioned artillery shipments had a lower priority than many other types of shipments overseas.[19]
Farming and food[edit]
Main article: Food and Fuel Control Act
Food Administration poster 1917
The food program was a major success, as output expanded, waste was reduced, and both the home front and the Allies received more food.[20] The U.S. Food Administration under Herbert Hoover launched a massive campaign to teach Americans to economize on their food budgets and grow victory gardens in their backyards.[21] It managed the nation's food distribution and prices.[22]
Gross farm income increased more than 230% from 1914 to 1919. Apart from 'wheatless Wednesdays' and 'meatless Tuesdays' due to poor harvests in 1916 and 1917, there were 'fuelless Mondays' and 'gasless Sundays' to preserve coal and gasoline.[23]
Economic confusion in 1917[edit]
In terms of munitions production, the first 15 months involved an amazing parade of mistakes, misguided enthusiasm, and confusion. Americans were willing enough, but they did not know their proper role. Washington was unable to figure out what to do when, or even to decide who was in charge. Typical of the confusion was the coal shortage that hit in December 1917. Because coal was by far the major source of energy and heat a grave crisis ensued. There was in fact plenty of coal being mined, but 44,000 loaded freight and coal cars were tied up in horrendous traffic jams in the rail yards of the East Coast. Two hundred ships were waiting in New York harbor for cargo that was delayed by the mess. The solution included nationalizing the coal mines and the railroads for the duration, shutting down factories one day a week to save fuel, and enforcing a strict system of priorities. Only in March, 1918, did Washington finally take control of the crisis[24] The transportation system then worked smoothly.[25]
Shipments to Europe[edit]
Shipbuilding became a major wartime industry, focused on merchant ships and tankers.[26] Merchant ships were often sunk until the convoy system was adopted using British and Canadian naval escorts. Convoys were slow but effective in stopping u-boat attacks.[27] The troops were shipped over on fast passenger liners that could easily outrun submarines.[28]
An oil crisis occurred in Britain due to the 1917 German submarine campaign. Standard Oil of NJ, for example, lost 6 tankers (including the brand new "John D. Archbold") between May and September. The solution was expanded oil shipments from America in convoys. The Allies formed the Inter-Allied Petroleum Conference with USA, Britain, France, and Italy as the members. Standard and Royal Dutch/Shell ran it and made it work. The introduction of convoys as an antidote to the German U-boats and the joint management system by Standard Oil and Royal Dutch/Shell helped to solve the Allies' supply problems. The close working relationship that evolved was in marked contrast to the feud between the government and Standard Oil years earlier. In 1917 and 1918, there was increased domestic demand for oil partly due to the cold winter that created a shortage of coal. Inventories and imported oil from Mexico were used to close the gap. In January 1918, the U.S. Fuel Administrator ordered industrial plants east of Mississippi to close for a week to free up oil for Europe.[29]
The coal shortage caused sharp increases in the demand and prices of oil and industry called for voluntary price control from the oil industry. While Standard Oil was agreeable, the independent oil companies were not. Demand continued to outpace supply because of the war and the growth in automobiles in America. An appeal for “Gasolineless Sundays” in US was made with exceptions for freight, doctors, police, emergency vehicles, and funeral cars.
Labor[edit]
1919 New York Herald cartoon portraying "reds" and IWW members as a violent mob held back by threat of a US Army machine gun
The American Federation of Labor (AFL) and affiliated trade unions were strong supporters of the war effort. Fear of disruptions to war production by labor radicals provided the AFL political leverage to gain recognition and mediation of labor disputes, often in favor of improvements for workers.[30] They resisted strikes in favor of arbitration and wartime policy, and wages soared as near-full employment was reached at the height of the war. The AFL unions strongly encouraged young men to enlist in the military, and fiercely opposed efforts to reduce recruiting and slow war production by pacifists, the anti-war Industrial Workers of the World (IWW) and radical socialists. To keep factories running smoothly, Wilson established the National War Labor Board in 1918, which forced management to negotiate with existing unions.[31] Wilson also appointed AFL president Samuel Gompers to the powerful Council of National Defense, where he set up the War Committee on Labor.
After initially resisting taking a stance, the IWW became actively anti-war, engaging in strikes and speeches and suffering both legal and illegal suppression by federal and local governments as well as pro-war vigilantes. The IWW was branded as anarchic, socialist, unpatriotic, alien and funded by German gold, and violent attacks on members and offices would continue into the 1920s.[32]
The AFL membership soared to 2.4 million in 1917. In 1919, the AFL tried to make their gains permanent and called a series of major strikes in meat, steel and other industries. The strikes ultimately failed, forcing unions back to membership and power similar to those around 1910.[33]
Women[edit]
See also: American women in World War I
During WWI (1914-1918), large numbers of women were recruited into jobs that had either been vacated by men who had gone to fight in the war, or had been created as part of the war effort. The high demand for weapons and the overall wartime situation resulted in munitions factories collectively becoming the largest employer of American women by 1918. While there was initial resistance to hiring women for jobs traditionally held by men, the war made the need for labor so urgent that women were hired in large numbers and the government even actively promoted the employment of women in war-related industries through recruitment drives. As a result, women not only began working in heavy industry, but also took other jobs traditionally reserved solely for men, such as railway guards, ticket collectors, bus and tram conductors, postal workers, police officers, firefighters, and clerks.
World War I saw women taking traditionally men's jobs in large numbers for the first time in American history. Many women worked on the assembly lines of factories, producing trucks and munitions, while department stores employed African American women as elevator operators and cafeteria waitresses for the first time. The Food Administration helped housewives prepare more nutritious meals with less waste and with optimum use of the foods available. Most important, the morale of the women remained high, as millions joined the Red Cross as volunteers to help soldiers and their families, and with rare exceptions, the women did not protest the draft.[34][35]
Girls too young for paid jobs learned how they could help the war effort.
Children[edit]
Main article: Effect of World War I on children in the United States
World War I affected children in the United States through several social and economic changes in the school curriculum and through shifts in parental relationships. For example, a number of fathers and brothers entered the war, and many were subsequently maimed in action or killed, causing many children to be brought up by single mothers.[36] Additionally, as the male workforce left for battle, mothers and sisters began working in factories to take their positions, and the family dynamic began to change; this affected children as they had less time to spend with family members and were expected to grow up faster and help with the war effort. Similarly, Woodrow Wilson called on children involved in youth organizations to help collect money for war bonds and stamps in order to raise money for the war effort.[37] This was very important because the children were having a direct effect on the financial state of the United States government during World War I. As children were collecting large amounts of money outside of school, within the classroom, curriculum also began to change as a result of the war. Woodrow Wilson again became involved with these children as he implemented government pamphlets and programs to encourage war support through things like mandatory patriotism and nationalism classes multiple times a week.[38] Even though war was not being fought on United States soil, children's lives were greatly affected as all of these changes were made to their daily lives as a result of the conflict.
Victory gardeners, 1918
Americanization of ethnics[edit]
The outbreak of war in 1914 increased concern about the millions of foreign born in the United States. The short-term concern was their loyalty to their native countries and the long-term was their assimilation into American society. Numerous agencies became active in promoting "Americanization" so that the ethnics would be psychologically and politically loyal to the U.S. The states set up programs through their Councils of National Defense; numerous federal agencies were involved, including the Bureau of Education, the United States Department of the Interior and the Food Administration. The most important private organization was the National Americanization Committee (NAC) directed by Frances Kellor. Second in importance was the Committee for Immigrants in America, which helped fund the Division of Immigrant Education in the federal Bureau of Education.[39]
The war prevented millions of recently arrived immigrants from returning to Europe as they originally intended. The great majority decided to stay in America. Foreign language use declined dramatically. They welcomed Americanization, often signing up for English classes and using their savings to buy homes and bring over other family members.[40]
Kellor, speaking for the NAC in 1916, proposed to combine efficiency and patriotism in her Americanization programs. It would be more efficient, she argued, once the factory workers could all understand English and therefore better understand orders and avoid accidents. Once Americanized, they would grasp American industrial ideals and be open to American influences and not subject only to strike agitators or foreign propagandists. The result, she argued would transform indifferent and ignorant residents into understanding voters, to make their homes into American homes, and to establish American standards of living throughout the ethnic communities. Ultimately, she argued it would "unite foreign-born and native alike in enthusiastic loyalty to our national ideals of liberty and justice.[41]
Alien internments[edit]
See also German American internment during World War I
German citizens were required to register with the federal government and carry their registration cards at all times. 2,048 German citizens were imprisoned beginning in 1917, and all were released by spring 1920. Allegations against them included spying for Germany or endorsing the German war effort. They ranged from immigrants suspected of sympathy for their native land, civilian German sailors on merchant ships in U.S. ports when war was declared, and Germans who worked part of the year in the United States, including 29 players from the Boston Symphony Orchestra and other prominent musicians.[42]
Anti-German activity[edit]
See also: Anti-German sentiment § First World War
1918 bond posters with germanophobic slogans
German Americans by this time usually had only weak ties to Germany; however, they were fearful of negative treatment they might receive if the United States entered the war (such mistreatment was already happening to German-descent citizens in Canada and Australia). Almost none called for intervening on Germany's side, instead calling for neutrality and speaking of the superiority of German culture. They were increasingly marginalized, however, and by 1917 had been excluded almost entirely from national discourse on the subject.[43]
When the war began, overt examples of German culture came under attack. Many churches cut back or ended their German language services. German parochial schools switched to the use of English in the classroom. Courses in German were dropped from public high school curricula. Some street names were changed. One person was killed by a mob at a tavern in a southern Illinois mining town.[44]
War bonds[edit]
Elaborate propaganda campaigns were launched to encourage Americans to buy Liberty bonds. In ethnic centers, ethnic groups were pitted against each other so that groups were encouraged to purchase more bonds compared to their historic rivals in order to demonstrate superior patriotism.[45]
Attacks on the USA[edit]
The Central Powers carried out a number of acts of sabotage and a single submarine attack against the mainland of the USA during the war, but never staged an invasion of the country, although there were rumors that German advisers were present at the Battle of Ambos Nogales.
Sabotage[edit]
Black Tom Pier shortly after the explosion.
Main article: Black Tom explosion
Numerous rumors of German plans for sabotage alarmed Americans. After midnight on July 30, 1916, a series of small fires were found on a pier in Jersey City, New Jersey. Sabotage was suspected and some guards fled, fearing an explosion; others attempted to fight the fires. Eventually they called the Jersey City Fire Department. An explosion occurred at 2:08 a.m., the first and biggest of the explosions. Shrapnel from the explosion traveled long distances, some lodging in the Statue of Liberty and other places. Seven people died.
On July 21, 1918, a German U-boat, SM U-156, positioned itself off of Orleans, Massachusetts opened fire and sank a tugboat and some barges until it was driven off by American warplanes.
See also[edit]
American entry into World War I
Victory garden
Woman's Land Army of America
Effect of World War I on Children in the United States
United States home front during World War II
German prisoners of war in the United States
Home front during World War I, covering all major countries involved
Women's roles in the World Wars#World War I
British home front during the First World War
History of Germany during World War I
History of France during World War I
Belgium in World War I
Notes and references[edit]
Jump up ^ On the historiography, see Justus D. Doenecke, "Neutrality Policy and the Decision for War" in Ross Kennedy ed., A Companion to Woodrow Wilson (2013) pp: 243-69 Online
Jump up ^ For detailed coverage of Wilson's speech see NY Times main headline, April 2, 1917, President Calls for War Declaration, Stronger Navy, New Army of 500,000 Men, Full Cooperation With Germany's Foes
Jump up ^ Staff, History.com. “U.S. Entry into World War I.” History.com, A&E Television Networks, 2017, www.history.com/topics/world-war-i/u-s-entry-into-world-war-i.
Jump up ^ Spencer Tucker and Priscilla Mary Roberts, eds., World War I: encyclopedia (2005), p. 1205
Jump up ^ Kennedy, Over Here, 61-62
Jump up ^ John Whiteclay Chambers II, To Raise an Army: The Draft Comes to Modern America (1987)
Jump up ^ Edward A. :Gutièrrez, Doughboys on the Great War: How American Soldiers Viewed Their Military Experience (2014)
Jump up ^ Schaffer, Ronald (1978). The United States in World War I. Santa Barbara: Clio Books. p. ?. ISBN 0874362741.
Jump up ^ Fischer, Nick (2011). "The American Protective League and the Australian Protective League – Two Responses to the Threat of Communism, c. 1917–1920". American Communist History. 10 (2): 133–149. doi:10.1080/14743892.2011.597222.
Jump up ^ Steel, Ronald (1980). Walter Lippmann and the American Century. Boston: Little, Brown. p. 124. ISBN 0316811904.
Jump up ^ Mock, James R.; Larson, Cedric (1939). Words that Won the War: The Story of the Committee on Public Information, 1917–1919. Princeton University Press. pp. 151–152.
Jump up ^ Steven Lobell, "The Political Economy of War Mobilization: From Britain's Limited Liability to a Continental Commitment," International Politics (2006) 43#3 pp 283–304
Jump up ^ Helmuth Carol Engelbrecht; Frank Cleary Hanighen (1934). Merchants of Death: A Study of the International Armament Industry. p. 187.
^ Jump up to: a b Westing, Frederick (1966), The locomotives that Baldwin built. Containing a complete facsimile of the original "History of the Baldwin Locomotive Works, 1831-1923", Crown Publishing Group, pp. 76–85, ISBN 978-0-517-36167-2
Jump up ^ Ayres, Leonard P. (1919). The War with Germany (Second ed.). Washington, DC: United States Government Printing Office. pp. 77&78.
Jump up ^ M. J. Daunton, "How to Pay for the War: State, Society and Taxation in Britain, 1917–24," English Historical Review (1996) 111# 443 pp. 882–919 in JSTOR
Jump up ^ "U.S. Cartridge Company" (PDF). Lowell Land Trust. Archived from the original (PDF) on 2013-04-26. Retrieved 2013-02-06.
Jump up ^ Brown, John K. (1995), The Baldwin Locomotive Works, 1831-1915: A Study in American Industrial Practice, Studies in Industry and Society series, Baltimore: Johns Hopkins University Press, pp. 216&228, ISBN 978-0-8018-5047-9
^ Jump up to: a b Crowell, pp. 25-30
Jump up ^ Beamish and March (1919). America's Part in the World War. pp. 319–35.
Jump up ^ "Teaching With Documents: Sow the Seeds of Victory! Posters from the Food Administration During World War I"
Jump up ^ Nash, George H. (1996). The Life of Herbert Hoover: Master of Emergencies, 1917–1918. New York: Norton. p. ?. ISBN 0393038416.
Jump up ^ Spencer C. Tucker; Priscilla Mary Roberts (2005). Encyclopedia Of World War I: A Political, Social, And Military History. ABC-CLIO. p. 1206.
Jump up ^ Kennedy, Over Here 113-25
Jump up ^ Beamish and March (1919). America's Part in the World War. pp. 336–50.
Jump up ^ Beamish and March (1919). America's Part in the World War. pp. 359–66.
Jump up ^ Brian Tennyson, and Roger Sarty. "Sydney, Nova Scotia and the U-Boat War, 1918." Canadian Military History 7.1 (2012): 4+ online
Jump up ^ Holger H. Herwig, and David F. David. "The Failure of Imperial Germany's Undersea Offensive Against World Shipping, February 1917–October 1918." Historian (1971) 33#4 pp: 611-636.
Jump up ^ Ronald W. Ferrier; J. H. Bamberg (1982). The History of the British Petroleum Company: Volume 1, The Developing Years, 1901-1932. Cambridge University Press. p. 356.
Jump up ^ Joseph A. McCartin, Labor's great war: the struggle for industrial democracy and the origins of modern American labor relations, 1912-1921 (1997).
Jump up ^ Richard B. Gregg, "The National War Labor Board." Harvard Law Review (1919): 39-63 in JSTOR
Jump up ^ Robert L. Tyler, Rebels of the woods: the IWW in the Pacific Northwest (U of Oregon Press, 1967)
Jump up ^ Philip Taft, The A.F.L. in the time of Gompers (1957)
Jump up ^ Gavin, Lettie (2006). American Women in World War I: They Also Served. Boulder: University Press of Colorado. ISBN 0870818252.
Jump up ^ Beamish and March (1919). America's Part in the World War. pp. 259–72.
Jump up ^ Greenwald, Maureen (1980). Maurine Weiner. Women, War, and Work: the Impact of World War I on Women Workers in the United States. Westport: Greenwood Press. p. 4. ISBN 0313213550.
Jump up ^ McDermott, T. P. "USA's Boy Scouts and World War I Liberty Loan Bonds". SOSSI Journal: 70.
Jump up ^ Spring, Joel (1992). Images of American Life. Albany: State University of New York Press. p. 20. ISBN 0791410692.
Jump up ^ McClymer, John F. (1980). War and Welfare: Social Engineering in America, 1890–1925. Westport: Greenwood Press. pp. 110–111. ISBN 0313211299.
Jump up ^ Archdeacon, Thomas J. (1984). Becoming American. London: Collier Macmillan. pp. 115, 186–187. ISBN 0029008301.
Jump up ^ McClymer, War and Welfare, pp 112-3
Jump up ^ New York Times: "Dr. Muck Bitter at Sailing," August 22, 1919, accessed January 13, 2010
Jump up ^ Frederick C. Luebke, Bonds of Loyalty: German-Americans and World War I (1974)
Jump up ^ Donald R. Hickey, "The Prager Affair: A Study in Wartime Hysteria," Journal of the Illinois State Historical Society (1969) 62#2 pp 126–127 in JSTOR
Jump up ^ June Alexander (2008). Ethnic Pride, American Patriotism: Slovaks And Other New Imiigrants. Temple UP. pp. 33–34.
Further reading[edit]
Further information: Presidency of Woodrow Wilson and Bibliography of World War I
Beamish, Richard Joseph and Francis Andrew March (1919). America's Part in the World War: A History of the Full Greatness of Our Country's Achievements; the Record of the Mobilization and Triumph of the Military, Naval, Industrial and Civilian Resources of the United States. Philadelphia: John C. Winston Company. ; comprehensive history of military and home front; full text online; has photos
Breen, William J. Uncle Sam at Home: Civilian Mobilization, Wartime Federalism, and the Council of National Defense, 1917-1919 (Greenwood Press, 1984)
Chambers, John W., II. To Raise an Army: The Draft Comes to Modern America (1987)
Clements, Kendrick A. The Presidency of Woodrow Wilson (1992)
Cooper, John Milton. Woodrow Wilson: A Biography (2009)
Crowell, Benedict (1919). America's Munitions 1917-1918. Washington, DC: Government Printing Office.
Dumenil, Lynn. The Second Line of Defense: American Women and World War I (U of North Carolina Press, 2017). xvi, 340 pp.
Encyclopædia Britannica (12th ed. 1922) comprises the 11th edition plus three new volumes 30-31-32 that cover events since 1911 with very thorough coverage of the war as well as every country and colony. Included also in 13th edition (1926) partly online
full text of vol 30 ABBE to ENGLISH HISTORY online free
Gannon, Barbara A. "The Great War and Modern Amnesia: Studying Pennsylvania’s Great War, Part 2' Pennsylvania History (2017) 84#3:287-91 Online
Kennedy, David M. Over Here: The First World War and American Society (2004), comprehensive coverage borrow for 14 days
Link, Arthur Stanley. Woodrow Wilson and the Progressive Era, 1910–1917 (1972) standard political history of the era borrow for 14 days
Link, Arthur Stanley. Wilson: The Struggle for Neutrality: 1914–1915 (1960); Wilson: Confusions and Crises: 1915–1916 (1964); Wilson: Campaigns for Progressivism and Peace: 1916–1917 (1965), the standard biography to 1918
Malin, James C. The United States after the World War (1930) online
Meyer G.J. The World Remade: America In World War I (2017), popular survey, 672pp
North, Diane M.T. California at War: The State and the People during World War I (2018).
Paxson, Frederic L. Pre-war years, 1913-1917 (1936) wide-ranging scholarly survey
Paxson, Frederic L. American at War 1917-1918 (1939) wide-ranging scholarly survey
Philadelphia War History Committee (1922). Philadelphia in the World War, 1914-1919. full text online
Schaffer, Ronald. America in the Great War: The Rise of the War-Welfare State (Oxford University Press, 1991), ISBN 0-19-504904-7
Tucker, Spencer C., and Priscilla Mary Roberts, eds. The Encyclopedia of World War I : A Political, Social, and Military History (5 vol. 2005)
Vaughn, Stephen. Holding Fast the Inner Lines: Democracy, Nationalism, and the Committee on Public Information (1980) in Questia
Venzon, Anne ed. The United States in the First World War: An Encyclopedia (1995), Very thorough coverage.
Williams, William John. The Wilson administration and the shipbuilding crisis of 1917: steel ships and wooden steamers (1992).
Wilson, Ross J. New York and the First World War: Shaping an American City (2014).
Young, Ernest William. The Wilson Administration and the Great War (1922) online edition
Zieger, Robert H. America's Great War: World War I and the American Experience 2000. 272 pp.
Economics and labor[edit]
Cuff, Robert D. The war industries board: Business-government relations during World War I (1973).
Cuff, Robert D. "The politics of labor administration during world war I." Labor History 21.4 (1980): 546-569.
Dubofsky, Melvyn. "Abortive reform: the Wilson administration and organized labor, 1913-1920." in Work, Community, and Power: The Experience of Labor in Europe and America, 1900-1925 edited by James E. Cronin and Sirianni, (1983): 197-220.
Haig, Robert Murray. “The Revenue Act of 1918,” Political Science Quarterly 34#3 (1919): 369-391. in JSTOR
Kester, Randall B. “The War Industries Board, 1917–1918; A Study in Industrial Mobilization,” American Political Science Review 34#4 (1940), pp. 655–84; in JSTOR
Rockoff, Hugh. "Until it's Over, Over There: The U.S. Economy in World War I," in Stephen Broadberry and Mark Harrison, eds. The Economics of World War I (2005) pp 310-43. online; online review
Soule, George. The Prosperity Decade: From War to Depression, 1917–1929 (1947), broad economic history of decade
Sutch, Richard. "The Fed, the Treasury, and the Liberty Bond Campaign–How William Gibbs McAdoo Won World War I." Central Banking in Historical Perspective: One Hundred Years of the Federal Reserve (2014) online; Illustrated with wartime government posters.
Historiography[edit]
Controvich, James T. The United States in World War I: A Bibliographic Guide (Scarecrow, 2012) 649 pp
Keene, Jennifer D. "Remembering the “Forgotten War”: American Historiography on World War I." Historian 78#3 (2016): 439-468.
Primary sources and year books[edit]
Creel, George. How We Advertised America: The First Telling of the Amazing Story of the Committee on Public Information That Carried the Gospel of Americanism to Every Corner of the Globe. New York: Harper & Brothers, 1920.
George Creel Sounds Call to Unselfish National Service to Newspaper Men Editor and Publisher, August 17, 1918.
United States. Committee on Public Information. National service handbook (1917) online free
Negro Year Book 1916
New International Year Book 1914, Comprehensive coverage of national and state affairs, 913pp
New International Year Book 1915, Comprehensive coverage of national and state affairs, 791pp
New International Year Book 1916 (1917), Comprehensive coverage of national and state affairs, 938pp
New International Year Book 1917 (1918), Comprehensive coverage of national and state affairs, 904 pp
New International Year Book 1918 (1919), Comprehensive coverage of national and state affairs, 904 pp
New InternationalYear Book 1919 (1920), Comprehensive coverage of national and state affairs, 744pp
New International Year Book 1920 (1921), Comprehensive coverage of national and state affairs, 844 pp
New International Year Book 1921 (1922), Comprehensive coverage of national and state affairs, 848 pp
External links[edit]
Wikimedia Commons has media related to World War I homefront in the United States.
Keene, Jennifer D.: United States of America , in: 1914-1918-online. International Encyclopedia of the First World War.
Ford, Nancy Gentile: Civilian and Military Power (USA) , in: 1914-1918-online. International Encyclopedia of the First World War.
Jensen, Kimberly: Women's Mobilization for War (USA) , in: 1914-1918-online. International Encyclopedia of the First World War.
Strauss, Lon: Social Conflict and Control, Protest and Repression (USA) , in: 1914-1918-online. International Encyclopedia of the First World War.
Taillon, Paul Michel: Labour Movements, Trade Unions and Strikes (USA) , in: 1914-1918-online. International Encyclopedia of the First World War.
Little, Branden: Making Sense of the War (USA) , in: 1914-1918-online. International Encyclopedia of the First World War.
Miller, Alisa: Press/Journalism (USA) , in: 1914-1918-online. International Encyclopedia of the First World War.
Wells, Robert A.: Propaganda at Home (USA) , in: 1914-1918-online. International Encyclopedia of the First World War.
Home front of Connecticut in World War I
North Carolinians and the Great War: Introduction to the Home Front
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Venn diagram
From Wikipedia, the free encyclopedia
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Venn diagram showing which uppercase letter glyphs are shared by the Greek, Latin and Russian alphabets
Part of a series on Statistics
Probability theory
Probability axioms
Probability space
Sample space
Elementary event
Event
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Complementary event
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Bayes' theorem
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Venn diagram
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A Venn diagram (also called primary diagram, set diagram or logic diagram) is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. The points inside a curve labelled S represent elements of the set S, while points outside the boundary represent elements not in the set S. Thus, for example, the set of all elements that are members of both sets S and T, S ∩ T, is represented visually by the area of overlap of the regions S and T. In Venn diagrams the curves are overlapped in every possible way, showing all possible relations between the sets. They are thus a special case of Euler diagrams, which do not necessarily show all relations. Venn diagrams were conceived around 1880 by John Venn. They are used to teach elementary set theory, as well as illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
A Venn diagram in which the area of each shape is proportional to the number of elements it contains is called an area-proportional or scaled Venn diagram.
Contents
[hide]
1 Example
2 History
3 Overview
4 Extensions to higher numbers of sets
4.1 Edwards–Venn diagrams
4.2 Other diagrams
5 Related concepts
6 See also
7 Notes
8 References
9 Further reading
10 External links
Example[edit]
Sets A (creatures with two legs) and B (creatures that can fly)
This example involves two sets, A and B, represented here as coloured circles. The orange circle, set A, represents all living creatures that are two-legged. The blue circle, set B, represents the living creatures that can fly. Each separate type of creature can be imagined as a point somewhere in the diagram. Living creatures that both can fly and have two legs—for example, parrots—are then in both sets, so they correspond to points in the region where the blue and orange circles overlap. That region contains all such and only such living creatures.
Humans and penguins are bipedal, and so are then in the orange circle, but since they cannot fly they appear in the left part of the orange circle, where it does not overlap with the blue circle. Mosquitoes have six legs, and fly, so the point for mosquitoes is in the part of the blue circle that does not overlap with the orange one. Creatures that are not two-legged and cannot fly (for example, whales and spiders) would all be represented by points outside both circles.
The combined region of sets A and B is called the union of A and B, denoted by A ∪ B. The union in this case contains all living creatures that are either two-legged or that can fly (or both).
The region in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A ∩ B. For example, the intersection of the two sets is not empty, because there are points that represent creatures that are in both the orange and blue circles.
History[edit]
Stained-glass window with Venn diagram in Cambridge
Venn diagrams were introduced in 1880 by John Venn in a paper entitled On the Diagrammatic and Mechanical Representation of Propositions and Reasonings in the "Philosophical Magazine and Journal of Science", about the different ways to represent propositions by diagrams.[1][2][3] The use of these types of diagrams in formal logic, according to Frank Ruskey and Mark Weston, is "not an easy history to trace, but it is certain that the diagrams that are popularly associated with Venn, in fact, originated much earlier. They are rightly associated with Venn, however, because he comprehensively surveyed and formalized their usage, and was the first to generalize them".[4]
Venn himself did not use the term "Venn diagram" and referred to his invention as "Eulerian Circles".[3] For example, in the opening sentence of his 1880 article Venn writes, "Schemes of diagrammatic representation have been so familiarly introduced into logical treatises during the last century or so, that many readers, even those who have made no professional study of logic, may be supposed to be acquainted with the general nature and object of such devices. Of these schemes one only, viz. that commonly called 'Eulerian circles,' has met with any general acceptance..."[1][2] The first to use the term "Venn diagram" was Clarence Irving Lewis in 1918, in his book "A Survey of Symbolic Logic".[4][5]
Venn diagrams are very similar to Euler diagrams, which were invented by Leonhard Euler in the 18th century.[note 1][6][7] M. E. Baron has noted that Leibniz (1646–1716) in the 17th century produced similar diagrams before Euler, but much of it was unpublished.[8] She also observes even earlier Euler-like diagrams by Ramon Lull in the 13th Century.[9]
In the 20th century, Venn diagrams were further developed. D. W. Henderson showed in 1963 that the existence of an n-Venn diagram with n-fold rotational symmetry implied that n was a prime number.[10] He also showed that such symmetric Venn diagrams exist when n is 5 or 7. In 2002 Peter Hamburger found symmetric Venn diagrams for n = 11 and in 2003, Griggs, Killian, and Savage showed that symmetric Venn diagrams exist for all other primes. Thus rotationally symmetric Venn diagrams exist if and only if n is a prime number.[11]
Venn diagrams and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement in the 1960s. Since then, they have also been adopted in the curriculum of other fields such as reading.[12]
Overview[edit]
See also: Set (mathematics) § Basic operations
Intersection of two sets
A ∩ B {\displaystyle ~A\cap B}
Union of two sets
A ∪ B {\displaystyle ~A\cup B}
Symmetric difference of two sets A Δ B {\displaystyle A~\Delta ~B}
Relative complement of A (left) in B (right)
A c ∩ B = B ∖ A {\displaystyle A^{c}\cap B~=~B\setminus A}
Absolute complement of A in U
A c = U ∖ A {\displaystyle A^{c}~=~U\setminus A}
A Venn diagram is constructed with a collection of simple closed curves drawn in a plane. According to Lewis,[5] the "principle of these diagrams is that classes [or sets] be represented by regions in such relation to one another that all the possible logical relations of these classes can be indicated in the same diagram. That is, the diagram initially leaves room for any possible relation of the classes, and the actual or given relation, can then be specified by indicating that some particular region is null or is not-null".[5]:157
Venn diagrams normally comprise overlapping circles. The interior of the circle symbolically represents the elements of the set, while the exterior represents elements that are not members of the set. For instance, in a two-set Venn diagram, one circle may represent the group of all wooden objects, while another circle may represent the set of all tables. The overlapping region or intersection would then represent the set of all wooden tables. Shapes other than circles can be employed as shown below by Venn's own higher set diagrams. Venn diagrams do not generally contain information on the relative or absolute sizes (cardinality) of sets; i.e. they are schematic diagrams.
Venn diagrams are similar to Euler diagrams. However, a Venn diagram for n component sets must contain all 2n hypothetically possible zones that correspond to some combination of inclusion or exclusion in each of the component sets. Euler diagrams contain only the actually possible zones in a given context. In Venn diagrams, a shaded zone may represent an empty zone, whereas in an Euler diagram the corresponding zone is missing from the diagram. For example, if one set represents dairy products and another cheeses, the Venn diagram contains a zone for cheeses that are not dairy products. Assuming that in the context cheese means some type of dairy product, the Euler diagram has the cheese zone entirely contained within the dairy-product zone—there is no zone for (non-existent) non-dairy cheese. This means that as the number of contours increases, Euler diagrams are typically less visually complex than the equivalent Venn diagram, particularly if the number of non-empty intersections is small.[13]
The difference between Euler and Venn diagrams can be seen in the following example. Take the three sets:
A = { 1 , 2 , 5 } {\displaystyle A=\{1,\,2,\,5\}}
B = { 1 , 6 } {\displaystyle B=\{1,\,6\}}
C = { 4 , 7 } {\displaystyle C=\{4,\,7\}}
The Venn and the Euler diagram of those sets are:
Euler diagram
Venn diagram
Extensions to higher numbers of sets[edit]
Venn diagrams typically represent two or three sets, but there are forms that allow for higher numbers. Shown below, four intersecting spheres form the highest order Venn diagram that has the symmetry of a simplex and can be visually represented. The 16 intersections correspond to the vertices of a tesseract (or the cells of a 16-cell respectively).

For higher numbers of sets, some loss of symmetry in the diagrams is unavoidable. Venn was keen to find "symmetrical figures...elegant in themselves,"[6] that represented higher numbers of sets, and he devised an elegant four-set diagram using ellipses (see below). He also gave a construction for Venn diagrams for any number of sets, where each successive curve that delimits a set interleaves with previous curves, starting with the three-circle diagram.
Venn's construction for 4 sets
Venn's construction for 5 sets
Venn's construction for 6 sets
Venn's four-set diagram using ellipses
Non-example: This Euler diagram is not a Venn diagram for four sets as it has only 13 regions (excluding the outside); there is no region where only the yellow and blue, or only the red and green circles meet.
Five-set Venn diagram using congruent ellipses in a 5-fold rotationally symmetrical arrangement devised by Branko Grünbaum. Labels have been simplified for greater readability; for example, A denotes A ∩ Bc ∩ Cc ∩ Dc ∩ Ec, while BCE denotes Ac ∩ B ∩ C ∩ Dc ∩ E.
Six-set Venn diagram made of only triangles (interactive version)
Edwards–Venn diagrams[edit]
Three sets
Four sets
Five sets
Six sets
Anthony William Fairbank Edwards constructed a series of Venn diagrams for higher numbers of sets by segmenting the surface of a sphere, which became known as Edwards–Venn diagrams.[14] For example, three sets can be easily represented by taking three hemispheres of the sphere at right angles (x = 0, y = 0 and z = 0). A fourth set can be added to the representation by taking a curve similar to the seam on a tennis ball, which winds up and down around the equator, and so on. The resulting sets can then be projected back to a plane to give cogwheel diagrams with increasing numbers of teeth, as shown here. These diagrams were devised while designing a stained-glass window in memory of Venn.[14]
Other diagrams[edit]
Edwards–Venn diagrams are topologically equivalent to diagrams devised by Branko Grünbaum, which were based around intersecting polygons with increasing numbers of sides. They are also two-dimensional representations of hypercubes.
Henry John Stephen Smith devised similar n-set diagrams using sine curves[14] with the series of equations
y i = sin  ( 2 i x ) 2 i where 0 ≤ i ≤ n − 2 and i ∈ N . {\displaystyle y_{i}={\frac {\sin(2^{i}x)}{2i}}{\text{ where }}0\leq i\leq n-2{\text{ and }}i\in \mathbb {N} .}
Charles Lutwidge Dodgson (aka Lewis Carroll) devised a five-set diagram known as Carroll's square.
Related concepts[edit]
Venn diagram as a truth table
Venn diagrams correspond to truth tables for the propositions x ∈ A {\displaystyle x\in A} , x ∈ B {\displaystyle x\in B} , etc., in the sense that each region of Venn diagram corresponds to one row of the truth table.[15][16] This type is also known as Johnston diagram. Another way of representing sets is with John F. Randolph's R-diagrams.
See also[edit]
Existential graph (by Charles Sanders Peirce)
Logical connectives
Spherical octahedron – A stereographic projection of a regular octahedron makes a 3-set Venn diagram, as 3 orthogonal great circles, each dividing space into two halves.
Marquand diagram (and as further derivation Veitch chart and Karnaugh map)
Notes[edit]
Jump up ^ In Euler's Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie [Letters to a German Princess on various physical and philosophical subjects] (Saint Petersburg, Russia: l'Academie Impériale des Sciences, 1768), volume 2, pages 95-126. In Venn's article, however, he suggests that the diagrammatic idea predates Euler, and is attributable to Christian Weise or Johann Christian Lange (in Lange's book Nucleus Logicae Weisianae (1712)).
References[edit]
^ Jump up to: a b Venn, John (July 1880). "I. On the Diagrammatic and Mechanical Representation of Propositions and Reasonings" (PDF). The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 5. Taylor & Francis. 10 (59): 1–18. doi:10.1080/14786448008626877. Archived (PDF) from the original on 2017-05-16. [1] [2]
^ Jump up to: a b Venn, John (1880). "On the employment of geometrical diagrams for the sensible representations of logical propositions". Proceedings of the Cambridge Philosophical Society. 4: 47–59.
^ Jump up to: a b Sandifer, Ed (2003). "How Euler Did It" (pdf). MAA Online. The Mathematical Association of America (MAA). Retrieved 2009-10-26.
^ Jump up to: a b Ruskey, Frank; Weston, Mark (2005-06-18). "A Survey of Venn Diagrams". The Electronic Journal of Combinatorics.
^ Jump up to: a b c Lewis, Clarence Irving (1918). A Survey of Symbolic Logic. Berkeley: University of California Press.
^ Jump up to: a b Venn, John (1881). Symbolic logic. Macmillan. p. 108. Retrieved 2013-04-09.
Jump up ^ Mac Queen, Gailand (October 1967). The Logic Diagram (PDF) (Thesis). McMaster University. Archived from the original (PDF) on 2017-04-14. Retrieved 2017-04-14. (NB. Has a detailed history of the evolution of logic diagrams including but not limited to the Venn diagram.)
Jump up ^ Leibniz, Gottfried Wilhelm (1903) [ca. 1690]. "De Formae Logicae per linearum ductus". In Couturat, Louis. Opuscules et fragmentes inedits de Leibniz (in Latin). pp. 292–321.
Jump up ^ Baron, Margaret E. (May 1969). "A Note on The Historical Development of Logic Diagrams". The Mathematical Gazette. 53 (384): 113–125. doi:10.2307/3614533. JSTOR 3614533.
Jump up ^ Henderson, D. W. (April 1963). "Venn diagrams for more than four classes". American Mathematical Monthly. 70 (4): 424–6. doi:10.2307/2311865. JSTOR 2311865.
Jump up ^ Ruskey, Frank; Savage, Carla D.; Wagon, Stan (December 2006). "The Search for Simple Symmetric Venn Diagrams" (PDF). Notices of the AMS. 53 (11): 1304–11.
Jump up ^ Strategies for Reading Comprehension Venn Diagrams
Jump up ^ "Euler Diagrams 2004: Brighton, UK: September 22–23". Reasoning with Diagrams project, University of Kent. 2004. Retrieved 2008-08-13.
^ Jump up to: a b c Edwards, Anthony William Fairbank (2004), Cogwheels of the Mind: The Story of Venn Diagrams, Baltimore, Maryland, USA: Johns Hopkins University Press, p. 65, ISBN 0-8018-7434-3 .
Jump up ^ Grimaldi, Ralph P. (2004). Discrete and combinatorial mathematics. Boston: Addison-Wesley. p. 143. ISBN 0-201-72634-3.
Jump up ^ Johnson, D. L. (2001). "3.3 Laws". Elements of logic via numbers and sets. Springer Undergraduate Mathematics Series. Berlin, Germany: Springer-Verlag. p. 62. ISBN 3-540-76123-3.
Further reading[edit]
Mahmoodian, Ebadollah S.; Rezaie, M.; Vatan, F. (March 1987). "Generalization of Venn Diagram" (PDF). Eighteenth Annual Iranian Mathematics Conference. Tehran and Isfahan, Iran. Archived (PDF) from the original on 2017-05-01. Retrieved 2017-05-01.
Edwards, Anthony William Fairbank (1989-01-07). "Venn diagrams for many sets". New Scientist. 121 (1646): 51–56.
Watkinson, John (1990). "4.10. Hamming distance". Coding for Digital Recording. Stoneham, MA, USA: Focal Press. pp. 94–99, foldout in backsleeve. ISBN 0-240-51293-6. ISBN 978-0-240-51293-8. (NB. The book comes with a 3-page foldout of a seven-bit cylindrical Venn diagram.)
Stewart, Ian (June 2003) [1992]. "Chapter 4. Cogwheels of the Mind". Another Fine Math You've Got Me Into (reprint of 1st ed.). Mineola, New York, USA: Dover Publications, Inc. (W. H. Freeman). pp. 51–64. ISBN 0-486-43181-9.
Glassner, Andrew (2004). "Venn and Now". Morphs, Mallards, and Montages: Computer-Aided Imagination. Wellesley, MA, USA: A. K. Peters. pp. 161–184. ISBN 978-1568812311.
Mamakani, Khalegh; Ruskey, Frank (2012-07-27). "A New Rose: The First Simple Symmetric 11-Venn Diagram". pp. 6452. arXiv:1207.6452  . Bibcode:2012arXiv1207.6452M. Archived from the original on 2017-05-01. Retrieved 2017-05-01.
External links[edit]
Wikimedia Commons has media related to Venn diagrams.
Hazewinkel, Michiel, ed. (2001) [1994], "Venn diagram", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Weisstein, Eric W. "Venn Diagram". MathWorld.
Lewis Carroll's Logic Game – Venn vs. Euler at Cut-the-knot
Generating Venn Diagrams to explore Google Suggest results
Seven sets interactive Venn diagram displaying color combinations
Six sets Venn diagrams made from triangles
"Postscript for 9-set Venn and more". qandr.org.
Venn Diagrams vs Euler Diagrams
Venn diagram in Excel
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