text:
August 8

Pre-1600

 * 685 BC – Spring and Autumn period: Battle of Qianshi: Upon the death of the previous Duke of Qi, Gongsun Wuzhi, Duke Zhuang of Lu sends an army into the Duchy of Qi to install the exiled Qi prince Gongzi Jiu as the new Duke of Qi — but is defeated at Qianshi by Jiu’s brother and rival claimant, the newly inaugurated Duke Huan of Qi.
 * 870 – Treaty of Meerssen: King Louis the German and his half-brother Charles the Bald partition the Middle Frankish Kingdom into two larger east and west divisions.
 * 1220 – Sweden is defeated by Estonian tribes in the Battle of Lihula.
 * 1264 – Mudéjar revolt: Muslim rebel forces took the Alcázar of Jerez de la Frontera after defeating the Castilian garrison.
 * 1503 – King James IV of Scotland marries Margaret Tudor, daughter of King Henry VII of England at Holyrood Abbey in Edinburgh, Scotland.
 * 1509 – Krishnadeva Raya is crowned Emperor of Vijayanagara at Chittoor.
 * 1576 – The cornerstone for Tycho Brahe's Uraniborg observatory is laid on the island of Hven.
 * 1585 – John Davis enters Cumberland Sound in search of the Northwest Passage.
 * 1588 – Anglo-Spanish War: Battle of Gravelines: The naval engagement ends, ending the Spanish Armada's attempt to invade England.

1601–1900

 * 1647 – The Irish Confederate Wars and Wars of the Three Kingdoms: Battle of Dungan's Hill: English Parliamentary forces defeat Irish forces.
 * 1648 – Mehmed IV (1648–1687) succeeds Ibrahim I (1640–1648) as Ottoman sultan.
 * 1709 – Bartolomeu de Gusmão demonstrates the lifting power of hot air in an audience before the king of Portugal in Lisbon, Portugal.
 * 1786 – Mont Blanc on the French-Italian border is climbed for the first time by Jacques Balmat and Dr. Michel-Gabriel Paccard.
 * 1794 – Joseph Whidbey leads an expedition to search for the Northwest Passage near Juneau, Alaska.
 * 1831 – Four hundred Shawnee people agree to relinquish their lands in Ohio in exchange for land west of the Mississippi River in the Treaty of Wapakoneta.
 * 1844 – The Quorum of the Twelve Apostles, headed by Brigham Young, is reaffirmed as the leading body of the Church of Jesus Christ of Latter-day Saints (LDS Church).
 * 1863 – American Civil War: Following his defeat in the Battle of Gettysburg, General Robert E. Lee sends a letter of resignation to Confederate President Jefferson Davis (which is refused upon receipt).
 * 1863  – Tennessee Military Governor Andrew Johnson frees his personal slaves in Greeneville, Tennessee despite them being exempt from the Emancipation Proclamation, now commemorated as Emancipation Day in the state.
 * 1870 – The Republic of Ploiești, a failed Radical-Liberal rising against Domnitor Carol of Romania.
 * 1876 – Thomas Edison receives a patent for his mimeograph.

1901–present

 * 1903 – Black Saturday occurs, killing 12 in a stadium collapse in Philadelphia.
 * 1908 – Wilbur Wright makes his first flight at a racecourse at Le Mans, France. It is the Wright Brothers' first public flight.
 * 1918 – World War I: The Battle of Amiens begins a string of almost continuous Allied victories with a push through the German front lines (Hundred Days Offensive).
 * 1919 – The Anglo-Afghan Treaty of 1919 is signed. It establishes peaceful relations between Afghanistan and the UK, and confirms the Durand line as the mutual border. In return, the UK is no longer obligated to subsidize the Afghan government.
 * 1929 – The German airship Graf Zeppelin begins a round-the-world flight.
 * 1940 – The "Aufbau Ost" directive is signed by Wilhelm Keitel.
 * 1942 – Quit India Movement is launched in India against the British rule in response to Mohandas Gandhi's call for swaraj or complete independence.
 * 1945 – The London Charter is signed by France, the United Kingdom, the Soviet Union and the United States, establishing the laws and procedures for the Nuremberg trials.
 * 1946 – First flight of the Convair B-36, the world's first mass-produced nuclear weapon delivery vehicle, the heaviest mass-produced piston-engined aircraft, with the longest wingspan of any military aircraft, and the first bomber with intercontinental range.
 * 1956 – Marcinelle mining disaster in Belgium. 262 coal miners, including a substantial number of Italian migrant workers, were killed in one of the largest mining accidents in Belgian history.
 * 1963 – Great Train Robbery: In England, a gang of 15 train robbers steal £2.6 million in bank notes.
 * 1963  – The Zimbabwe African National Union (ZANU), the current ruling party of Zimbabwe, is formed by a split from the Zimbabwe African People's Union.
 * 1967 – The Association of Southeast Asian Nations (ASEAN) is founded by Indonesia, Malaysia, the Philippines, Singapore and Thailand.
 * 1969 – At a zebra crossing in London, photographer Iain Macmillan takes the iconic photo that becomes the cover image of the Beatles' album Abbey Road.
 * 1973 – Kim Dae-jung, a South Korean politician and later president of South Korea, is kidnapped.
 * 1974 – President Richard Nixon, in a nationwide television address, announces his resignation from the office of the President of the United States effective noon the next day.
 * 1988 – The 8888 Uprising begins in Rangoon (Yangon), Burma (Myanmar). Led by students, hundreds of thousands join in nationwide protests against the one-party regime. On September 18, the demonstrations end in a military crackdown, killing thousands.
 * 1988  – The first night baseball game in the history of Chicago's Wrigley Field (game was rained out in the fourth inning).
 * 1989 – Space Shuttle program: STS-28 Mission: Space Shuttle Columbia takes off on a secret five-day military mission.
 * 1990 – Iraq occupies Kuwait and the state is annexed to Iraq. This would lead to the Gulf War shortly afterward.
 * 1991 – The Warsaw radio mast, then the tallest construction ever built, collapses.
 * 1993 – The 7.8 Guam earthquake shakes the island with a maximum Mercalli intensity of IX (Violent), causing around $250 million in damage and injuring up to 71 people.
 * 1998 – Iranian consulate in Mazar-i-Sharif, Afghanistan is raided by Taliban leading to the deaths of ten Iranian diplomats and a journalist.
 * 2000 – Confederate submarine H.L. Hunley is raised to the surface after 136 years on the ocean floor and 30 years after its discovery by undersea explorer E. Lee Spence.
 * 2001 – Albanian rebels ambush a convoy of the Army of the Republic of Macedonia near Tetovo, killing 10 soldiers.
 * 2004 – A tour bus belonging to the Dave Matthews Band dumps approximately 800 pounds of human waste onto a boat full of passengers.
 * 2007 – An EF2 tornado touches down in Kings County and Richmond County, New York, the most powerful tornado in New York to date and the first in Brooklyn since 1889.
 * 2008 – A EuroCity express train en route from Kraków, Poland to Prague, Czech Republic strikes a part of a motorway bridge that had fallen onto the railroad track near Studénka railway station in the Czech Republic and derails, killing eight people and injuring 64 others.
 * 2008  – The 29th modern summer Olympic Games took place in Beijing, China until August 24.
 * 2010 – China Floods: A mudslide in Zhugqu County, Gansu, China, kills more than 1,400 people.
 * 2013 – A suicide bombing at a funeral in the Pakistani city of Quetta kills at least 31 people.
 * 2015 – Eight people are killed in a shooting in Harris County, Texas.
 * 2016 – Terrorists attack a government hospital in Quetta, Pakistan with a suicide blast and shooting, killing between 70 and 94 people, and injuring around 130 others.
 * 2019 – An explosion at the State Central Navy Testing Range in Nyonoksa, Russia, kills five people.
 * 2022 – The Federal Bureau of Investigation (FBI) executes a search warrant at former president Donald Trump's residence in Mar-a-Lago, Palm Beach, Florida.
 * 2023 – 2023 Hawaii wildfires: 17,000 acres of land are burned and at least 101 people are killed, with two others missing, when a series of wildfires break out on the island of Maui in Hawaii.

Pre-1600

 * 422 – Casper, ruler of the Maya city of Palenque
 * 1079 – Emperor Horikawa of Japan (d. 1107)
 * 1170 – Saint Dominic, founder of the Dominicans (d. 1221)
 * 1306 – Rudolf II, Duke of Bavaria (d. 1353)
 * 1492 – Matteo Tafuri, Italian alchemist (d. 1582)
 * 1518 – Conrad Lycosthenes, French-German scholar and author (d. 1561)
 * 1558 – George Clifford, 3rd Earl of Cumberland, English noble (d. 1605)

1601–1900

 * 1605 – Cecil Calvert, 2nd Baron Baltimore, English lawyer and politician, Governor of Newfoundland (d. 1675)
 * 1640 – Amalia Catharina, German poet and composer (d. 1697)
 * 1646 – Godfrey Kneller, German-English painter (d. 1723)
 * 1673 – John Ker, Scottish spy (d. 1726)
 * 1693 – Laurent Belissen, French composer (d. 1762)
 * 1694 – Francis Hutcheson, Irish philosopher and academic (d. 1746)
 * 1709 – Hermann Anton Gelinek, German-Italian monk and violinist (d. 1779)
 * 1720 – Carl Fredrik Pechlin, Swedish general and politician (d. 1796)
 * 1754 – Hipólito Ruiz López, Spanish botanist (d. 1816)
 * 1758 – Friedrich Georg Weitsch, German painter (d. 1828)
 * 1790 – Ferenc Kölcsey, Hungarian poet, critic, and politician (d. 1838)
 * 1807 – Emilie Flygare-Carlén, Swedish author (d. 1892)
 * 1814 – Esther Hobart Morris, American suffragette and judge (d. 1902)
 * 1822 – George Stoneman, Jr., United States Army cavalry officer (d. 1894)
 * 1839 – Nelson A. Miles, American general (d. 1925)
 * 1851 – George Turner, Australian politician, 18th Premier of Victoria (d. 1916)
 * 1856 – Thomas Anstey Guthrie, English journalist and author (d. 1934)
 * 1857 – Cécile Chaminade, French pianist and composer (d. 1944)
 * 1863 – Jean Leon Gerome Ferris, American painter (d. 1930)
 * 1866 – Matthew Henson, American explorer (d. 1955)
 * 1874 – Albert Stanley, 1st Baron Ashfield, English businessman and politician, President of the Board of Trade (d. 1948)
 * 1875 – Artur Bernardes, Brazilian lawyer and politician, 12th President of Brazil (d. 1955)
 * 1876 – Varghese Payyappilly Palakkappilly, Indian-Syrian priest, founded the Sisters of the Destitute (d. 1929)
 * 1879 – Bob Smith, American physician and surgeon, co-founded Alcoholics Anonymous (d. 1950)
 * 1879  – Emiliano Zapata, Mexican general and politician (d. 1919)
 * 1880 – Earle Page, Australian lawyer, academic, and politician, 11th Prime Minister of Australia (d. 1961)
 * 1881 – Paul Ludwig Ewald von Kleist, German field marshal (d. 1954)
 * 1882 – Ladislas Starevich, Russian-French animator, screenwriter, and cinematographer (d. 1965)
 * 1884 – Sara Teasdale, American poet and educator (d. 1933)
 * 1889 – Hans Egede Budtz, Danish actor (d. 1968)
 * 1889  – Jack Ryder, Australian cricketer (d. 1977)
 * 1891 – Adolf Busch, German violinist and composer (d. 1952)
 * 1896 – Marjorie Kinnan Rawlings, American author and academic (d. 1953)
 * 1898 – Marguerite Bise, French chef (d. 1965)

1901–present

 * 1901 – Ernest Lawrence, American physicist and academic, Nobel Prize laureate (d. 1958)
 * 1902 – Paul Dirac, English-American physicist and academic, Nobel Prize laureate (d. 1984)
 * 1904 – Achille Varzi, Italian racing driver (d. 1948)
 * 1905 – André Jolivet, French composer (d. 1974)
 * 1907 – Benny Carter, American saxophonist, trumpet player, and composer (d. 2003)
 * 1907 – Jimmy Steele (Irish republican), life long militant and editor (d. 1970)
 * 1908 – Arthur Goldberg, American jurist and politician, 6th United States Ambassador to the United Nations (d. 1990)
 * 1909 – Charles Lyttelton, 10th Viscount Cobham, English cricketer and politician, 9th Governor-General of New Zealand (d. 1977)
 * 1909  – Jack Renshaw, Australian politician, 31st Premier of New South Wales (d. 1987)
 * 1909  – Bill Voce, England cricketer and coach (d. 1984)
 * 1910 – Jimmy Murphy, Welsh-English footballer and manager (d. 1989)
 * 1910  – Sylvia Sidney, American actress (d. 1999)
 * 1911 – Rosetta LeNoire, American actress (d. 2002)
 * 1915 – James Elliott, American runner and coach (d. 1981)
 * 1919 – Dino De Laurentiis, Italian actor and producer (d. 2010)
 * 1919  – John David Wilson, English animator and producer (d. 2013)
 * 1920 – Leo Chiosso, Italian songwriter and producer (d. 2006)
 * 1920  – Jimmy Witherspoon, American jump blues singer (d. 1997)
 * 1921 – William Asher, American director, producer, and screenwriter (d. 2012)
 * 1921  – Webb Pierce, American singer-songwriter and guitarist (d. 1991)
 * 1921  – Esther Williams, American swimmer and actress (d. 2013)
 * 1922 – Rory Calhoun, American actor (d. 1999)
 * 1922  – Rudi Gernreich, Austrian-American fashion designer, created the Monokini (d. 1985)
 * 1922  – Gertrude Himmelfarb, American historian, author, and academic (d. 2019)
 * 1922  – Károly Reich, Hungarian illustrator (d. 1988)
 * 1925 – Alija Izetbegović, Bosnian lawyer and politician, 1st President of Bosnia and Herzegovina (d. 2003)
 * 1925  – Aziz Sattar, Malaysian actor, comedian, singer and director (d. 2014)
 * 1926 – Richard Anderson, American actor and producer (d. 2017)
 * 1927 – Johnny Temple, American baseball player and coach (d. 1994)
 * 1927  – Maia Wojciechowska, Polish-American author (d. 2002)
 * 1928 – Don Burrows, Australian saxophonist, clarinet player, and flute player (d. 2020)
 * 1929 – Larisa Bogoraz, Russian linguist and activist (d. 2004)
 * 1929  – Luis García Meza Tejada, Bolivian general and politician, 68th President of Bolivia (d. 2018)
 * 1929  – Ronnie Biggs, English criminal (d. 2013)
 * 1930 – Terry Nation, Welsh-American author and screenwriter (d. 1997)
 * 1930  – Jerry Tarkanian, American basketball player and coach (d. 2015)
 * 1931 – Roger Penrose, English physicist, mathematician, and philosopher, Nobel Prize laureate
 * 1932 – Mel Tillis, American singer-songwriter and guitarist (d. 2017)
 * 1933 – Joe Tex, American soul singer-songwriter (d. 1982)
 * 1934 – Sarat Pujari, Indian actor, director, and screenwriter (d. 2014)
 * 1935 – Donald P. Bellisario, American director, producer, and screenwriter
 * 1935  – John Laws, Papua New Guinean-Australian singer and radio host
 * 1936 – Frank Howard, American baseball player and manager (d. 2023)
 * 1936  – Jan Pieńkowski, Polish-English author and illustrator (d. 2022)
 * 1937 – Dustin Hoffman, American actor and director
 * 1937  – Sheila Varian, American horse breeder (d. 2016)
 * 1937  – Cornelis Vreeswijk, Dutch-Swedish singer-songwriter, guitarist, and actor (d. 1987)
 * 1938 – Jack Baldwin, English chemist and academic (d. 2020)
 * 1938  – Jacques Hétu, Canadian composer and educator (d. 2010)
 * 1938  – Connie Stevens, American actress and businesswoman
 * 1939 – Jana Andrsová, Czech actress and ballerina (d. 2023)
 * 1939  – Viorica Viscopoleanu, Romanian long jumper
 * 1939  – Alexander Watson, American diplomat, United States Ambassador to Peru
 * 1940 – Dilip Sardesai, Indian cricketer (d. 2007)
 * 1940  – Dennis Tito, American engineer and businessman, founded Wilshire Associates
 * 1942 – James Blanchard, American diplomat and politician, 45th Governor of Michigan
 * 1942  – Dennis Canavan, Scottish educator and politician
 * 1942  – John Gustafson, English singer-songwriter and bass player (d. 2014)
 * 1942  – Vardo Rumessen, Estonian pianist and musicologist (d. 2015)
 * 1944 – John C. Holmes, American film actor (d. 1988)
 * 1944  – Michael Johnson, American singer-songwriter, guitarist, and producer (d. 2017)
 * 1944  – John Renbourn, English-Scottish guitarist and songwriter (d. 2015)
 * 1944  – Simon Taylor, English journalist and author
 * 1946 – Joe Bethancourt, American singer-songwriter (d. 2014)
 * 1947 – Ken Dryden, Canadian ice hockey player, lawyer, and politician
 * 1947  – Larry Wilcox, American actor, director, and producer
 * 1948 – Svetlana Savitskaya, Russian engineer and astronaut
 * 1948  – Margaret Urban Walker, American philosopher
 * 1949 – Terry Burnham, American actress (d. 2013)
 * 1949  – Keith Carradine, American actor
 * 1949  – Ricardo Londoño, Colombian racing driver (d. 2009)
 * 1950 – Willie Hall, American drummer and producer
 * 1950  – Ken Kutaragi, Japanese businessman, created PlayStation
 * 1951 – Martin Brest, American director, producer, and screenwriter
 * 1951  – Phil Carlson, Australian cricketer (d. 2022)
 * 1951  – Mohamed Morsi, Egyptian engineer, academic, and politician, 5th President of Egypt (d. 2019)
 * 1951  – Mamoru Oshii, Japanese director, producer, and screenwriter
 * 1951  – Randy Shilts, American journalist and author (d. 1994)
 * 1951  – Louis van Gaal, Dutch footballer and manager
 * 1952 – Anton Fig, South African-American drummer
 * 1952  – Jostein Gaarder, Norwegian author
 * 1952  – Doug Melvin, Canadian baseball player and manager
 * 1952  – Robin Quivers, American nurse, radio host/personality, and author
 * 1952  – Sudhakar Rao, Indian cricketer
 * 1953 – Nigel Mansell, English racing driver
 * 1953  – Don Most, American actor and singer
 * 1954 – Nick Holtam, English bishop
 * 1955 – Diddú, Icelandic singer-songwriter
 * 1955  – Herbert Prohaska, Austrian footballer and manager
 * 1955  – Michael Roe, Irish racing driver
 * 1956 – Chris Foreman, English singer-songwriter and guitarist
 * 1956  – David Grant, English singer
 * 1956  – Cecilia Roth, Argentinian actress
 * 1957 – Dennis Drew, American keyboard player
 * 1958 – Deborah Norville, American journalist
 * 1959 – Caroline Ansink, Dutch flute player, composer, and educator
 * 1960 – Mustafa Balbay, Turkish journalist and politician
 * 1960  – Ulrich Maly, German politician, 16th Mayor of Nuremberg
 * 1961 – The Edge, British-Irish musician, singer and songwriter
 * 1961  – Daniel House, American bass player and producer
 * 1961  – Ron Klain, American lawyer and politician, White House Chief of Staff
 * 1961  – Bruce Matthews, American football player and coach
 * 1961  – Rikki Rockett, American glam rock drummer
 * 1962 – Kool Moe Dee, American musician, singer and actor
 * 1963 – Hur Jin-ho, South Korean director and screenwriter
 * 1963  – Ron Karkovice, American baseball player and manager
 * 1963  – Emi Shinohara, Japanese voice actress and singer
 * 1963  – Jon Turteltaub, American director and producer
 * 1963  – Stephen Walkom, Canadian ice hockey player, referee, and manager
 * 1964 – Anastasia M. Ashman, American blogger and author
 * 1964  – Giuseppe Conte, Prime Minister of Italy
 * 1964  – Scott Sandelin, American ice hockey player and coach
 * 1964  – Paul Taylor, English cricketer
 * 1965 – Angus Fraser, English cricketer, manager, and journalist
 * 1965  – Kate Langbroek, Australian talk show host
 * 1966 – Chris Eubank, English boxer
 * 1966  – John Hudek, American baseball player and coach
 * 1967 – Marcelo Balboa, American soccer player, coach, and sportscaster
 * 1967 – Yūki Amami, Japanese theater and film actress
 * 1968 – Yvie Burnett, Scottish soprano
 * 1968  – Aldo Calderón van Dyke, Honduran journalist (d. 2013)
 * 1968  – Abey Kuruvilla, Indian cricketer and coach
 * 1968  – Huey Morgan, American singer-songwriter and guitarist
 * 1969 – Monika Tsõganova, Estonian chess player
 * 1969  – Faye Wong, Chinese singer-songwriter and actress
 * 1970 – Trev Alberts, American football player and journalist
 * 1970  – Ben G. Davis, English chemist and academic
 * 1970  – José Francisco Molina, Spanish footballer and manager
 * 1970  – Chester Williams, South African rugby player and coach (d. 2019)
 * 1971 – Johnny Balentina, Dutch baseball player
 * 1972 – Joely Collins, Canadian actress and producer
 * 1972  – Andrea de Rossi, Italian rugby player and coach
 * 1972  – Axel Merckx, Belgian cyclist
 * 1972  – Steven Tweed, Scottish footballer and manager
 * 1973 – Shane Lee, Australian cricketer and guitarist
 * 1973  – Gert Olesk, Estonian footballer and manager
 * 1973  – Scott Stapp, American singer-songwriter and producer
 * 1973  – Mark Wills, American singer-songwriter
 * 1973  – Ilka Agricola, German mathematician
 * 1974 – Manjul Bhargava, Canadian-American mathematician and academic
 * 1974  – Scott D'Amore, Canadian wrestler and manager
 * 1974  – Brian Harvey, English singer-songwriter
 * 1974  – Andy Priaulx, Guernseyan racing driver
 * 1975 – Mick Moss, English singer-songwriter
 * 1976 – JC Chasez, American singer and dancer
 * 1976  – Drew Lachey, American singer and actor
 * 1977 – Lindsay Sloane, American actress
 * 1977  – Darren Manzella, American sergeant (d. 2013)
 * 1977  – Rocky Thompson, Canadian ice hockey player and coach
 * 1977  – Nicolas Vogondy, French cyclist
 * 1977  – Mohammad Wasim, Pakistani cricketer
 * 1978 – Alan Maybury, Irish footballer and coach
 * 1978  – Louis Saha, French footballer
 * 1978  – Miho Shiraishi, Japanese actress
 * 1979 – Richard Harwood, English cellist
 * 1979  – Rashard Lewis, American basketball player
 * 1979  – Richard Lyons, Northern Irish racing driver
 * 1980 – Shayna Baszler, American mixed martial artist and wrestler
 * 1980  – Craig Breslow, American baseball pitcher and executive
 * 1980  – Jack Cassel, American baseball player
 * 1980  – Denisse Guerrero, Mexican singer-songwriter
 * 1980  – Sabine Klaschka, German tennis player
 * 1980  – Diego Markwell, Dutch baseball player
 * 1980  – Pat Noonan, American soccer player
 * 1980  – Michael Urie, American actor, director, and producer
 * 1981 – Vanessa Amorosi, Australian singer-songwriter
 * 1981  – Roger Federer, Swiss tennis player
 * 1981  – Meagan Good, American actress and producer
 * 1981  – Harel Skaat, Israeli singer-songwriter
 * 1982 – David Florence, English canoe racer
 * 1982  – Ross Ohlendorf, American baseball player
 * 1983 – Guy Burnet, English actor and producer
 * 1983  – Willie Tonga, Australian rugby league player
 * 1984 – Kirk Broadfoot, Scottish footballer
 * 1984  – Norbert Michelisz, Hungarian racing driver
 * 1984  – Martrez Milner, American football player
 * 1985 – Toby Flood, English rugby player
 * 1985  – Ryan Koolwijk, Dutch footballer
 * 1985  – James Morgan, Welsh actor and producer
 * 1985  – Brett Ratliff, American football player
 * 1985  – Anita Włodarczyk, Polish track and field athlete
 * 1986 – Kateryna Bondarenko, Ukrainian tennis player
 * 1986  – Jackie Cruz, Dominican-American actress and singer
 * 1986  – Pierre Garçon, American football player
 * 1986  – Chris Pressley, American football player
 * 1987 – Pierre Boulanger, French actor
 * 1987  – Katie Leung, Scottish actress
 * 1987  – Tatjana Maria, German tennis player
 * 1988 – Princess Beatrice, British royal
 * 1988  – Danilo Gallinari, Italian basketball player
 * 1988  – Rinku Singh, Indian baseball player and wrestler
 * 1988  – Laura Slade Wiggins, American actress and singer
 * 1989 – Ken Baumann, American actor and author
 * 1989  – Anthony Rizzo, American baseball player
 * 1989  – Hannah Miley, English-Scottish swimmer
 * 1989  – Prajakta Mali, Indian actress
 * 1990 – Vladimír Darida, Czech footballer
 * 1990  – Parker Kligerman, American race car driver
 * 1990  – Aleksandra Szwed, Polish actress and singer
 * 1990  – Kane Williamson, New Zealand cricket captain
 * 1991 – Yandy Díaz, Cuban baseball player
 * 1991  – Nélson Oliveira, Portuguese footballer
 * 1991  – Tyrone Peachey, Australian rugby league player
 * 1991  – Joël Matip, Cameroonian footballer
 * 1992 – Josip Drmić, Swiss footballer
 * 1992  – Casey Cott, American actor
 * 1993 – Emilie Mehl, Norwegian politician
 * 1997 – Karim Walid, Egyptian footballer
 * 1998 – Ryan Garcia, American boxer
 * 1998  – Shawn Mendes, Canadian singer-songwriter and guitarist
 * 2000 – Félix Auger-Aliassime, Canadian tennis player

Pre-1600

 * 117 – Trajan, Roman emperor (b. 53)
 * 753 – Hildegar, bishop of Cologne
 * 869 – Lothair II, Frankish king (b. 835)
 * 998 – Sŏ Hŭi, Korean politician and diplomat (b. 942)
 * 1002 – Almanzor, chief minister and de facto ruler of Córdoba
 * 1171 – Henry of Blois, bishop of Winchester (b. 1111)
 * 1303 – Henry of Castile the Senator, Spanish nobleman (b. 1230)
 * 1533 – Lucas van Leyden, Dutch artist (b. 1494)
 * 1555 – Oronce Finé, French mathematician and cartographer (b. 1494)
 * 1588 – Alonso Sánchez Coello, Spanish painter (b. 1532)

1601–1900

 * 1604 – Horio Tadauji, Japanese daimyō (b. 1578)
 * 1616 – Cornelis Ketel, Dutch painter (b. 1548)
 * 1631 – Konstantinas Sirvydas, Lithuanian priest, lexicographer, and academic (b. 1579)
 * 1684 – George Booth, 1st Baron Delamer, English politician (b. 1622)
 * 1724 – Christoph Ludwig Agricola, German painter (b. 1665)
 * 1747 – Madeleine de Verchères, Canadian raid leader (b. 1678)
 * 1746 – Francis Hutcheson, Irish philosopher (b. 1694)
 * 1759 – Carl Heinrich Graun, German tenor and composer (b. 1704)
 * 1827 – George Canning, English lawyer and politician, Prime Minister of the United Kingdom (b. 1770)
 * 1828 – Carl Peter Thunberg, Swedish botanist and psychologist (b. 1743)
 * 1858 – Marie-Claire Heureuse Félicité Bonheur, Haitian Empress (b. 1758)
 * 1863 – Angus MacAskill, Scottish-Canadian giant (b. 1825)
 * 1879 – Immanuel Hermann Fichte, German philosopher and academic (b. 1797)
 * 1887 – Alexander William Doniphan, American colonel, lawyer, and politician (b. 1808)
 * 1897 – Jacob Burckhardt, Swiss historian and academic (b. 1818)
 * 1898 – Eugène Boudin, French painter (b. 1824)

1901–present

 * 1902 – James Tissot, French painter and illustrator (b. 1836)
 * 1902  – John Henry Twachtman, American painter and academic (b. 1853)
 * 1909 – Mary MacKillop, Australian nun and saint, co-founded the Sisters of St Joseph of the Sacred Heart (b. 1842)
 * 1911 – William P. Frye, American lawyer and politician (b. 1830)
 * 1920 – Eduard Birnbaum, Polish-born German cantor (b. 1855)
 * 1921 – Juhani Aho, Finnish journalist and author (b. 1861)
 * 1928 – Stjepan Radić, Croatian politician (b. 1871)
 * 1930 – Launceston Elliot, Scottish wrestler and weightlifter (b. 1874)
 * 1934 – Wilbert Robinson, American baseball player, coach, and manager (b. 1863)
 * 1937 – Jimmie Guthrie, Scottish motorcycle racer (b. 1897)
 * 1940 – Johnny Dodds, American clarinet player and saxophonist (b. 1892)
 * 1944 – Erwin von Witzleben, German field marshal (b. 1881)
 * 1944  – Michael Wittmann, German commander (b. 1914)
 * 1950 – Fergus McMaster, Australian businessman, founded Qantas (b. 1879)
 * 1959 – Albert Namatjira, Australian painter (b. 1902)
 * 1965 – Shirley Jackson, American novelist and short story writer (b. 1916)
 * 1969 – Otmar Freiherr von Verschuer, German biologist and eugenicist (b. 1896)
 * 1971 – Freddie Spencer Chapman, English lieutenant (b. 1907)
 * 1973 – Vilhelm Moberg, Swedish historian and author (b. 1898)
 * 1974 – Elisabeth Abegg, German anti-Nazi resistance fighter (b. 1882)
 * 1975 – Cannonball Adderley, American saxophonist (b. 1928)
 * 1979 – Nicholas Monsarrat, English lieutenant and author (b. 1910)
 * 1980 – Paul Triquet, Canadian general, Victoria Cross recipient (b. 1910)
 * 1981 – Thomas McElwee, Irish republican, PIRA volunteer and Hunger Striker (b. 1957)
 * 1982 – Eric Brandon, English racing driver and businessman (b. 1920)
 * 1984 – Richard Deacon, American actor (b. 1921)
 * 1984  – Ellen Raskin, American author and illustrator (b. 1928)
 * 1985 – Louise Brooks, American actress (b. 1906)
 * 1987 – Danilo Blanuša, Croatian mathematician and physicist (b. 1903)
 * 1988 – Félix Leclerc, Canadian singer-songwriter and guitarist (b. 1914)
 * 1988  – Alan Napier, English actor (b. 1903)
 * 1991 – James Irwin, American colonel, pilot, and astronaut (b. 1930)
 * 1992 – Abu al-Qasim al-Khoei, Iranian religious leader and scholar (b. 1899)
 * 1996 – Nevill Francis Mott, English physicist and academic, Nobel Prize laureate (b. 1905)
 * 1996  – Jüri Randviir, Estonian chess player and journalist (b. 1927)
 * 1998 – Mahmoud Saremi, Iranian journalist (b. 1968)
 * 2003 – Dirk Hoogendam, Dutch-German SS officer (b. 1922)
 * 2003  – Falaba Issa Traoré, Malian director and playwright (b. 1930)
 * 2004 – Leon Golub, American painter and academic (b. 1922)
 * 2004  – Fay Wray, Canadian-American actress (b. 1907)
 * 2005 – Barbara Bel Geddes, American actress (b. 1922)
 * 2005  – Ahmed Deedat, South African missionary and author (b. 1918)
 * 2005  – John H. Johnson, American publisher, founded the Johnson Publishing Company (b. 1918)
 * 2005  – Gene Mauch, American baseball player and manager (b. 1925)
 * 2005  – Dean Rockwell, American commander, wrestler, and coach (b. 1912)
 * 2005  – Monica Sjöö, Swedish-English painter (b. 1938)
 * 2007 – Ma Lik, Chinese journalist and politician (b. 1952)
 * 2007  – Melville Shavelson, American director, producer, and screenwriter (b. 1917)
 * 2008 – Orville Moody, American golfer (b. 1933)
 * 2009 – Daniel Jarque, Spanish footballer (b. 1983)
 * 2010 – Patricia Neal, American actress (b. 1926)
 * 2012 – Fay Ajzenberg-Selove, German-American physicist and academic (b. 1926)
 * 2012  – Ruth Etchells, English poet and academic (b. 1931)
 * 2012  – Surya Lesmana, Indonesian footballer and manager (b. 1944)
 * 2012  – Kurt Maetzig, German director and screenwriter (b. 1911)
 * 2013 – Karen Black, American actress (b. 1939)
 * 2013  – Johannes Bluyssen, Dutch bishop (b. 1926)
 * 2013  – Fernando Castro Pacheco, Mexican painter, engraver, and illustrator (b. 1918)
 * 2013  – Igor Kurnosov, Russian chess player (b. 1985)
 * 2013  – Regina Resnik, American soprano and actress (b. 1922)
 * 2014 – Menahem Golan, Israeli director and producer (b. 1929)
 * 2014  – Charles Keating, English-American actor (b. 1941)
 * 2014  – Leonardo Legaspi, Filipino archbishop (b. 1935)
 * 2014  – Peter Sculthorpe, Australian composer and conductor (b. 1929)
 * 2014  – Red Wilson, American football and baseball player (b. 1929)
 * 2015 – Sean Price, American rapper (b. 1972)
 * 2015  – Gus Mortson, Canadian ice hockey player and coach (b. 1925)
 * 2017 – Glen Campbell, American singer-songwriter, guitarist, and actor (b. 1936)
 * 2018 – Nicholas Bett, Kenyan track and field athlete (b. 1990)
 * 2020 – Gabriel Ochoa Uribe, Colombian football player and manager (b. 1929)
 * 2020  – Alfredo Lim, former Philippine senator and Mayor of Manila (b. 1929)
 * 2021 – Bill Davis, Canadian politician, 18th premier of Ontario (b. 1929)
 * 2022 – Olivia Newton-John, English-Australian singer-songwriter and actress (b. 1948)
 * 2023 – Rodriguez, American singer and songwriter (b. 1942)

Holidays and observances

 * Ceasefire Day (end of Iran–Iraq War) (Iraqi Kurdistan)
 * Christian Feast Day:
 * Altmann of Passau
 * Cyriacus
 * Dominic de Guzmán, founder of the Dominican Order.
 * Four Crowned Martyrs
 * Largus
 * Mary MacKillop
 * Saint Smaragdus (and companions)
 * Severus of Vienne
 * August 8 (Eastern Orthodox liturgics)
 * Father's Day or Bā bā Day (爸爸節), Bā Bā is Mandarin for "father" and "8-8", or August 8. (Mongolia, Taiwan)
 * Happiness Happens Day
 * International Cat Day
 * Namesday of the Queen (Sweden)
 * Nane Nane Day (Tanzania)
 * Signal Troops Day (Ukraine)

title: August 8


text:
April 16

Pre-1600

 * 1457 BC – Battle of Megido - the first battle to have been recorded in what is accepted as relatively reliable detail.
 * 69 – Defeated by Vitellius' troops at Bedriacum, Roman emperor Otho commits suicide.
 * 73 – Masada, a Jewish fortress, falls to the Romans after several months of siege, ending the First Jewish–Roman War.
 * 1346 – Stefan Dušan, "the Mighty", is crowned Emperor of the Serbs at Skopje, his empire occupying much of the Balkans.
 * 1520 – The Revolt of the Comuneros begins in Spain against the rule of Charles V.
 * 1582 – Spanish conquistador Hernando de Lerma founds the settlement of Salta, Argentina.

1601–1900

 * 1746 – The Battle of Culloden is fought between the French-supported Jacobites and the British Hanoverian forces commanded by William Augustus, Duke of Cumberland, in Scotland.
 * 1780 – Franz Friedrich Wilhelm von Fürstenberg founds the University of Münster.
 * 1799 – French Revolutionary Wars: The Battle of Mount Tabor: Napoleon drives Ottoman Turks across the River Jordan near Acre.
 * 1818 – The United States Senate ratifies the Rush–Bagot Treaty, limiting naval armaments on the Great Lakes and Lake Champlain.
 * 1838  – The French Army captures Veracruz in the Pastry War.
 * 1847 – Shooting of a Māori by an English sailor results in the opening of the Wanganui Campaign of the New Zealand Wars.
 * 1853 – The Great Indian Peninsula Railway opens the first passenger rail in India, from Bori Bunder to Thane.
 * 1858 – The Wernerian Natural History Society, a former Scottish learned society, is dissolved.
 * 1862 – American Civil War: Battle at Lee's Mills in Virginia.
 * 1862  – American Civil War: The District of Columbia Compensated Emancipation Act, a bill ending slavery in the District of Columbia, becomes law.
 * 1863 – American Civil War: During the Vicksburg Campaign, gunboats commanded by acting Rear Admiral David Dixon Porter run downriver past Confederate artillery batteries at Vicksburg.
 * 1878 – The Senate of the Grand Duchy of Finland issues a declaration establishing a city of Kotka on the southern part islands from the old Kymi parish.
 * 1881 – In Dodge City, Kansas, Bat Masterson fights his last gun battle.

1901–present

 * 1908 – Natural Bridges National Monument is established in Utah.
 * 1910 – The oldest existing indoor ice hockey arena still used for the sport in the 21st century, Boston Arena, opens for the first time.
 * 1912 – Harriet Quimby becomes the first woman to fly an airplane across the English Channel.
 * 1917 – Russian Revolution: Vladimir Lenin returns to Petrograd, Russia, from exile in Switzerland.
 * 1919 – Mohandas Gandhi organizes a day of "prayer and fasting" in response to the killing of Indian protesters in the Jallianwala Bagh massacre by the British colonial troops three days earlier.
 * 1919  – Polish–Lithuanian War: The Polish Army launches the Vilna offensive to capture Vilnius in modern Lithuania.
 * 1922 – The Treaty of Rapallo, pursuant to which Germany and the Soviet Union re-establish diplomatic relations, is signed.
 * 1925 – During the Communist St Nedelya Church assault in Sofia, Bulgaria, 150 are killed and 500 are wounded.
 * 1941 – World War II: The Italian-German Tarigo convoy is attacked and destroyed by British ships.
 * 1941  – World War II: The Nazi-affiliated Ustaše is put in charge of the Independent State of Croatia by the Axis powers after Operation 25 is effected.
 * 1942 – King George VI awarded the George Cross to the people of Malta in appreciation of their heroism.
 * 1943 – Albert Hofmann accidentally discovers the hallucinogenic effects of the research drug LSD. He intentionally takes the drug three days later on April 19.
 * 1944 – World War II: Allied forces start bombing Belgrade, killing about 1,100 people. This bombing fell on the Orthodox Christian Easter.
 * 1945 – World War II: The Red Army begins the final assault on German forces around Berlin, with nearly one million troops fighting in the Battle of the Seelow Heights.
 * 1945  – The United States Army liberates Nazi Sonderlager (high security) prisoner-of-war camp Oflag IV-C (better known as Colditz).
 * 1945  – More than 7,000 die when the German transport ship Goya is sunk by a Soviet submarine.
 * 1947 – An explosion on board a freighter in port causes the city of Texas City, Texas, United States, to catch fire, killing almost 600 people.
 * 1947  – Bernard Baruch first applies the term "Cold War" to describe the relationship between the United States and the Soviet Union.
 * 1948 – The Organization of European Economic Co-operation is formed.
 * 1961 – In a nationally broadcast speech, Cuban leader Fidel Castro declares that he is a Marxist–Leninist and that Cuba is going to adopt Communism.
 * 1963 – U.S. civil rights campaigner Dr. Martin Luther King Jr. writes his open letter from Birmingham Jail, sometimes known as "The Negro Is Your Brother", while incarcerated in Birmingham, Alabama, for protesting against segregation.
 * 1972 – Apollo program: The launch of Apollo 16 from Cape Canaveral, Florida.
 * 2001 – India and Bangladesh begin a five-day border conflict, but are unable to resolve the disputes about their border.
 * 2003 – The Treaty of Accession is signed in Athens admitting ten new member states to the European Union.
 * 2007 – Virginia Tech shooting: Seung-Hui Cho guns down 32 people and injures 17 before committing suicide.
 * 2008 – The U.S. Supreme Court rules in the Baze v. Rees decision that execution by lethal injection does not violate the Eighth Amendment ban against cruel and unusual punishment.
 * 2012 – The trial for Anders Behring Breivik, the perpetrator of the 2011 Norway attacks, begins in Oslo, Norway.
 * 2012  – The Pulitzer Prize winners were announced, it was the first time since 1977 that no book won the Fiction Prize.
 * 2013 – A 7.8-magnitude earthquake strikes Sistan and Baluchestan Province, Iran, killing at least 35 people and injuring 117 others.
 * 2013  – The 2013 Baga massacre is started when Boko Haram militants engage government soldiers in Baga.
 * 2014 – The South Korean ferry MV Sewol capsizes and sinks near Jindo Island, killing 304 passengers and crew and leading to widespread criticism of the South Korean government, media, and shipping authorities.
 * 2016 – Ecuador's worst earthquake in nearly 40 years kills 676 and injures more than 230,000.
 * 2018 – The New York Times and the New Yorker win the Pulitzer Prize for Public Service for breaking news of the Harvey Weinstein sexual abuse scandal.
 * 2024 - The historic Børsen in Copenhagen, Denmark, is severely damaged by a fire.

Pre-1600

 * 1488 – Jungjong of Joseon (d. 1544)
 * 1495 – Petrus Apianus, German mathematician and astronomer (d. 1557)
 * 1516 – Tabinshwehti, Burmese king (d. 1550)
 * 1569 – John Davies, English poet and lawyer (d. 1626)

1601–1900

 * 1635 – Frans van Mieris the Elder, Dutch painter (d. 1681)
 * 1646 – Jules Hardouin-Mansart, French architect (probable; d. 1708)
 * 1660 – Hans Sloane, Irish-English physician and academic (d. 1753)
 * 1661 – Charles Montagu, 1st Earl of Halifax, English poet and politician, First Lord of the Treasury (d. 1715)
 * 1682 – John Hadley, English mathematician, invented the octant (d. 1744)
 * 1697 – Johann Gottlieb Görner, German organist and composer (d. 1778)
 * 1728 – Joseph Black, French-Scottish physician and chemist (d. 1799)
 * 1730 – Henry Clinton, English general and politician (d. 1795)
 * 1755 – Louise Élisabeth Vigée Le Brun, French painter (d. 1842)
 * 1786 – John Franklin, English admiral and politician, fourth Lieutenant Governor of Van Diemen's Land (d. 1847)
 * 1800 – George Bingham, 3rd Earl of Lucan, English field marshal and politician (d. 1888)
 * 1808 – Caleb Blood Smith, American journalist, lawyer, and politician, sixth United States Secretary of the Interior (d. 1864)
 * 1821 – Ford Madox Brown, French-English soldier and painter (d. 1893)
 * 1823 – Gotthold Eisenstein, German mathematician and academic (d. 1852)
 * 1826 – Sir James Corry, 1st Baronet, British politician (d. 1891)
 * 1827 – Octave Crémazie, Canadian poet and bookseller (d. 1879)
 * 1839 – Antonio Starabba, Marchese di Rudinì, Italian politician, 12th Prime Minister of Italy (d. 1908)
 * 1834 – Charles Lennox Richardson, English merchant (d. 1862)
 * 1844 – Anatole France, French journalist, novelist, and poet, Nobel Prize laureate (d. 1924)
 * 1847 – Hans Auer, Swiss-Austrian architect, designed the Federal Palace of Switzerland (d. 1906)
 * 1848 – Kandukuri Veeresalingam, Indian author and activist (d. 1919)
 * 1851 – Ponnambalam Ramanathan, Sri Lankan lawyer and politician, third Solicitor General of Sri Lanka (d. 1930)
 * 1864 – Rose Talbot Bullard, American medical doctor and professor (d. 1915)
 * 1865 – Harry Chauvel, Australian general (d. 1945)
 * 1866 – José de Diego, Puerto Rican journalist, lawyer, and politician (d. 1918)
 * 1867 – Wilbur Wright, American inventor (d. 1912)
 * 1871 – John Millington Synge, Irish author, poet, and playwright (d. 1909)
 * 1874 – Jōtarō Watanabe, Japanese general (d. 1936)
 * 1878 – R. E. Foster, English cricketer and footballer (d. 1914)
 * 1882 – Seth Bingham, American organist and composer (d. 1972)
 * 1884 – Ronald Barnes, 3rd Baron Gorell, English cricketer, journalist, and politician (d. 1963)
 * 1885 – Leó Weiner, Hungarian composer and educator (d. 1960)
 * 1886 – Michalis Dorizas, Greek-American football player and javelin thrower (d. 1957)
 * 1886  – Ernst Thälmann, German politician (d. 1944)
 * 1888 – Billy Minter, English footballer and manager (d. 1940)
 * 1889 – Charlie Chaplin, English actor, director, producer, screenwriter, and composer (d. 1977)
 * 1890 – Fred Root, English cricketer and umpire (d. 1954)
 * 1890  – Gertrude Chandler Warner, American author and educator (d. 1979)
 * 1891 – Dorothy P. Lathrop, American author and illustrator (d. 1980)
 * 1892 – Dora Richter, German transgender woman and the first known person to undergo complete male-to-female gender-affirming surgery (d. unknown)
 * 1892 – Howard Mumford Jones, American author, critic, and academic (d. 1980)
 * 1893 – Germaine Guèvremont, Canadian journalist and author (d. 1968)
 * 1893  – John Norton, American hurdler (d. 1979)
 * 1895 – Ove Arup, English-Danish engineer and businessman, founded Arup (d. 1988)
 * 1896 – Robert Henry Best, American journalist (d. 1952)
 * 1896  – Árpád Weisz, Hungarian footballer (d. 1944)
 * 1899 – Osman Achmatowicz, Polish chemist and academic (d. 1988)
 * 1900 – Polly Adler, Russian-American madam and author (d. 1962)

1901–present

 * 1903 – Paul Waner, American baseball player and manager (d. 1965)
 * 1904 – Fifi D'Orsay, Canadian-American vaudevillian, actress, and singer (d. 1983)
 * 1905 – Frits Philips, Dutch businessman (d. 2005)
 * 1907 – Joseph-Armand Bombardier, Canadian inventor and businessman, founded Bombardier Inc. (d. 1964)
 * 1907  – August Eigruber, Austrian-German politician (d. 1947)
 * 1908 – Ellis Marsalis, Sr., American businessman and activist (d. 2004)
 * 1908  – Ray Ventura, French jazz bandleader (d. 1979)
 * 1910 – Berton Roueché, American journalist and author (d. 1994)
 * 1911 – Guy Burgess, English-Russian spy (d. 1963)
 * 1914 – John Hodiak, American actor (d. 1955)
 * 1915  – Robert Speck, Canadian politician, first Mayor of Mississauga (d. 1972)
 * 1916 – Behçet Necatigil, Turkish author, poet, and translator (d. 1979)
 * 1917 – Victoria Eugenia Fernández de Córdoba, 18th Duchess of Medinaceli (d. 2013)
 * 1917  – Barry Nelson, American actor (d. 2007)
 * 1918 – Hsuan Hua, Chinese-American monk and author (d. 1995)
 * 1918  – Spike Milligan, Irish actor, comedian, and writer (d. 2002)
 * 1919 – Merce Cunningham, American dancer and choreographer (d. 2009)
 * 1919  – Nilla Pizzi, Italian singer (d. 2011)
 * 1919  – Pedro Ramírez Vázquez, Mexican architect (d. 2013)
 * 1920 – Ananda Dassanayake, Sri Lankan politician (d. 2012)
 * 1920  – Prince Georg of Denmark (d. 1986)
 * 1921 – Wolfgang Leonhard, German historian and author (d. 2014)
 * 1921  – Peter Ustinov, English actor, director, producer, and screenwriter (d. 2004)
 * 1922 – Kingsley Amis, English novelist, poet, and critic (d. 1995)
 * 1922  – Lawrence N. Guarino, American colonel (d. 2014)
 * 1922  – Leo Tindemans, Belgian politician, 43rd Prime Minister of Belgium (d. 2014)
 * 1923 – Warren Barker, American composer (d. 2006)
 * 1923  – Arch A. Moore Jr., American sergeant, lawyer, and politician, 28th Governor of West Virginia (d. 2015)
 * 1924 – John Harvey-Jones, English academic and businessman (d. 2008)
 * 1924  – Henry Mancini, American composer and conductor (d. 1994)
 * 1924  – Madanjeet Singh, Indian diplomat, author, and philanthropist (d. 2013)
 * 1926 – Pierre Fabre, French pharmacist, founded Laboratoires Pierre Fabre (d. 2013)
 * 1927 – Edie Adams, American actress and singer (d. 2008)
 * 1927  – Pope Benedict XVI  (d. 2022)
 * 1927  – Rolf Schult, German actor (d. 2013)
 * 1928 – Night Train Lane, American football player (d. 2002)
 * 1929 – Roy Hamilton, American singer (d. 1969)
 * 1929  – Ralph Slatyer, Australian biologist and ecologist (d. 2012)
 * 1929  – Ed Townsend, American singer-songwriter and producer (d. 2003)
 * 1930 – Doug Beasy, Australian footballer and educator (d. 2013)
 * 1930  – Herbie Mann, American flute player and composer (d. 2003)
 * 1931 – Julian Carroll, American politician, 54th Governor of Kentucky (d. 2023)
 * 1932 – Maury Meyers, American lawyer and politician (d. 2014)
 * 1933 – Marcos Alonso Imaz, Spanish footballer (d. 2012)
 * 1933  – Joan Bakewell, English journalist and author
 * 1933  – Perry Botkin Jr., American composer, arranger and musician (d. 2021)
 * 1933  – Vera Krepkina, Russian long jumper (d. 2023)
 * 1933  – Ike Pappas, American journalist and actor (d. 2008)
 * 1934 – Vince Hill, English singer-songwriter (d. 2023)
 * 1934  – Robert Stigwood, Australian producer and manager (d. 2016)
 * 1934  – Barrie Unsworth, Australian politician, 36th Premier of New South Wales
 * 1934  – Vicar, Chilean cartoonist (d. 2012)
 * 1935 – Marcel Carrière, Canadian director and screenwriter
 * 1935  – Sarah Kirsch, German poet and author (d. 2013)
 * 1935  – Lennart Risberg, Swedish boxer (d. 2013)
 * 1935  – Dominique Venner, French journalist and historian (d. 2013)
 * 1935  – Bobby Vinton, American singer
 * 1936 – Vadim Kuzmin, Russian physicist and academic (d. 2015)
 * 1937 – Gert Potgieter, South African hurdler and coach
 * 1937  – George Steele, American wrestler and actor (d. 2017)
 * 1938 – Rich Rollins, American baseball player
 * 1938  – Gordon Wilson, Scottish lawyer and politician (d. 2017)
 * 1939 – John Amabile, American football player and coach (d. 2012)
 * 1939  – Dusty Springfield, English singer and record producer (d. 1999)
 * 1940 – Benoît Bouchard, Canadian academic and politician, 18th Canadian Minister of Transport
 * 1940  – David Holford, Barbadian cricketer (d. 2022)
 * 1940  – Queen Margrethe II of Denmark
 * 1940  – Joan Snyder, American painter
 * 1940  – Thomas Stonor, 7th Baron Camoys, English banker and politician, Lord Chamberlain of the United Kingdom (d. 2023)
 * 1941 – Allan Segal, American director and producer (d. 2012)
 * 1942 – Jim Lonborg, American baseball pitcher
 * 1942  – Sir Frank Williams, English businessman, founded the Williams F1 Racing Team (d. 2021)
 * 1943 – Petro Tyschtschenko, Austrian-German businessman
 * 1943  – John Watkins, Australian cricketer
 * 1945 – Tom Allen, American lawyer and politician
 * 1946 – Margot Adler, American journalist and author (d. 2014)
 * 1946  – Ernst Bakker, Dutch politician (d. 2014)
 * 1946  – Johnnie Lewis, Liberian lawyer and politician, 18th Chief Justice of Liberia (d. 2015)
 * 1946  – R. Carlos Nakai, American flute player
 * 1947 – Kareem Abdul-Jabbar, American basketball player and coach
 * 1947  – Gerry Rafferty, Scottish singer-songwriter (d. 2011)
 * 1948 – Reg Alcock, Canadian businessman and politician, 17th Canadian President of the Treasury Board (d. 2011)
 * 1950 – David Graf, American actor (d. 2001)
 * 1950  – Colleen Hewett, Australian singer and actress
 * 1951 – Ioan Mihai Cochinescu, Romanian author and photographer
 * 1952 – Michel Blanc, French actor and director
 * 1952  – Esther Roth-Shahamorov, Israeli sprinter and hurdler
 * 1953 – Peter Garrett, Australian singer-songwriter and politician
 * 1954 – Ellen Barkin, American actress
 * 1954  – John Bowe, Australian racing driver
 * 1954  – Mike Zuke, Canadian ice hockey player
 * 1955 – Henri, Grand Duke of Luxembourg
 * 1956 – David M. Brown, American captain, pilot, and astronaut (d. 2003)
 * 1956  – T Lavitz, American keyboard player, composer, and producer (d. 2010)
 * 1956  – Lise-Marie Morerod, Swiss skier
 * 1957 – Patricia De Martelaere, Belgian philosopher, author, and academic (d. 2009)
 * 1958 – Tim Flach, English photographer and director
 * 1958  – Ulf Wakenius, Swedish guitarist
 * 1959 – Alison Ramsay, English-Scottish field hockey player and lawyer
 * 1960 – Wahab Akbar, Filipino politician (d. 2007)
 * 1960  – Rafael Benítez, Spanish footballer and manager
 * 1960  – Pierre Littbarski, German footballer and manager
 * 1961 – Jarbom Gamlin, Indian lawyer and politician, seventh Chief Minister of Arunachal Pradesh (d. 2014)
 * 1962 – Anna Dello Russo, Italian journalist
 * 1963 – Saleem Malik, Pakistani cricketer
 * 1963  – Jimmy Osmond, American singer
 * 1964 – Esbjörn Svensson, Swedish pianist (d. 2008)
 * 1965 – Yves-François Blanchet, Canadian politician
 * 1965  – Jon Cryer, American actor, director, producer, and screenwriter
 * 1965  – Martin Lawrence, American actor, director, producer, and screenwriter
 * 1966 – Jarle Vespestad, Norwegian drummer
 * 1968 – Vickie Guerrero, American wrestler and manager
 * 1968  – Rüdiger Stenzel, German runner
 * 1969 – Patrik Järbyn, Swedish skier
 * 1969  – Fernando Viña, American baseball player and sportscaster
 * 1970 – Dero Goi, German singer-songwriter and drummer
 * 1970  – Margreth Olin, Norwegian filmmaker
 * 1970  – Walt Williams, American basketball player
 * 1971 – Cameron Blades, Australian rugby player
 * 1971  – Selena, American singer-songwriter, actress, and fashion designer  (d. 1995)
 * 1971  – Seigo Yamamoto, Japanese racing driver
 * 1971  – Natasha Zvereva, Belarusian tennis player
 * 1972 – Conchita Martínez, Spanish-American tennis player
 * 1972  – Tracy K. Smith, American poet and educator
 * 1973 – Akon, Senegalese-American singer, rapper and songwriter
 * 1973  – Charlotta Sörenstam, Swedish golfer
 * 1973  – Teddy Cobeña, Spanish-Ecuadorian expressionist and representational sculptor
 * 1976 – Lukas Haas, American actor and musician
 * 1976  – Kelli O'Hara, American actress and singer
 * 1977 – Freddie Ljungberg, Swedish footballer
 * 1979 – Christijan Albers, Dutch racing driver
 * 1979  – Lars Börgeling, German pole vaulter
 * 1979  – Daniel Browne, New Zealand rugby player
 * 1981 – Anestis Agritis, Greek footballer
 * 1981  – Maya Dunietz, Israeli singer-songwriter and pianist
 * 1981  – Matthieu Proulx, Canadian football player
 * 1982 – Gina Carano, American mixed martial artist and actress
 * 1982  – Boris Diaw, French basketball player
 * 1982  – Jonathan Vilma, American football player
 * 1983 – Marié Digby, American singer-songwriter, guitarist, and actress
 * 1983  – Cat Osterman, American softball player
 * 1984 – Teddy Blass, American composer and producer
 * 1984  – Claire Foy, English actress
 * 1984  – Tucker Fredricks, American speed skater
 * 1984  – Paweł Kieszek, Polish footballer
 * 1984  – Kerron Stewart, Jamaican sprinter
 * 1985 – Luol Deng, Sudanese-English basketball player
 * 1985  – Nate Diaz, American mixed martial artist
 * 1985  – Brendon Leonard, New Zealand rugby player
 * 1985  – Taye Taiwo, Nigerian footballer
 * 1986 – Shinji Okazaki, Japanese footballer
 * 1986  – Peter Regin, Danish ice hockey player
 * 1986  – Epke Zonderland, Dutch gymnast
 * 1987 – Cenk Akyol, Turkish basketball player
 * 1987  – Aaron Lennon, English international footballer
 * 1988 – Kyle Okposo, American ice hockey player
 * 1990 – Reggie Jackson, American basketball player
 * 1990  – Vangelis Mantzaris, Greek basketball player
 * 1990  – Tony McQuay, American sprinter
 * 1991 – Nolan Arenado, American baseball player
 * 1991  – Kim Kyung-jung, South Korean footballer
 * 1993 – Chance the Rapper, American rapper
 * 1993  – Mirai Nagasu, Japanese-American figure skater
 * 1996 – Anya Taylor-Joy, Argentine-British actress
 * 1996  – Taylor Townsend, American tennis player
 * 2002 – Sadie Sink, American actress

Pre-1600

 * AD 69 – Otho, Roman emperor (b. AD 32)
 * 665 – Fructuosus of Braga, French archbishop and saint
 * 1090 – Sikelgaita, duchess of Apulia (b. c. 1040)
 * 1113 – Sviatopolk II of Kiev (b. 1050)
 * 1118 – Adelaide del Vasto, regent of Sicily, mother of Roger II of Sicily, queen of Baldwin I of Jerusalem
 * 1198 – Frederick I, Duke of Austria (b. 1175)
 * 1234 – Richard Marshal, 3rd Earl of Pembroke (b. 1191)
 * 1375 – John Hastings, 2nd Earl of Pembroke, English nobleman and soldier (b. 1347)
 * 1496 – Charles II, Duke of Savoy (b. 1489)
 * 1587 – Anne Seymour, Duchess of Somerset (b. 1497)

1601–1900

 * 1640 – Countess Charlotte Flandrina of Nassau (b. 1579)
 * 1645 – Tobias Hume, Scottish soldier, viol player, and composer (b. 1569)
 * 1687 – George Villiers, 2nd Duke of Buckingham, English poet and politician, Lord Lieutenant of the West Riding of Yorkshire (b. 1628)
 * 1689 – Aphra Behn, English author and playwright (b. 1640)
 * 1742 – Stefano Benedetto Pallavicino, Italian poet and translator (b. 1672)
 * 1756 – Jacques Cassini, French astronomer (b. 1677)
 * 1783 – Christian Mayer, Czech astronomer and educator (b. 1719)
 * 1788 – Georges-Louis Leclerc, Comte de Buffon, French mathematician, cosmologist, and author (b. 1707)
 * 1828 – Francisco Goya, Spanish-French painter and illustrator (b. 1746)
 * 1846 – Domenico Dragonetti, Italian bassist and composer (b. 1763)
 * 1850 – Marie Tussaud, French-English sculptor, founded the Madame Tussauds Wax Museum (b. 1761)
 * 1859 – Alexis de Tocqueville, French historian and philosopher, French Minister of Foreign Affairs (b. 1805)
 * 1879 – Bernadette Soubirous, French nun and saint (b. 1844)
 * 1888 – Zygmunt Florenty Wróblewski, Polish physicist and chemist (b. 1845)
 * 1899 – Emilio Jacinto, Filipino journalist and activist (b. 1875)

1901–present

 * 1904 – Maximilian Kronberger, German poet and author (b. 1888)
 * 1904  – Samuel Smiles, Scottish-English author (b. 1812)
 * 1914 – George William Hill, American astronomer and mathematician (b. 1838)
 * 1915 – Nelson W. Aldrich, American businessman and politician (b. 1841)
 * 1925 – Stefan Nerezov, Bulgarian general (b. 1867)
 * 1928 – Henry Birks, Canadian businessman, founded Henry Birks and Sons (b. 1840)
 * 1928  – Roman Steinberg, Estonian wrestler (b. 1900)
 * 1930 – José Carlos Mariátegui, Peruvian journalist, philosopher, and activist (b. 1894)
 * 1935 – Panait Istrati, Romanian journalist and author (b. 1884)
 * 1937 – Jay Johnson Morrow, American military engineer and politician, third Governor of the Panama Canal Zone (b. 1870)
 * 1938 – Steve Bloomer, English footballer and manager (b. 1874)
 * 1940 – Tony D'Arcy, Irish Republican died while on hunger strike (b. 1908)
 * 1941 – Josiah Stamp, 1st Baron Stamp, English economist and civil servant (b. 1880)
 * 1942 – Princess Alexandra of Saxe-Coburg and Gotha (b. 1878)
 * 1942  – Denis St. George Daly, Irish polo player (b. 1862)
 * 1946 – Arthur Chevrolet, Swiss-American race car driver and engineer (b. 1884)
 * 1947 – Rudolf Höss, German SS officer (b. 1900)
 * 1950 – Eduard Oja, Estonian composer, conductor, and critic (b. 1905)
 * 1950  – Anders Peter Nielsen, Danish target shooter (b. 1867)
 * 1955 – David Kirkwood, Scottish engineer and politician (b. 1872)
 * 1958 – Rosalind Franklin, English biophysicist and academic (b. 1920)
 * 1960 – Mihály Fekete, Hungarian actor, screenwriter and film director (b. 1884)
 * 1961 – Carl Hovland, American psychologist and academic (b. 1912)
 * 1965 – Francis Balfour, English soldier and colonial administrator (b. 1884)
 * 1965 – Sydney Chaplin, English actor, comedian, brother of Charlie Chaplin (b. 1885)
 * 1966 – Eric Lambert, Australian author (b. 1918)
 * 1968 – Fay Bainter, American actress (b. 1893)
 * 1968  – Edna Ferber, American novelist, short story writer, and playwright (b. 1885)
 * 1969 – Hem Vejakorn, Thai illustrator and painter (b. 1904)
 * 1970 – Richard Neutra, Austrian-American architect, designed the Los Angeles County Hall of Records (b. 1892)
 * 1970  – Péter Veres, Hungarian politician, Hungarian Minister of Defence (b. 1897)
 * 1972 – Yasunari Kawabata, Japanese novelist and short story writer, Nobel Prize laureate (b. 1899)
 * 1972  – Frank O'Connor, Australian public servant (b. 1894)
 * 1973 – István Kertész, Hungarian conductor and educator (b. 1929)
 * 1978 – Lucius D. Clay, American officer and military governor in occupied Germany (b. 1898)
 * 1980 – Morris Stoloff, American composer (b. 1898)
 * 1985 – Scott Brady, American actor (b. 1924)
 * 1988 – Khalil al-Wazir, Palestinian commander, founded Fatah (b. 1935)
 * 1988  – Youri Egorov, Russian pianist (b. 1954)
 * 1989 – Jocko Conlan, American baseball player and umpire (b. 1899)
 * 1989  – Kaoru Ishikawa Japanese author and educator (b. 1915)
 * 1989  – Miles Lawrence, English cricketer (b. 1940)
 * 1989 – Hakkı Yeten, Turkish footballer, manager and president (b. 1910)
 * 1991 – David Lean, English director, producer, and screenwriter (b. 1908)
 * 1992 – Neville Brand, American actor (b. 1920)
 * 1992  – Alexandru Nicolschi, Romanian spy and activist (b. 1915)
 * 1992  – Andy Russell, American singer and actor (b. 1919)
 * 1994 – Paul-Émilien Dalpé, Canadian labor unionist (b. 1919)
 * 1994  – Ralph Ellison, American novelist and critic (b. 1913)
 * 1996 – Lucille Bremer, American actress and dancer (b. 1917)
 * 1997 – Esmeralda Arboleda Cadavid, Colombian politician (b. 1921)
 * 1997  – Roland Topor, French actor, director, and painter (b. 1938)
 * 1998 – Alberto Calderón, Argentinian-American mathematician and academic (b. 1920)
 * 1998  – Fred Davis, English snooker player (b. 1913)
 * 1998  – Marie-Louise Meilleur, Canadian super-centenarian (b. 1880)
 * 1999 – Skip Spence, Canadian-American singer-songwriter and guitarist (b. 1946)
 * 2001 – Robert Osterloh, American actor (b. 1918)
 * 2001  – Michael Ritchie, American director, producer, and screenwriter (b. 1938)
 * 2001  – Alec Stock, English footballer and manager (b. 1917)
 * 2002 – Billy Ayre, English footballer and manager (b. 1952)
 * 2002  – Ruth Fertel, American businesswoman, founded Ruth's Chris Steak House (b. 1927)
 * 2002  – Robert Urich, American actor (b. 1946)
 * 2003 – Graham Jarvis, Canadian actor (b. 1930)
 * 2003  – Graham Stuart Thomas, English horticulturalist and author (b. 1909)
 * 2005 – Kay Walsh, English actress, singer, and dancer (b. 1911)
 * 2007 – Frank Bateson, New Zealand astronomer (b. 1909)
 * 2007  – Gaétan Duchesne, Canadian ice hockey player (b. 1962)
 * 2007  – Maria Lenk, Brazilian swimmer (b. 1915)
 * 2007  – Chandrabose Suthaharan, Sri Lankan journalist
 * 2008 – Edward Norton Lorenz, American mathematician and meteorologist (b. 1917)
 * 2010 – Rasim Delić, Bosnian general and convicted war criminal (b. 1949)
 * 2010  – Daryl Gates, American police officer, created the D.A.R.E. Program (b. 1926)
 * 2011 – Gerry Alexander, Jamaican cricketer and veterinarian (b. 1928)
 * 2011  – Allan Blakeney, Canadian scholar and politician, tenth Premier of Saskatchewan (b. 1925)
 * 2011  – Sol Saks, American screenwriter and producer (b. 1910)
 * 2012 – Sári Barabás, Hungarian soprano (b. 1914)
 * 2012  – Marian Biskup, Polish author and academic (b. 1922)
 * 2012  – Alan Hacker, English clarinet player and conductor (b. 1938)
 * 2012  – George Kunda, Zambian lawyer and politician, 11th Vice-President of Zambia (b. 1956)
 * 2012  – Mærsk Mc-Kinney Møller, Danish businessman (b. 1913)
 * 2012  – Carlo Petrini, Italian footballer and coach (b. 1948)
 * 2013 – Charles Bruzon, Gibraltarian politician (b. 1938)
 * 2013  – Ali Kafi, Algerian politician (b. 1928)
 * 2013  – Siegfried Ludwig, Austrian politician, 18th Governor of Lower Austria (b. 1926)
 * 2013  – Pentti Lund, Finnish-Canadian ice hockey player (b. 1925)
 * 2013  – George Beverly Shea, Canadian-American singer-songwriter (b. 1909)
 * 2013  – Pat Summerall, American football player and sportscaster (b. 1930)
 * 2013  – Pedro Ramírez Vázquez, Mexican architect, designed the Tijuana Cultural Center and National Museum of Anthropology (b. 1919)
 * 2014 – Gyude Bryant, Liberian businessman and politician (b. 1949)
 * 2014  – Aulis Rytkönen, Finnish footballer and manager (b. 1929)
 * 2014  – Ernst Florian Winter, Austrian-American historian and political scientist (b. 1923)
 * 2015 – Valery Belousov, Russian ice hockey player and coach (b. 1948)
 * 2015 – Stanislav Gross, Czech lawyer and politician, fifth Prime Minister of the Czech Republic (b. 1969)
 * 2018 – Harry Anderson, American actor and magician  (b. 1952)
 * 2021 – Andrew Peacock, Australian politician (b. 1939)
 * 2021 – Helen McCrory, British actress (b. 1968)
 * 2021 – Liam Scarlett, British choreographer (b. 1986)
 * 2021 – John Dawes, Welsh rugby union player (b. 1940)
 * 2024 – Carl Erskine, American baseball player (b. 1926)
 * 2024 – Bob Graham, American lawyer, author, and politician, 38th governor of Florida (b. 1936)

Holidays and observances

 * Christian feast day:
 * Benedict Joseph Labre
 * Bernadette Soubirous
 * Drogo
 * Engratia
 * Fructuosus of Braga
 * Isabella Gilmore (Church of England)
 * Martyrs of Zaragoza
 * Molly Brant (Konwatsijayenni) (Anglican Church of Canada, Episcopal Church)
 * Turibius of Astorga
 * April 16 (Eastern Orthodox liturgics)
 * Birthday of José de Diego (Puerto Rico, United States)
 * Birthday of Queen Margrethe II (Denmark)
 * Emancipation Day (Washington, D.C., United States)
 * Memorial Day for the Victims of the Holocaust (Hungary)
 * National Healthcare Decisions Day (United States)
 * Remembrance of Chemical Attack on Balisan and Sheikh Wasan (Iraqi Kurdistan)
 * World Voice Day

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: April 16


text:
Associative property

In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.

Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations:

$$\begin{align} (2 + 3) + 4 &= 2 + (3 + 4) = 9 \,\\ 2 \times (3 \times 4) &= (2 \times 3) \times 4 = 24. \end{align}$$

Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, it can be said that "addition and multiplication of real numbers are associative operations".

Associativity is not the same as commutativity, which addresses whether the order of two operands affects the result. For example, the order does not matter in the multiplication of real numbers, that is, $a × b = b × a$, so we say that the multiplication of real numbers is a commutative operation. However, operations such as function composition and matrix multiplication are associative, but not (generally) commutative.

Associative operations are abundant in mathematics; in fact, many algebraic structures (such as semigroups and categories) explicitly require their binary operations to be associative.

However, many important and interesting operations are non-associative; some examples include subtraction, exponentiation, and the vector cross product. In contrast to the theoretical properties of real numbers, the addition of floating point numbers in computer science is not associative, and the choice of how to associate an expression can have a significant effect on rounding error.

Definition
Formally, a binary operation $S×S×S$ on a set $S$ is called associative if it satisfies the associative law:

$S×S×S$ for all $S$, $S$, $x$ in $y$.

Here, ∗ is used to replace the symbol of the operation, which may be any symbol, and even the absence of symbol (juxtaposition) as for multiplication.

The associative law can also be expressed in functional notation thus: $∗$.

Generalized associative law
If a binary operation is associative, repeated application of the operation produces the same result regardless of how valid pairs of parentheses are inserted in the expression. This is called the generalized associative law.

The number of possible bracketings is just the Catalan number, $(x ∗ y) ∗ z = x ∗ (y ∗ z)$, for n operations on n+1 values. For instance, a product of 3 operations on 4 elements may be written (ignoring permutations of the arguments), in $(xy)z = x(yz) = xyz$ possible ways:

If the product operation is associative, the generalized associative law says that all these expressions will yield the same result. So unless the expression with omitted parentheses already has a different meaning (see below), the parentheses can be considered unnecessary and "the" product can be written unambiguously as

As the number of elements increases, the number of possible ways to insert parentheses grows quickly, but they remain unnecessary for disambiguation.

An example where this does not work is the logical biconditional $f(f(x, y), z) = f(x, f(y, z))$. It is associative; thus, $C_{n}$ is equivalent to $C_{3} = 5$, but $((ab)c)d$ most commonly means $(ab)(cd)$, which is not equivalent.

Examples
Some examples of associative operations include the following.

{{unordered list
 * 1= The concatenation of the three strings,  ,   can be computed by concatenating the first two strings (giving  ) and appending the third string , or by joining the second and third string (giving  ) and concatenating the first string  with the result. The two methods produce the same result; string concatenation is associative (but not commutative).
 * 2= In arithmetic, addition and multiplication of real numbers are associative; i.e.,

$$ \left. \begin{matrix} (x+y)+z=x+(y+z)=x+y+z\quad \\ (x\,y)z=x(y\,z)=x\,y\,z\qquad\qquad\qquad\quad\ \ \, \end{matrix} \right\} \mbox{for all }x,y,z\in\mathbb{R}. $$

Because of associativity, the grouping parentheses can be omitted without ambiguity.
 * 3= The trivial operation $(a(bc))d$ (that is, the result is the first argument, no matter what the second argument is) is associative but not commutative. Likewise, the trivial operation $a((bc)d)$ (that is, the result is the second argument, no matter what the first argument is) is associative but not commutative.
 * 4= Addition and multiplication of complex numbers and quaternions are associative. Addition of octonions is also associative, but multiplication of octonions is non-associative.
 * 5= The greatest common divisor and least common multiple functions act associatively.

$$ \left. \begin{matrix} \operatorname{gcd}(\operatorname{gcd}(x,y),z)= \operatorname{gcd}(x,\operatorname{gcd}(y,z))= \operatorname{gcd}(x,y,z)\ \quad \\ \operatorname{lcm}(\operatorname{lcm}(x,y),z)= \operatorname{lcm}(x,\operatorname{lcm}(y,z))= \operatorname{lcm}(x,y,z)\quad \end{matrix} \right\}\mbox{ for all }x,y,z\in\mathbb{Z}. $$ $$ \left. \begin{matrix} (A\cap B)\cap C=A\cap(B\cap C)=A\cap B\cap C\quad \\ (A\cup B)\cup C=A\cup(B\cup C)=A\cup B\cup C\quad \end{matrix} \right\}\mbox{for all sets }A,B,C. $$
 * 6= Taking the intersection or the union of sets:
 * 7= If $z$ is some set and $S$ denotes the set of all functions from $x$ to $y$, then the operation of function composition on $z$ is associative:$$(f\circ g)\circ h=f\circ(g\circ h)=f\circ g\circ h\qquad\mbox{for all }f,g,h\in S.$$
 * 8= Slightly more generally, given four sets $S$, $a$, $b$ and $c$, with $a(b(cd))$, $abcd$, and $↔$, then

$$(f\circ g)\circ h=f\circ(g\circ h)=f\circ g\circ h$$

as before. In short, composition of maps is always associative.
 * 9= In category theory, composition of morphisms is associative by definition. Associativity of functors and natural transformations follows from associativity of morphisms.
 * 10= Consider a set with three elements, $d$, $e$, and $M$. The following operation:

is associative. Thus, for example, $A ↔ (B ↔ C)$. This operation is not commutative.
 * 11= Because matrices represent linear functions, and matrix multiplication represents function composition, one can immediately conclude that matrix multiplication is associative.
 * 12= For real numbers (and for any totally ordered set), the minimum and maximum operation is associative: $$\max(a, \max(b, c)) = \max(\max(a, b), c) \quad \text{ and } \quad \min(a, \min(b, c)) = \min(\min(a, b), c).$$

}}

Rule of replacement
In standard truth-functional propositional logic, association, or associativity are two valid rules of replacement. The rules allow one to move parentheses in logical expressions in logical proofs. The rules (using logical connectives notation) are:

$$(P \lor (Q \lor R)) \Leftrightarrow ((P \lor Q) \lor R)$$

and

$$(P \land (Q \land R)) \Leftrightarrow ((P \land Q) \land R),$$

where "$$\Leftrightarrow$$" is a metalogical symbol representing "can be replaced in a proof with".

Truth functional connectives
Associativity is a property of some logical connectives of truth-functional propositional logic. The following logical equivalences demonstrate that associativity is a property of particular connectives. The following (and their converses, since $(A ↔ B) ↔ C$ is commutative) are truth-functional tautologies.

 * Associativity of disjunction
 * $$((P \lor Q) \lor R) \leftrightarrow (P \lor (Q \lor R))$$

 * Associativity of conjunction
 * $$((P \land Q) \land R) \leftrightarrow (P \land (Q \land R))$$

 * Associativity of equivalence
 * $$((P \leftrightarrow Q) \leftrightarrow R) \leftrightarrow (P \leftrightarrow (Q \leftrightarrow R))$$

Joint denial is an example of a truth functional connective that is not associative.

Non-associative operation
A binary operation $$*$$ on a set S that does not satisfy the associative law is called non-associative. Symbolically,

$$(x*y)*z\ne x*(y*z)\qquad\mbox{for some }x,y,z\in S.$$

For such an operation the order of evaluation does matter. For example:
 * Subtraction

(5-3)-2 \, \ne \, 5-(3-2) $$
 * Division

(4/2)/2 \, \ne \, 4/(2/2) $$
 * Exponentiation

2^{(1^2)} \, \ne \, (2^1)^2 $$
 * Vector cross product
 * $$\begin{align}

\mathbf{i} \times (\mathbf{i} \times \mathbf{j}) &= \mathbf{i} \times \mathbf{k} = -\mathbf{j} \\ (\mathbf{i} \times \mathbf{i}) \times \mathbf{j} &= \mathbf{0} \times \mathbf{j} = \mathbf{0} \end{align}$$

Also although addition is associative for finite sums, it is not associative inside infinite sums (series). For example, $$ (1+-1)+(1+-1)+(1+-1)+(1+-1)+(1+-1)+(1+-1)+\dots = 0 $$ whereas $$ 1+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+\dots =  1. $$

Some non-associative operations are fundamental in mathematics. They appear often as the multiplication in structures called non-associative algebras, which have also an addition and a scalar multiplication. Examples are the octonions and Lie algebras. In Lie algebras, the multiplication satisfies Jacobi identity instead of the associative law; this allows abstracting the algebraic nature of infinitesimal transformations.

Other examples are quasigroup, quasifield, non-associative ring, and commutative non-associative magmas.

Nonassociativity of floating point calculation
In mathematics, addition and multiplication of real numbers is associative. By contrast, in computer science, the addition and multiplication of floating point numbers is not associative, as different rounding errors may be introduced when dissimilar-sized values are joined together in a different order.

To illustrate this, consider a floating point representation with a 4-bit significand:

(1.0002×20 + 1.0002×20) + 1.0002×24 = 1.0002×2undefined + 1.0002×24 = 1.002×24

1.0002×20 + (1.0002×20 + 1.0002×24) = 1.0002×2undefined + 1.0002×24 = 1.002×24

Even though most computers compute with 24 or 53 bits of significand, this is still an important source of rounding error, and approaches such as the Kahan summation algorithm are ways to minimise the errors. It can be especially problematic in parallel computing.

Notation for non-associative operations
In general, parentheses must be used to indicate the order of evaluation if a non-associative operation appears more than once in an expression (unless the notation specifies the order in another way, like $$\dfrac{2}{3/4}$$). However, mathematicians agree on a particular order of evaluation for several common non-associative operations. This is simply a notational convention to avoid parentheses.

A left-associative operation is a non-associative operation that is conventionally evaluated from left to right, i.e.,

$$ \left. \begin{array}{l} a*b*c=(a*b)*c \\ a*b*c*d=((a*b)*c)*d \\ a*b*c*d*e=(((a*b)*c)*d)*e\quad \\ \mbox{etc.} \end{array} \right\} \mbox{for all }a,b,c,d,e\in S $$

while a right-associative operation is conventionally evaluated from right to left:

$$ \left. \begin{array}{l} x*y*z=x*(y*z) \\ w*x*y*z=w*(x*(y*z))\quad \\ v*w*x*y*z=v*(w*(x*(y*z)))\quad\\ \mbox{etc.} \end{array} \right\} \mbox{for all }z,y,x,w,v\in S $$

Both left-associative and right-associative operations occur. Left-associative operations include the following:
 * Subtraction and division of real numbers
 * $$x-y-z=(x-y)-z$$
 * $$x/y/z=(x/y)/z$$

 * Function application
 * $$(f \, x \, y) = ((f \, x) \, y)$$

This notation can be motivated by the currying isomorphism, which enables partial application.

Right-associative operations include the following:
 * Exponentiation of real numbers in superscript notation
 * $$x^{y^z}=x^{(y^z)}$$ Exponentiation is commonly used with brackets or right-associatively because a repeated left-associative exponentiation operation is of little use. Repeated powers would mostly be rewritten with multiplication:
 * $$(x^y)^z=x^{(yz)}$$ Formatted correctly, the superscript inherently behaves as a set of parentheses; e.g. in the expression $$2^{x+3}$$ the addition is performed before the exponentiation despite there being no explicit parentheses $$2^{(x+3)}$$ wrapped around it. Thus given an expression such as $$x^{y^z}$$, the full exponent $$y^z$$ of the base $$x$$ is evaluated first. However, in some contexts, especially in handwriting, the difference between $${x^y}^z=(x^y)^z$$, $$x^{yz}=x^{(yz)}$$ and $$x^{y^z}=x^{(y^z)}$$ can be hard to see. In such a case, right-associativity is usually implied.

 * Function definition
 * $$\mathbb{Z} \rarr \mathbb{Z} \rarr \mathbb{Z} = \mathbb{Z} \rarr (\mathbb{Z} \rarr \mathbb{Z})$$
 * $$x \mapsto y \mapsto x - y = x \mapsto (y \mapsto x - y)$$ Using right-associative notation for these operations can be motivated by the Curry–Howard correspondence and by the currying isomorphism.

Non-associative operations for which no conventional evaluation order is defined include the following.
 * Exponentiation of real numbers in infix notation
 * $$(x^\wedge y)^\wedge z\ne x^\wedge(y^\wedge z)$$

 * Knuth's up-arrow operators
 * $$ a \uparrow \uparrow (b \uparrow \uparrow c) \ne (a \uparrow \uparrow b) \uparrow \uparrow c$$
 * $$ a \uparrow \uparrow \uparrow (b \uparrow \uparrow \uparrow c) \ne (a \uparrow \uparrow \uparrow b) \uparrow \uparrow \uparrow c$$

 * Taking the cross product of three vectors
 * $$\vec a \times (\vec b \times \vec c) \neq (\vec a \times \vec b ) \times \vec c \qquad \mbox{ for some } \vec a,\vec b,\vec c \in \mathbb{R}^3$$

 * Taking the pairwise average of real numbers
 * $${(x+y)/2+z\over2}\ne{x+(y+z)/2\over2} \qquad \mbox{for all }x,y,z\in\mathbb{R} \mbox{ with }x\ne z.$$

 * Taking the relative complement of sets
 * $$(A\backslash B)\backslash C \neq A\backslash (B\backslash C)$$. (Compare material nonimplication in logic.)

History
William Rowan Hamilton seems to have coined the term "associative property" around 1844, a time when he was contemplating the non-associative algebra of the octonions he had learned about from John T. Graves.

title: Associative property


text:
The Apache Software Foundation

The Apache Software Foundation (ASF) is an American nonprofit corporation (classified as a 501(c)(3) organization in the United States) to support a number of open-source software projects. The ASF was formed from a group of developers of the Apache HTTP Server, and incorporated on March 25, 1999. it includes approximately 1000 members.

The Apache Software Foundation is a decentralized open source community of developers. The software they produce is distributed under the terms of the Apache License, a permissive open-source license for free and open-source software (FOSS). The Apache projects are characterized by a collaborative, consensus-based development process and an open and pragmatic software license, which is to say that it allows developers, who receive the software freely, to redistribute it under non-free terms. Each project is managed by a self-selected team of technical experts who are active contributors to the project. The ASF is a meritocracy, implying that membership of the foundation is granted only to volunteers who have actively contributed to Apache projects. The ASF is considered a second-generation open-source organization, in that commercial support is provided without the risk of platform lock-in.

Among the ASF's objectives are: to provide legal protection to volunteers working on Apache projects, and to prevent the "Apache" brand name from being used by other organizations without permission.

The ASF also holds several ApacheCon conferences each year, highlighting Apache projects and related technology.

History
The history of the Apache Software Foundation is linked to the Apache HTTP Server, development beginning in February 1993. A group of eight developers started working on enhancing the NCSA HTTPd daemon. They came to be known as the Apache Group. On March 25, 1999, the Apache Software Foundation was formed. The first official meeting of the Apache Software Foundation was held on April 13, 1999. The initial members of the Apache Software Foundation consisted of the Apache Group: Brian Behlendorf, Ken Coar, Miguel Gonzales, Mark Cox, Lars Eilebrecht, Ralf S. Engelschall, Roy T. Fielding, Dean Gaudet, Ben Hyde, Jim Jagielski, Alexei Kosut, Martin Kraemer, Ben Laurie, Doug MacEachern, Aram Mirzadeh, Sameer Parekh, Cliff Skolnick, Marc Slemko, William (Bill) Stoddard, Paul Sutton, Randy Terbush and Dirk-Willem van Gulik. After a series of additional meetings to elect board members and resolve other legal matters regarding incorporation, the effective incorporation date of the Apache Software Foundation was set to June 1, 1999.

Co-founder Brian Behlendorf states how the name 'Apache' was chosen: "I suggested the name Apache partly because the web technologies at the time that were launching were being called cyber this or spider that or something on those themes and I was like we need something a little more interesting, a little more romantic, not to be a cultural appropriator or anything like that, I had just seen a documentary about Geronimo and the last days of a Native American tribe called the Apaches right, who succumbed to the invasion from the West, from the United States, and they were the last tribe to give up their territory and for me that almost romantically represented what I felt we were doing with this web-server project..."

Projects
Apache divides its software development activities into separate semi-autonomous areas called "top-level projects" (formally known as a "Project Management Committee" in the bylaws ), some of which have a number of sub-projects. Unlike some other organizations that host FOSS projects, before a project is hosted at Apache it has to be licensed to the ASF with a grant or contributor agreement. In this way, the ASF gains the necessary intellectual property rights for the development and distribution of all its projects.

Board of directors
The Board of Directors of The Apache Software Foundation (ASF) is responsible for management and oversight of the business and affairs of the corporation in accordance with the Bylaws. This includes management of the corporate assets (funds, intellectual property, trademarks, and support equipment), appointment of a President and corporate officers managing the core operations of the ASF, and allocation of corporate resources for the benefit of Apache projects. Technical decision-making authority for every Apache project is assigned to their independent project management committee; the participants in each project provide direction, not the board. The board is elected annually by the ASF membership.

Since March 8, 2024, the board of directors has been:

 * Rich Bowen
 * Shane Curcuru
 * Christofer Dutz
 * Willem Ning Jiang
 * Jeff Jirsa
 * Justin Mclean
 * Jean-Baptiste Onofré
 * Craig L Russell
 * Sander Striker

title: The Apache Software Foundation