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List of World Series champions
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This article is about winners of the World Series of Major League Baseball that began in 1903. For earlier league and inter-league championships, see List of pre-World Series baseball champions.
At the first World Series, held in 1903, the Boston Americans (front row) defeated the Pittsburgh Pirates (back row) in eight games.
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The World Series is the annual championship series of Major League Baseball (MLB) and concludes the MLB postseason. First played in 1903,[1] the World Series championship is determined through a best-of-seven playoff and is a contest between the champions of baseball's National League (NL) and American League (AL).[2] Often referred to as the "Fall Classic",[3] the modern World Series has been played every year since 1903 with two exceptions: in 1904, when the NL champion New York Giants declined to play the AL champion Boston Americans; and in 1994, when the series was canceled due to the players' strike.[1][2][4][5]
The best-of-seven style has been the format of all World Series except in 1903, 1919, 1920, and 1921, when the winner was determined through a best-of-nine playoff.[1][2] Although the large majority of contests have been played entirely during the month of October, a small number of Series have also had games played during September and November. The Series-winning team is awarded the Commissioner's Trophy.[6] Players, coaches, and others associated with the team are generally given World Series rings to commemorate their victory; however, they have received other items such as pocket watches and medallions in the past.[7] The winning team is traditionally invited to the White House to meet the President of the United States.[8]
A total of 113 Series have been contested, with the NL champion winning 48 and the AL champion winning 65. The New York Yankees of the AL have played in 40 World Series through 2017—winning 27—the most Series appearances, victories, and losses (13, shared with the Los Angeles Dodgers) of any Major League Baseball franchise. The St. Louis Cardinals, who represented the NL for a 19th time in 2013, have won 11 championships, which is the second-most among all 30 Major League Baseball teams as well as most among NL teams.[3] Both the Giants and the Dodgers have been NL champions more times, with the Giants winning 23 NL pennants and the Dodgers winning 22.
The Seattle Mariners and the Washington Nationals (formerly Montreal Expos) are the only current Major League Baseball franchises to have never appeared in a World Series; the San Diego Padres, Colorado Rockies, Texas Rangers (formerly the 1961–1971 version of the Washington Senators), Tampa Bay Rays, and Milwaukee Brewers (formerly Seattle Pilots) have all played in the Series but have never won. The Toronto Blue Jays are the only franchise from outside the United States to appear in a World Series, winning in 1992 and 1993. The current World Series champions are the Houston Astros.
Contents
[hide]
1 Winners
2 Series appearances by club
2.1 Appearances by club
2.2 Years of appearance
2.3 Frequent matchups
3 Notes
4 See also
5 References
6 External links
Winners[edit]
Numbers in parentheses in the table are World Series appearances as of the date of that World Series, and are used as follows:
Winning team and losing team columns indicate the number of times that team has appeared in a World Series as well as each respective teams' World Series record to date.
National League team
American League team
Year
Winning team
Manager
Games
Losing team
Manager
Ref.
1903
Boston Americans (1, 1–0) Collins, JimmyJimmy Collins 5–3[V] Pittsburgh Pirates (1, 0–1) Clarke, FredFred Clarke [9]
1904
No World Series [1]
1905
New York Giants (1, 1–0) McGraw, JohnJohn McGraw 4–1 Philadelphia Athletics (1, 0–1) Mack, ConnieConnie Mack [10]
1906
Chicago White Sox (1, 1–0) Jones, FielderFielder Jones 4–2 Chicago Cubs (1, 0–1) Chance, FrankFrank Chance [11]
1907
Chicago Cubs (1, 1–1) Chance, FrankFrank Chance 4–0–(1)[T] Detroit Tigers (1, 0–1) Jennings, HughHugh Jennings [12]
1908
Chicago Cubs (2, 2–1) Chance, FrankFrank Chance 4–1 Detroit Tigers (2, 0–2) Jennings, HughHugh Jennings [13]
1909
Pittsburgh Pirates (2, 1–1) Clarke, FredFred Clarke 4–3 Detroit Tigers (3, 0–3) Jennings, HughHugh Jennings [14]
1910
Philadelphia Athletics (2, 1–1) Mack, ConnieConnie Mack 4–1 Chicago Cubs (4, 2–2) Chance, FrankFrank Chance [15]
1911
Philadelphia Athletics (3, 2–1) Mack, ConnieConnie Mack 4–2 New York Giants (2, 1–1) McGraw, JohnJohn McGraw [16]
1912
Boston Red Sox (2, 2–0) Stahl, JakeJake Stahl 4–3–(1)[T] New York Giants (3, 1–2) McGraw, JohnJohn McGraw [17]
1913
Philadelphia Athletics (4, 3–1) Mack, ConnieConnie Mack 4–1 New York Giants (4, 1–3) McGraw, JohnJohn McGraw [18]
1914
Boston Braves (1, 1–0) Stallings, GeorgeGeorge Stallings 4–0 Philadelphia Athletics (5, 3–2) Mack, ConnieConnie Mack [19]
1915
Boston Red Sox (3, 3–0) Carrigan, BillBill Carrigan 4–1 Philadelphia Phillies (1, 0–1) Moran, PatPat Moran [20]
1916
Boston Red Sox (4, 4–0) Carrigan, BillBill Carrigan 4–1 Brooklyn Robins (1, 0–1) Robinson, WilbertWilbert Robinson [21]
1917
Chicago White Sox (2, 2–0) Rowland, PantsPants Rowland 4–2 New York Giants (5, 1–4) McGraw, JohnJohn McGraw [22]
1918
Boston Red Sox (5, 5–0) Barrow, EdEd Barrow 4–2 Chicago Cubs (5, 2–3) Mitchell, FredFred Mitchell [23]
1919
Cincinnati Reds (1, 1–0) Moran, PatPat Moran 5–3[V] Chicago White Sox (3, 2–1) Gleason, KidKid Gleason [24]
1920
Cleveland Indians (1, 1–0) Speaker, TrisTris Speaker 5–2[V] Brooklyn Robins (2, 0–2) Robinson, WilbertWilbert Robinson [25]
1921
New York Giants (6, 2–4) McGraw, JohnJohn McGraw 5–3[V] New York Yankees (1, 0–1) Huggins, MillerMiller Huggins [26]
1922
New York Giants (7, 3–4) McGraw, JohnJohn McGraw 4–0–(1)[T] New York Yankees (2, 0–2) Huggins, MillerMiller Huggins [27]
1923
New York Yankees (3, 1–2) Huggins, MillerMiller Huggins 4–2 New York Giants (8, 3–5) McGraw, JohnJohn McGraw [28]
1924
Washington Senators (1, 1–0) Harris, BuckyBucky Harris 4–3 New York Giants (9, 3–6) McGraw, JohnJohn McGraw [29]
1925
Pittsburgh Pirates (3, 2–1) McKechnie, BillBill McKechnie 4–3 Washington Senators (2, 1–1) Harris, BuckyBucky Harris [30]
1926
St. Louis Cardinals (1, 1–0) Hornsby, RogersRogers Hornsby 4–3 New York Yankees (4, 1–3) Huggins, MillerMiller Huggins [31]
1927
New York Yankees (5, 2–3) Huggins, MillerMiller Huggins 4–0 Pittsburgh Pirates (4, 2–2) Donie Bush [32]
1928
New York Yankees (6, 3–3) Huggins, MillerMiller Huggins 4–0 St. Louis Cardinals (2, 1–1) McKechnie, BillBill McKechnie [33]
1929
Philadelphia Athletics (6, 4–2) Mack, ConnieConnie Mack 4–1 Chicago Cubs (6, 2–4) McCarthy, JoeJoe McCarthy [34]
1930
Philadelphia Athletics (7, 5–2) Mack, ConnieConnie Mack 4–2 St. Louis Cardinals (3, 1–2) Street, GabbyGabby Street [35]
1931
St. Louis Cardinals (4, 2–2) Street, GabbyGabby Street 4–3 Philadelphia Athletics (8, 5–3) Mack, ConnieConnie Mack [36]
1932
New York Yankees (7, 4–3) McCarthy, JoeJoe McCarthy 4–0 Chicago Cubs (7, 2–5) Grimm, CharlieCharlie Grimm [37]
1933
New York Giants (10, 4–6) Terry, BillBill Terry 4–1 Washington Senators (3, 1–2) Cronin, JoeJoe Cronin [38]
1934
St. Louis Cardinals (5, 3–2) Frisch, FrankFrank Frisch 4–3 Detroit Tigers (4, 0–4) Cochrane, MickeyMickey Cochrane [39]
1935
Detroit Tigers (5, 1–4) Cochrane, MickeyMickey Cochrane 4–2 Chicago Cubs (8, 2–6) Grimm, CharlieCharlie Grimm [40]
1936
New York Yankees (8, 5–3) McCarthy, JoeJoe McCarthy 4–2 New York Giants (11, 4–7) Terry, BillBill Terry [41]
1937
New York Yankees (9, 6–3) McCarthy, JoeJoe McCarthy 4–1 New York Giants (12, 4–8) Terry, BillBill Terry [42]
1938
New York Yankees (10, 7–3) McCarthy, JoeJoe McCarthy 4–0 Chicago Cubs (9, 2–7) Hartnett, GabbyGabby Hartnett [43]
1939
New York Yankees (11, 8–3) McCarthy, JoeJoe McCarthy 4–0 Cincinnati Reds (2, 1–1) McKechnie, BillBill McKechnie [44]
1940
Cincinnati Reds (3, 2–1) McKechnie, BillBill McKechnie 4–3 Detroit Tigers (6, 1–5) Baker, DelDel Baker [45]
1941
New York Yankees (12, 9–3) McCarthy, JoeJoe McCarthy 4–1 Brooklyn Dodgers (3, 0–3) Durocher, LeoLeo Durocher [46]
1942
St. Louis Cardinals (6, 4–2) Southworth, BillyBilly Southworth 4–1 New York Yankees (13, 9–4) McCarthy, JoeJoe McCarthy [47]
1943
New York Yankees (14, 10–4) McCarthy, JoeJoe McCarthy 4–1 St. Louis Cardinals (7, 4–3) Southworth, BillyBilly Southworth [48]
1944
St. Louis Cardinals (8, 5–3) Southworth, BillyBilly Southworth 4–2 St. Louis Browns (1, 0–1) Sewell, LukeLuke Sewell [49]
1945
Detroit Tigers (7, 2–5) O'Neill, SteveSteve O'Neill 4–3 Chicago Cubs (10, 2–8) Grimm, CharlieCharlie Grimm [50]
1946
St. Louis Cardinals (9, 6–3) Dyer, EddieEddie Dyer 4–3 Boston Red Sox (6, 5–1) Cronin, JoeJoe Cronin [51]
1947
New York Yankees (15, 11–4) Harris, BuckyBucky Harris 4–3 Brooklyn Dodgers (4, 0–4) Shotton, BurtBurt Shotton [52]
1948
Cleveland Indians (2, 2–0) Boudreau, LouLou Boudreau 4–2 Boston Braves (2, 1–1) Southworth, BillyBilly Southworth [53]
1949
New York Yankees (16, 12–4) Stengel, CaseyCasey Stengel 4–1 Brooklyn Dodgers (5, 0–5) Shotton, BurtBurt Shotton [54]
1950
New York Yankees (17, 13–4) Stengel, CaseyCasey Stengel 4–0 Philadelphia Phillies (2, 0–2) Sawyer, EddieEddie Sawyer [55]
1951
New York Yankees (18, 14–4) Stengel, CaseyCasey Stengel 4–2 New York Giants (13, 4–9) Durocher, LeoLeo Durocher [56]
1952
New York Yankees (19, 15–4) Stengel, CaseyCasey Stengel 4–3 Brooklyn Dodgers (6, 0–6) Dressen, CharlieCharlie Dressen [57]
1953
New York Yankees (20, 16–4) Stengel, CaseyCasey Stengel 4–2 Brooklyn Dodgers (7, 0–7) Dressen, CharlieCharlie Dressen [58]
1954
New York Giants (14, 5–9) Durocher, LeoLeo Durocher 4–0 Cleveland Indians (3, 2–1) Lopez, AlAl Lopez [59]
1955
Brooklyn Dodgers (8, 1–7) Alston, WalterWalter Alston 4–3 New York Yankees (21, 16–5) Stengel, CaseyCasey Stengel [60]
1956
New York Yankees (22, 17–5) Stengel, CaseyCasey Stengel 4–3 Brooklyn Dodgers (9, 1–8) Alston, WalterWalter Alston [61]
1957
Milwaukee Braves (3, 2–1) Haney, FredFred Haney 4–3 New York Yankees (23, 17–6) Stengel, CaseyCasey Stengel [62]
1958
New York Yankees (24, 18–6) Stengel, CaseyCasey Stengel 4–3 Milwaukee Braves (4, 2–2) Haney, FredFred Haney [63]
1959
Los Angeles Dodgers (10, 2–8) Alston, WalterWalter Alston 4–2 Chicago White Sox (4, 2–2) Lopez, AlAl Lopez [64]
1960
Pittsburgh Pirates (5, 3–2) Murtaugh, DannyDanny Murtaugh 4–3 New York Yankees (25, 18–7) Stengel, CaseyCasey Stengel [65]
1961
New York Yankees (26, 19–7) Houk, RalphRalph Houk 4–1 Cincinnati Reds (4, 2–2) Hutchinson, FredFred Hutchinson [66]
1962
New York Yankees (27, 20–7) Houk, RalphRalph Houk 4–3 San Francisco Giants (15, 5–10) Dark, AlvinAlvin Dark [67]
1963
Los Angeles Dodgers (11, 3–8) Alston, WalterWalter Alston 4–0 New York Yankees (28, 20–8) Houk, RalphRalph Houk [68]
1964
St. Louis Cardinals (10, 7–3) Keane, JohnnyJohnny Keane 4–3 New York Yankees (29, 20–9) Berra, YogiYogi Berra [69]
1965
Los Angeles Dodgers (12, 4–8) Alston, WalterWalter Alston 4–3 Minnesota Twins (4, 1–3) Mele, SamSam Mele [70]
1966
Baltimore Orioles (2, 1–1) Bauer, HankHank Bauer 4–0 Los Angeles Dodgers (13, 4–9) Alston, WalterWalter Alston [71]
1967
St. Louis Cardinals (11, 8–3) Schoendienst, RedRed Schoendienst 4–3 Boston Red Sox (7, 5–2) Williams, DickDick Williams [72]
1968
Detroit Tigers (8, 3–5) Smith, MayoMayo Smith 4–3 St. Louis Cardinals (12, 8–4) Schoendienst, RedRed Schoendienst [73]
1969
New York Mets (1, 1–0) Hodges, GilGil Hodges 4–1 Baltimore Orioles (3, 1–2) Weaver, EarlEarl Weaver [74]
1970
Baltimore Orioles (4, 2–2) Weaver, EarlEarl Weaver 4–1 Cincinnati Reds (5, 2–3) Anderson, SparkySparky Anderson [75]
1971
Pittsburgh Pirates (6, 4–2) Murtaugh, DannyDanny Murtaugh 4–3 Baltimore Orioles (5, 2–3) Weaver, EarlEarl Weaver [76]
1972
Oakland Athletics (9, 6–3) Williams, DickDick Williams 4–3 Cincinnati Reds (6, 2–4) Anderson, SparkySparky Anderson [77]
1973
Oakland Athletics (10, 7–3) Williams, DickDick Williams 4–3 New York Mets (2, 1–1) Berra, YogiYogi Berra [78]
1974
Oakland Athletics (11, 8–3) Dark, AlvinAlvin Dark 4–1 Los Angeles Dodgers (14, 4–10) Alston, WalterWalter Alston [79]
1975
Cincinnati Reds (7, 3–4) Anderson, SparkySparky Anderson 4–3 Boston Red Sox (8, 5–3) Johnson, DarrellDarrell Johnson [80]
1976
Cincinnati Reds (8, 4–4) Anderson, SparkySparky Anderson 4–0 New York Yankees (30, 20–10) Martin, BillyBilly Martin [81]
1977
New York Yankees (31, 21–10) Martin, BillyBilly Martin 4–2 Los Angeles Dodgers (15, 4–11) Lasorda, TommyTommy Lasorda [82]
1978
New York Yankees (32, 22–10) Lemon, BobBob Lemon 4–2 Los Angeles Dodgers (16, 4–12) Lasorda, TommyTommy Lasorda [83]
1979
Pittsburgh Pirates (7, 5–2) Tanner, ChuckChuck Tanner 4–3 Baltimore Orioles (6, 2–4) Weaver, EarlEarl Weaver [84]
1980
Philadelphia Phillies (3, 1–2) Green, DallasDallas Green 4–2 Kansas City Royals (1, 0–1) Frey, JimJim Frey [85]
1981
Los Angeles Dodgers (17, 5–12) Lasorda, TommyTommy Lasorda 4–2 New York Yankees (33, 22–11) Lemon, BobBob Lemon [86]
1982
St. Louis Cardinals (13, 9–4) Herzog, WhiteyWhitey Herzog 4–3 Milwaukee Brewers[L1] (1, 0–1) Kuenn, HarveyHarvey Kuenn [87]
1983
Baltimore Orioles (7, 3–4) Altobelli, JoeJoe Altobelli 4–1 Philadelphia Phillies (4, 1–3) Owens, PaulPaul Owens [88]
1984
Detroit Tigers (9, 4–5) Anderson, SparkySparky Anderson 4–1 San Diego Padres (1, 0–1) Williams, DickDick Williams [89]
1985
Kansas City Royals (2, 1–1) Howser, DickDick Howser 4–3 St. Louis Cardinals (14, 9–5) Herzog, WhiteyWhitey Herzog [90]
1986
New York Mets (3, 2–1) Johnson, DaveyDavey Johnson 4–3 Boston Red Sox (9, 5–4) McNamara, JohnJohn McNamara [91]
1987
Minnesota Twins (5, 2–3) Kelly, TomTom Kelly 4–3 St. Louis Cardinals (15, 9–6) Herzog, WhiteyWhitey Herzog [92]
1988
Los Angeles Dodgers (18, 6–12) Lasorda, TommyTommy Lasorda 4–1 Oakland Athletics (12, 8–4) La Russa, TonyTony La Russa [93]
1989
Oakland Athletics (13, 9–4) La Russa, TonyTony La Russa 4–0 San Francisco Giants (16, 5–11) Craig, RogerRoger Craig [94]
1990
Cincinnati Reds (9, 5–4) Piniella, LouLou Piniella 4–0 Oakland Athletics (14, 9–5) La Russa, TonyTony La Russa [95]
1991
Minnesota Twins (6, 3–3) Kelly, TomTom Kelly 4–3 Atlanta Braves (5, 2–3) Cox, BobbyBobby Cox [96]
1992
Toronto Blue Jays (1, 1–0) Gaston, CitoCito Gaston 4–2 Atlanta Braves (6, 2–4) Cox, BobbyBobby Cox [97]
1993
Toronto Blue Jays (2, 2–0) Gaston, CitoCito Gaston 4–2 Philadelphia Phillies (5, 1–4) Fregosi, JimJim Fregosi [98]
1994
No World Series due to a players' strike
1995
Atlanta Braves (7, 3–4) Cox, BobbyBobby Cox 4–2 Cleveland Indians (4, 2–2) Hargrove, MikeMike Hargrove [99]
1996
New York Yankees (34, 23–11) Torre, JoeJoe Torre 4–2 Atlanta Braves (8, 3–5) Cox, BobbyBobby Cox [100]
1997
Florida Marlins[W] (1, 1–0) Leyland, JimJim Leyland 4–3 Cleveland Indians (5, 2–3) Hargrove, MikeMike Hargrove [101]
1998
New York Yankees (35, 24–11) Torre, JoeJoe Torre 4–0 San Diego Padres (2, 0–2) Bruce Bochy [102]
1999
New York Yankees (36, 25–11) Torre, JoeJoe Torre 4–0 Atlanta Braves (9, 3–6) Cox, BobbyBobby Cox [103]
2000
New York Yankees (37, 26–11) Torre, JoeJoe Torre 4–1 New York Mets[W] (4, 2–2) Valentine, BobbyBobby Valentine [104]
2001
Arizona Diamondbacks (1, 1–0) Brenly, BobBob Brenly 4–3 New York Yankees (38, 26–12) Torre, JoeJoe Torre [105]
2002
Anaheim Angels[W] (1, 1–0) Scioscia, MikeMike Scioscia 4–3 San Francisco Giants[W] (17, 5–12) Baker, DustyDusty Baker [106]
2003
Florida Marlins[W] (2, 2–0) McKeon, JackJack McKeon 4–2 New York Yankees (39, 26–13) Torre, JoeJoe Torre [107]
2004
Boston Red Sox[W] (10, 6–4) Francona, TerryTerry Francona 4–0 St. Louis Cardinals (16, 9–7) La Russa, TonyTony La Russa [108]
2005
Chicago White Sox (5, 3–2) Guillén, OzzieOzzie Guillén 4–0 Houston Astros[W][L2] (1, 0–1) Garner, PhilPhil Garner [109]
2006
St. Louis Cardinals (17, 10–7) La Russa, TonyTony La Russa 4–1 Detroit Tigers[W] (10, 4–6) Leyland, JimJim Leyland [110]
2007
Boston Red Sox (11, 7–4) Francona, TerryTerry Francona 4–0 Colorado Rockies[W] (1, 0–1) Hurdle, ClintClint Hurdle [111]
2008
Philadelphia Phillies (6, 2–4) Manuel, CharlieCharlie Manuel 4–1 Tampa Bay Rays (1, 0–1) Maddon, JoeJoe Maddon [112]
2009
New York Yankees (40, 27–13) Girardi, JoeJoe Girardi 4–2 Philadelphia Phillies (7, 2–5) Manuel, CharlieCharlie Manuel [113]
2010
San Francisco Giants (18, 6–12) Bochy, BruceBruce Bochy 4–1 Texas Rangers (1, 0–1) Washington, RonRon Washington [114]
2011
St. Louis Cardinals[W] (18, 11–7) La Russa, TonyTony La Russa 4–3 Texas Rangers (2, 0–2) Washington, RonRon Washington [115]
2012
San Francisco Giants (19, 7–12) Bochy, BruceBruce Bochy 4–0 Detroit Tigers (11, 4–7) Leyland, JimJim Leyland [116]
2013
Boston Red Sox (12, 8–4) Farrell, JohnJohn Farrell 4–2 St. Louis Cardinals (19, 11–8) Matheny, MikeMike Matheny [117]
2014
San Francisco Giants[W] (20, 8–12) Bochy, BruceBruce Bochy 4–3 Kansas City Royals[W] (3, 1–2) Yost, NedNed Yost [118]
2015
Kansas City Royals (4, 2–2) Yost, NedNed Yost 4–1 New York Mets (5, 2–3) Collins, TerryTerry Collins [119]
2016
Chicago Cubs (11, 3–8) Maddon, JoeJoe Maddon 4–3 Cleveland Indians (6, 2–4) Francona, TerryTerry Francona [120]
2017
Houston Astros[L2] (2, 1–1) Hinch, A. J.A. J. Hinch 4–3 Los Angeles Dodgers (19, 6–13) Roberts, DaveDave Roberts [121]
Series appearances by club[edit]
Appearances by club[edit]
Series
appearances
Team
League
Winners
Runners-up
Win %
Most recent
Games
won
Games
lost
Games
tied
Game
win %
Most Recent
game win
Founded
win
appearance
40
New York Yankees
AL 27 13 .675 2009 2009 134 90 1 .598 2009 1903
20
San Francisco Giants (New York)
NL 8 12 .400 2014 2014 57 57 2 .500 2014 1883
19
St. Louis Cardinals
NL 11 8 .579 2011 2013 58 60 0 .492 2011 1882
19
Los Angeles Dodgers (Brooklyn)
NL 6 13 .316 1988 2017 48 64 0 .429 2017 1884
14
Oakland Athletics (Kansas City/Philadelphia)
AL 9 5 .643 1989 1990 41 34 0 .547 1989 1901
12
Boston Red Sox (Boston)
AL 8 4 .667 2013 2013 45 28 1 .615 2013 1901
11
Detroit Tigers
AL 4 7 .364 1984 2012 27 37 1 .423 2006 1901
11
Chicago Cubs
NL 3 8 .273 2016 2016 23 36 1 .392 2016 1870
9
Cincinnati Reds
NL 5 4 .556 1990 1990 26 25 0 .510 1990 1881
9
Atlanta Braves (Milwaukee/Boston)
NL 3 6 .333 1995 1999 24 29 0 .453 1996 1871
7
Pittsburgh Pirates
NL 5 2 .714 1979 1979 23 24 0 .489 1979 1887
7
Baltimore Orioles (St. Louis Browns)
AL 3 4 .429 1983 1983 21 18 0 .538 1983 1900
7
Philadelphia Phillies
NL 2 5 .286 2008 2009 14 23 0 .378 2009 1883
6
Minnesota Twins (Washington Senators)
AL 3 3 .500 1991 1991 19 21 0 .475 1991 1901
6
Cleveland Indians
AL 2 4 .333 1948 2016 17 20 0 .459 2016 1901
5
Chicago White Sox
AL 3 2 .600 2005 2005 17 13 0 .567 2005 1900
5
New York Mets
NL 2 3 .400 1986 2015 13 16 0 .448 2015 1962
4
Kansas City Royals
AL 2 2 .500 2015 2015 13 12 0 .520 2015 1969
2
Miami Marlins (Florida)
NL 2 0 1.000 2003 2003 8 5 0 .615 2003 1993
2
Toronto Blue Jays
AL 2 0 1.000 1993 1993 8 4 0 .667 1993 1977
2
Houston Astros
NL/AL[L2] 1 1 .500 2017 2017 4 7 0 .364 2017 1962
2
Texas Rangers (Washington Senators)
AL 0 2 .000 0 !— 2011 4 8 0 .333 2011 1961
2
San Diego Padres
NL 0 2 .000 0 !— 1998 1 8 0 .111 1984 1969
1
Los Angeles Angels
(Anaheim/California/Los Angeles)
AL 1 0 1.000 2002 2002 4 3 0 .571 2002 1961
1
Arizona Diamondbacks
NL 1 0 1.000 2001 2001 4 3 0 .571 2001 1998
1
Tampa Bay Rays
AL 0 1 .000 0 !— 2008 1 4 0 .200 2008 1998
1
Colorado Rockies
NL 0 1 .000 0 !— 2007 0 4 0 .000 0 !— 1993
1
Milwaukee Brewers (Seattle Pilots)
AL/NL[L1] 0 1 .000 0 !— 1982 3 4 0 .429 1982 1969
0
Washington Nationals (Montreal Expos)
NL 0 0 0 !— 0 !— 0 !— 0 0 0 – 0 !— 1969
0
Seattle Mariners
AL 0 0 0 !— 0 !— 0 !— 0 0 0 – 0 !— 1977
Years of appearance[edit]
In the sortable table below, teams are ordered first by number of appearances, then by number of wins, and finally by year of first appearance. In the "Season(s)" column, bold years indicate winning World Series appearances.
Series
appearances
Team
Wins
Losses
Win %
Season(s)
40
New York Yankees
27 13 .675 1921, 1922, 1923, 1926, 1927, 1928, 1932, 1936, 1937, 1938, 1939, 1941, 1942, 1943, 1947, 1949, 1950, 1951, 1952, 1953, 1955, 1956, 1957, 1958, 1960, 1961, 1962, 1963, 1964, 1976, 1977, 1978, 1981, 1996, 1998, 1999, 2000, 2001, 2003, 2009
20
San Francisco Giants (New York)
8 12 .400 1905, 1911, 1912, 1913, 1917, 1921, 1922, 1923, 1924, 1933, 1936, 1937, 1951, 1954, 1962, 1989, 2002, 2010, 2012, 2014
19
St. Louis Cardinals
11 8 .579 1926, 1928, 1930, 1931, 1934, 1942, 1943, 1944, 1946, 1964, 1967, 1968, 1982, 1985, 1987, 2004, 2006, 2011, 2013
19
Los Angeles Dodgers (Brooklyn)
6 13 .316 1916, 1920, 1941, 1947, 1949, 1952, 1953, 1955, 1956, 1959, 1963, 1965, 1966, 1974, 1977, 1978, 1981, 1988, 2017
14
Oakland Athletics (Kansas City/Philadelphia)
9 5 .643 1905, 1910, 1911, 1913, 1914, 1929, 1930, 1931, 1972, 1973, 1974, 1988, 1989, 1990
12
Boston Red Sox (Americans)
8 4 .667 1903, 1912, 1915, 1916, 1918, 1946, 1967, 1975, 1986, 2004, 2007, 2013
11
Detroit Tigers
4 7 .364 1907, 1908, 1909, 1934, 1935, 1940, 1945, 1968, 1984, 2006, 2012
11
Chicago Cubs
3 8 .273 1906, 1907, 1908, 1910, 1918, 1929, 1932, 1935, 1938, 1945, 2016
9
Cincinnati Reds
5 4 .556 1919, 1939, 1940, 1961, 1970, 1972, 1975, 1976, 1990
9
Atlanta Braves (Milwaukee/Boston)
3 6 .333 1914, 1948, 1957, 1958, 1991, 1992, 1995, 1996, 1999
7
Pittsburgh Pirates
5 2 .714 1903, 1909, 1925, 1927, 1960, 1971, 1979
7
Baltimore Orioles (St. Louis Browns)
3 4 .429 1944, 1966, 1969, 1970, 1971, 1979, 1983
7
Philadelphia Phillies
2 5 .286 1915, 1950, 1980, 1983, 1993, 2008, 2009
6
Minnesota Twins (Washington Senators)
3 3 .500 1924, 1925, 1933, 1965, 1987, 1991
6
Cleveland Indians
2 4 .333 1920, 1948, 1954, 1995, 1997, 2016
5
Chicago White Sox
3 2 .600 1906, 1917, 1919, 1959, 2005
5
New York Mets
2 3 .400 1969, 1973, 1986, 2000, 2015
4
Kansas City Royals
2 2 .500 1980, 1985, 2014, 2015
2
Toronto Blue Jays
2 0 1.000 1992, 1993
2
Miami Marlins (Florida)
2 0 1.000 1997, 2003
2
Houston Astros
1 1 .500 2005, 2017
2
San Diego Padres
0 2 .000 1984, 1998
2
Texas Rangers (Washington Senators)
0 2 .000 2010, 2011
1
Arizona Diamondbacks
1 0 1.000 2001
1
Los Angeles Angels
(Anaheim/California/Los Angeles)
1 0 1.000 2002
1
Milwaukee Brewers (Seattle Pilots)
0 1 .000 1982
1
Colorado Rockies
0 1 .000 2007
1
Tampa Bay Rays
0 1 .000 2008
0
Washington Nationals (Montreal Expos)
0 0 0 !—
0
Seattle Mariners
0 0 0 !—
Frequent matchups[edit]
The following are the 19 matchups of teams that have occurred two or more times in the World Series. All teams which have participated in these were "Classic Eight" members of either the American or National League; no expansion team (created in 1961 or later) has faced an opponent more than once in a World Series.
Count
Matchup
Record
Years
11 Brooklyn & Los Angeles Dodgers vs. New York Yankees Yankees, 8–3 1941, 1947, 1949, 1952, 1953, 1955, 1956, 1963, 1977, 1978, 1981
7 New York Yankees vs. New York & San Francisco Giants Yankees, 5–2 1921, 1922, 1923, 1936, 1937, 1951, 1962
5 New York Yankees vs. St. Louis Cardinals Cardinals, 3–2 1926, 1928, 1942, 1943, 1964
4 Milwaukee & Atlanta Braves vs. New York Yankees Yankees, 3–1 1957, 1958, 1996, 1999
4 Boston Red Sox vs. St. Louis Cardinals Tied, 2–2 1946, 1967, 2004, 2013
4 Chicago Cubs vs. Detroit Tigers Tied, 2–2 1907, 1908, 1935, 1945
4 Philadelphia & Oakland Athletics vs. New York & San Francisco Giants Athletics, 3–1 1905, 1911, 1913, 1989
3 Cincinnati Reds vs. New York Yankees Yankees, 2–1 1939, 1961, 1976
3 Detroit Tigers vs. St. Louis Cardinals Cardinals, 2–1 1934, 1968, 2006
2 Boston & Atlanta Braves vs. Cleveland Indians Tied, 1–1 1948, 1995
2 Baltimore Orioles vs. Pittsburgh Pirates Pirates, 2–0 1971, 1979
2 Chicago Cubs vs. New York Yankees Yankees, 2–0 1932, 1938
2 Chicago Cubs vs. Philadelphia Athletics (now Oakland) Athletics, 2–0 1910, 1929
2 Cincinnati Reds vs. Oakland Athletics Tied, 1–1 1972, 1990
2 Los Angeles Dodgers vs. Oakland Athletics Tied, 1–1 1974, 1988
2 Washington Senators (now Minnesota Twins) vs. New York Giants (now San Francisco) Tied, 1–1 1924, 1933
2 New York Yankees vs. Philadelphia Phillies Yankees, 2–0 1950, 2009
2 New York Yankees vs. Pittsburgh Pirates Tied, 1–1 1927, 1960
2 Philadelphia Athletics (now Oakland) vs. St. Louis Cardinals Tied, 1–1 1930, 1931
Notes[edit]
T The 1907, 1912, and 1922 World Series each included one tied game.
V The 1903, 1919, 1920, and 1921 World Series were in a best-of-nine format (carried by the first team to win five games).
W Indicates a team which made the playoffs as a wild card team (rather than by winning a division).[1]
L1 The Brewers were in the American League from 1969–1997, after which they switched to the National League.[122]
L2 The Astros were in the National League from 1962–2012, after which they switched to the American League.
See also[edit]
Baseball portal
List of National League pennant winners
List of American League pennant winners
List of Major League Baseball franchise postseason streaks
List of Major League Baseball franchise postseason droughts
List of pre-World Series baseball champions
References[edit]
^ Jump up to: a b c d e "Baseball-Reference Playoff and World Series Index". Baseball-Reference.com. Retrieved November 5, 2009.
^ Jump up to: a b c "World Series Overview". Major League Baseball. Retrieved January 2, 2010.
^ Jump up to: a b "World Series History: Championships by Club". Major League Baseball. Retrieved January 2, 2010.
Jump up ^ "History of the World Series – 1904". The Sporting News. Archived from the original on December 3, 2009. Retrieved September 27, 2011.
Jump up ^ "Season interrupted". Sports Illustrated. August 26, 2002. Retrieved January 2, 2010.
Jump up ^ "Phillies Announce World Series Trophy Tour Presented by Teva Pharmaceuticals and Comcast SportsNet". PR Newswire Association. January 9, 2009. Archived from the original on February 23, 2009. Retrieved January 1, 2010.
Jump up ^ Lukas, Paul (October 30, 2009). "World Series rings, the real scoop". ESPN. Retrieved December 9, 2009.
Jump up ^ "White Sox Visit White House, Meet Obama". The Huffington Post. April 20, 2009. Retrieved January 1, 2010.
Jump up ^ "1903 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1905 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1906 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1907 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1908 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1909 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1910 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1911 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1912 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1913 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1914 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1915 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1916 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1917 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1918 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1919 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1920 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1921 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1922 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1923 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1924 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1925 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1926 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1927 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1928 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1929 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1930 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1931 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1932 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1933 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1934 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1935 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1936 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1937 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1938 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1939 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1940 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1941 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1942 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1943 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1944 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1945 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1946 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1947 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1948 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1949 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1950 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1951 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1952 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1953 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1954 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1955 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1956 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1957 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1958 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1959 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1960 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1961 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1962 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1963 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1964 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1965 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1966 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1967 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1968 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1969 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1970 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1971 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1972 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1973 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1974 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1975 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1976 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1977 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1978 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1979 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1980 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1981 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1982 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1983 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1984 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1985 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1986 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1987 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1988 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1989 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1990 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1991 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1992 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1993 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1995 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1996 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1997 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1998 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "1999 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2000 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2001 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2002 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2003 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2004 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2005 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2006 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2007 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2008 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2009 World Series". Baseball-Reference.com. Retrieved January 2, 2010.
Jump up ^ "2010 World Series". Baseball-Reference.com. Retrieved November 2, 2010.
Jump up ^ "2011 World Series". Baseball-Reference.com. Retrieved November 2, 2010.
Jump up ^ "2012 World Series". Baseball-Reference.com. Retrieved October 31, 2013.
Jump up ^ "2013 World Series". Baseball-Reference.com. Retrieved December 19, 2013.
Jump up ^ "2014 World Series". Baseball-Reference.com. Retrieved October 29, 2014.
Jump up ^ "2015 World Series". Baseball-Reference.com. Retrieved November 1, 2015.
Jump up ^ "2016 World Series". Baseball-Reference.com. Retrieved November 3, 2016.
Jump up ^ "2017 World Series". Baseball-Reference.com. Retrieved November 1, 2017.
Jump up ^ "Brewers switch leagues, join Reds in NL Central". The Kentucky Post (Associated Press). E. W. Scripps Company. November 6, 1997. Archived from the original on May 5, 2005.
External links[edit]
Wikimedia Commons has media related to World Series.
WorldSeries.com – official website
List of World Series winning rosters
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World Series champions
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1911: Philadelphia Athletics
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1943: New York Yankees
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1962: New York Yankees
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1993: Toronto Blue Jays
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1998: New York Yankees
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2004: Boston Red Sox
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2006: St. Louis Cardinals
2007: Boston Red Sox
2008: Philadelphia Phillies
2009: New York Yankees
2010: San Francisco Giants
2011: St. Louis Cardinals
2012: San Francisco Giants
2013: Boston Red Sox
2014: San Francisco Giants
2015: Kansas City Royals
2016: Chicago Cubs
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[show]
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No World Series was held in 1904 because the NL champions refused to participate; no World Series was held in 1994 due to a players' strike.
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Abacus
From Wikipedia, the free encyclopedia
Jump to: navigation, search
For other uses, see Abacus (disambiguation).
"Abaci" and "Abacuses" redirect here. For the Turkish surname, see Abacı. For the medieval book, see Liber Abaci.
A Chinese abacus, Suanpan
Calculating-Table by Gregor Reisch: Margarita Philosophica, 1503. The woodcut shows Arithmetica instructing an algorist and an abacist (inaccurately represented as Boethius and Pythagoras). There was keen competition between the two from the introduction of the Algebra into Europe in the 12th century until its triumph in the 16th.[1]
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system.[1] The exact origin of the abacus is still unknown. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal.
Abaci come in different designs. Some designs, like the bead frame consisting of beads divided into tens, are used mainly to teach arithmetic, although they remain popular in the post-Soviet states as a tool. Other designs, such as the Japanese soroban, have been used for practical calculations even involving several digits. For any particular abacus design, there usually are numerous different methods to perform a certain type of calculation, which may include basic operations like addition and multiplication, or even more complex ones, such as calculating square roots. Some of these methods may work with non-natural numbers (numbers such as 1.5 and 3⁄4).
Although today many use calculators and computers instead of abaci to calculate, abaci still remain in common use in some countries. Merchants, traders and clerks in some parts of Eastern Europe, Russia, China and Africa use abaci, and they are still used to teach arithmetic to children.[1] Some people who are unable to use a calculator because of visual impairment may use an abacus.
Contents
[hide]
1 Etymology
2 History
2.1 Mesopotamian
2.2 Egyptian
2.3 Persian
2.4 Greek
2.5 Chinese
2.6 Roman
2.7 Indian
2.8 Japanese
2.9 Korean
2.10 Native American
2.11 Russian
3 School abacus
4 Renaissance abaci gallery
5 Uses by the blind
6 Binary abacus
7 See also
8 Notes
9 Footnotes
10 References
11 Further reading
12 External links
12.1 Tutorials
12.2 Abacus curiosities
Etymology[edit]
The use of the word abacus dates before 1387 AD, when a Middle English work borrowed the word from Latin to describe a sandboard abacus. The Latin word came from Greek ἄβαξ abax which means something without base, and improperly, any piece of rectangular board or plank.[2][3][4] Alternatively, without reference to ancient texts on etymology, it has been suggested that it means "a square tablet strewn with dust",[5] or "drawing-board covered with dust (for the use of mathematics)"[6] (the exact shape of the Latin perhaps reflects the genitive form of the Greek word, ἄβακoς abakos). Whereas the table strewn with dust definition is popular, there are those that do not place credence in this at all and in fact state that it is not proven.[7][nb 1] Greek ἄβαξ itself is probably a borrowing of a Northwest Semitic, perhaps Phoenician, word akin to Hebrew ʾābāq (אבק), "dust" (or in post-Biblical sense meaning "sand used as a writing surface").[8]
The preferred plural of abacus is a subject of disagreement, with both abacuses[9] and abaci[9] in use. The user of an abacus is called an abacist.[10]
History[edit]
Mesopotamian[edit]
The period 2700–2300 BC saw the first appearance of the Sumerian abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.[11]
Some scholars point to a character from the Babylonian cuneiform which may have been derived from a representation of the abacus.[12] It is the belief of Old Babylonian[13] scholars such as Carruccio that Old Babylonians "may have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations".[14]
Egyptian[edit]
The use of the abacus in Ancient Egypt is mentioned by the Greek historian Herodotus, who writes that the Egyptians manipulated the pebbles from right to left, opposite in direction to the Greek left-to-right method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered.[15]
Persian[edit]
During the Achaemenid Empire, around 600 BC the Persians first began to use the abacus.[16] Under the Parthian, Sassanian and Iranian empires, scholars concentrated on exchanging knowledge and inventions with the countries around them – India, China, and the Roman Empire, when it is thought to have been exported to other countries.
Greek[edit]
An early photograph of the Salamis Tablet, 1899. The original is marble and is held by the National Museum of Epigraphy, in Athens.
The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC.[17] Also Demosthenes (384 BC–322 BC) talked of the need to use pebbles for calculations too difficult for your head.[18][19] A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Polybius mention men that sometimes stood for more and sometimes for less, like the pebbles on an abacus.[19] The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus saw use in Achaemenid Persia, the Etruscan civilization, Ancient Rome and, until the French Revolution, the Western Christian world.
A tablet found on the Greek island Salamis in 1846 AD (the Salamis Tablet), dates back to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble 149 cm (59 in) long, 75 cm (30 in) wide, and 4.5 cm (2 in) thick, on which are 5 groups of markings. In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semicircle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.[20] Also from this time frame the Darius Vase was unearthed in 1851. It was covered with pictures including a "treasurer" holding a wax tablet in one hand while manipulating counters on a table with the other.[18]
Chinese[edit]
Main article: Suanpan
A Chinese abacus (suanpan) (the number represented in the picture is 6,302,715,408)
Abacus
Chinese
算盤
Literal meaning
"calculating tray"
[show]Transcriptions
Standard Mandarin
Hanyu Pinyin
suànpán
IPA
[swân.pʰǎn]
Yue: Cantonese
Yale Romanization
syun-pùhn
IPA
[sȳːnpʰǔːn]
Jyutping
syun3-pun4
Southern Min
Hokkien POJ
sǹg-pôaⁿ
Tâi-lô
sǹg-puânn
The earliest known written documentation of the Chinese abacus dates to the 2nd century BC.[21]
The Chinese abacus, known as the suanpan (算盤, lit. "counting tray"), is typically 20 cm (8 in) tall and comes in various widths depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. If you move them toward the beam, you count their value. If you move away, you don't count their value.[22] The suanpan can be reset to the starting position instantly by a quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center.
Suanpan can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed. There are currently schools teaching students how to use it.
In the long scroll Along the River During the Qingming Festival painted by Zhang Zeduan during the Song dynasty (960–1297), a suanpan is clearly visible beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao).
The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, as there is some evidence of a trade relationship between the Roman Empire and China. However, no direct connection can be demonstrated, and the similarity of the abaci may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Korean and Japanese) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2. (Incidentally, this allows use with a hexadecimal numeral system, which was used for traditional Chinese measures of weight.) Instead of running on wires as in the Chinese, Korean, and Japanese models, the beads of Roman model run in grooves, presumably making arithmetic calculations much slower.
Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a place holder. The zero was probably introduced to the Chinese in the Tang dynasty (618–907) when travel in the Indian Ocean and the Middle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians.
Roman[edit]
Main article: Roman abacus
Copy of a Roman abacus
The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles (calculi) were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens etc. as in the Roman numeral system. This system of 'counter casting' continued into the late Roman empire and in medieval Europe, and persisted in limited use into the nineteenth century.[23] Due to Pope Sylvester II's reintroduction of the abacus with very useful modifications, it became widely used in Europe once again during the 11th century[24][25] This abacus used beads on wires, unlike the traditional Roman counting boards, which meant the abacus could be used much faster.[26]
Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin layer of black wax on which columns and figures were inscribed using a stylus.[27]
One example of archaeological evidence of the Roman abacus, shown here in reconstruction, dates to the 1st century AD. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each. The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives –five units, five tens etc., essentially in a bi-quinary coded decimal system, obviously related to the Roman numerals. The short grooves on the right may have been used for marking Roman "ounces" (i.e. fractions).
Indian[edit]
There is no clear evidence for use of the abacus in India. The decimal number system invented in India replaced the abacus in Western Europe.[28]
The Abhidharmakośabhāṣya of Vasubandhu (316-396), a Sanskrit work on Buddhist philosophy, says that the second-century CE philosopher Vasumitra said that "placing a wick (Sanskrit vartikā) on the number one (ekāṅka) means it is a one, while placing the wick on the number hundred means it is called a hundred, and on the number one thousand means it is a thousand". It is unclear exactly what this arrangement may have been. Around the 5th century, Indian clerks were already finding new ways of recording the contents of the Abacus.[29] Hindu texts used the term śūnya (zero) to indicate the empty column on the abacus.[30]
Japanese[edit]
Main article: Soroban
Japanese soroban
In Japanese, the abacus is called soroban (算盤, そろばん, lit. "Counting tray"), imported from China in the 14th century.[31] It was probably in use by the working class a century or more before the ruling class started, as the class structure did not allow for devices used by the lower class to be adopted or used by the ruling class.[32] The 1/4 abacus, which is suited to decimal calculation, appeared circa 1930, and became widespread as the Japanese abandoned hexadecimal weight calculation which was still common in China. The abacus is still manufactured in Japan today even with the proliferation, practicality, and affordability of pocket electronic calculators. The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation. Using visual imagery of a soroban, one can arrive at the answer in the same time as, or even faster than, is possible with a physical instrument.[33]
Korean[edit]
The Chinese abacus migrated from China to Korea around 1400 AD.[18][34][35] Koreans call it jupan (주판), supan (수판) or jusan (주산).[36]
Native American[edit]
Representation of an Inca quipu
A yupana as used by the Incas.
Some sources mention the use of an abacus called a nepohualtzintzin in ancient Aztec culture.[37] This Mesoamerican abacus used a 5-digit base-20 system.[38] The word Nepōhualtzintzin [nepoːwaɬˈt͡sint͡sin] comes from Nahuatl and it is formed by the roots; Ne – personal -; pōhual or pōhualli [ˈpoːwalːi] – the account -; and tzintzin [ˈt͡sint͡sin] – small similar elements. Its complete meaning was taken as: counting with small similar elements by somebody. Its use was taught in the Calmecac to the temalpouhqueh [temaɬˈpoʍkeʔ], who were students dedicated to take the accounts of skies, from childhood.
The Nepōhualtzintzin was divided in two main parts separated by a bar or intermediate cord. In the left part there were four beads, which in the first row have unitary values (1, 2, 3, and 4), and in the right side there are three beads with values of 5, 10, and 15 respectively. In order to know the value of the respective beads of the upper rows, it is enough to multiply by 20 (by each row), the value of the corresponding account in the first row.
Altogether, there were 13 rows with 7 beads in each one, which made up 91 beads in each Nepōhualtzintzin. This was a basic number to understand, 7 times 13, a close relation conceived between natural phenomena, the underworld and the cycles of the heavens. One Nepōhualtzintzin (91) represented the number of days that a season of the year lasts, two Nepōhualtzitzin (182) is the number of days of the corn's cycle, from its sowing to its harvest, three Nepōhualtzintzin (273) is the number of days of a baby's gestation, and four Nepōhualtzintzin (364) completed a cycle and approximate a year (11/4 days short). When translated into modern computer arithmetic, the Nepōhualtzintzin amounted to the rank from 10 to the 18 in floating point, which calculated stellar as well as infinitesimal amounts with absolute precision, meant that no round off was allowed.
The rediscovery of the Nepōhualtzintzin was due to the Mexican engineer David Esparza Hidalgo,[39] who in his wanderings throughout Mexico found diverse engravings and paintings of this instrument and reconstructed several of them made in gold, jade, encrustations of shell, etc.[40] There have also been found very old Nepōhualtzintzin attributed to the Olmec culture, and even some bracelets of Mayan origin, as well as a diversity of forms and materials in other cultures.
George I. Sanchez, "Arithmetic in Maya", Austin-Texas, 1961 found another base 5, base 4 abacus in the Yucatán peninsula that also computed calendar data. This was a finger abacus, on one hand 0, 1, 2, 3, and 4 were used; and on the other hand 0, 1, 2 and 3 were used. Note the use of zero at the beginning and end of the two cycles. Sanchez worked with Sylvanus Morley, a noted Mayanist.
The quipu of the Incas was a system of colored knotted cords used to record numerical data,[41] like advanced tally sticks – but not used to perform calculations. Calculations were carried out using a yupana (Quechua for "counting tool"; see figure) which was still in use after the conquest of Peru. The working principle of a yupana is unknown, but in 2001 an explanation of the mathematical basis of these instruments was proposed by Italian mathematician Nicolino De Pasquale. By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence would keep the number of grains within any one field at a minimum.[42]
Russian[edit]
Russian abacus
The Russian abacus, the schoty (счёты), usually has a single slanted deck, with ten beads on each wire (except one wire, usually positioned near the user, with four beads for quarter-ruble fractions). Older models have another 4-bead wire for quarter-kopeks, which were minted until 1916. The Russian abacus is often used vertically, with wires from left to right in the manner of a book. The wires are usually bowed to bulge upward in the center, to keep the beads pinned to either of the two sides. It is cleared when all the beads are moved to the right. During manipulation, beads are moved to the left. For easy viewing, the middle 2 beads on each wire (the 5th and 6th bead) usually are of a different color from the other eight beads. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color.
As a simple, cheap and reliable device, the Russian abacus was in use in all shops and markets throughout the former Soviet Union, and the usage of it was taught in most schools until the 1990s.[43][44] Even the 1874 invention of mechanical calculator, Odhner arithmometer, had not replaced them in Russia and likewise the mass production of Felix arithmometers since 1924 did not significantly reduce their use in the Soviet Union.[45] The Russian abacus began to lose popularity only after the mass production of microcalculators had started in the Soviet Union in 1974. Today it is regarded as an archaism and replaced by the handheld calculator.
The Russian abacus was brought to France around 1820 by the mathematician Jean-Victor Poncelet, who served in Napoleon's army and had been a prisoner of war in Russia.[46] The abacus had fallen out of use in western Europe in the 16th century with the rise of decimal notation and algorismic methods. To Poncelet's French contemporaries, it was something new. Poncelet used it, not for any applied purpose, but as a teaching and demonstration aid.[47] The Turks and the Armenian people also used abaci similar to the Russian schoty. It was named a coulba by the Turks and a choreb by the Armenians.[48]
School abacus[edit]
Early 20th century abacus used in Danish elementary school.
A twenty bead rekenrek
Around the world, abaci have been used in pre-schools and elementary schools as an aid in teaching the numeral system and arithmetic.
In Western countries, a bead frame similar to the Russian abacus but with straight wires and a vertical frame has been common (see image). It is still often seen as a plastic or wooden toy.
The wire frame may be used either with positional notation like other abaci (thus the 10-wire version may represent numbers up to 9,999,999,999), or each bead may represent one unit (so that e.g. 74 can be represented by shifting all beads on 7 wires and 4 beads on the 8th wire, so numbers up to 100 may be represented). In the bead frame shown, the gap between the 5th and 6th wire, corresponding to the color change between the 5th and the 6th bead on each wire, suggests the latter use.
The red-and-white abacus is used in contemporary primary schools for a wide range of number-related lessons. The twenty bead version, referred to by its Dutch name rekenrek ("calculating frame"), is often used, sometimes on a string of beads, sometimes on a rigid framework.[49]
Renaissance abaci gallery[edit]
Uses by the blind[edit]
An adapted abacus, invented by Tim Cranmer, called a Cranmer abacus is still commonly used by individuals who are blind. A piece of soft fabric or rubber is placed behind the beads so that they do not move inadvertently. This keeps the beads in place while the users feel or manipulate them. They use an abacus to perform the mathematical functions multiplication, division, addition, subtraction, square root and cube root.[50]
Although blind students have benefited from talking calculators, the abacus is still very often taught to these students in early grades, both in public schools and state schools for the blind. The abacus teaches mathematical skills that can never be replaced with talking calculators and is an important learning tool for blind students.[51] Blind students also complete mathematical assignments using a braille-writer and Nemeth code (a type of braille code for mathematics) but large multiplication and long division problems can be long and difficult. The abacus gives blind and visually impaired students a tool to compute mathematical problems that equals the speed and mathematical knowledge required by their sighted peers using pencil and paper. Many blind people find this number machine a very useful tool throughout life.[50]
Binary abacus[edit]
Two binary abaci constructed by Dr. Robert C. Good, Jr., made from two Chinese abaci
The binary abacus is used to explain how computers manipulate numbers.[52] The abacus shows how numbers, letters, and signs can be stored in a binary system on a computer, or via ASCII. The device consists of a series of beads on parallel wires arranged in three separate rows. The beads represent a switch on the computer in either an "on" or "off" position.
See also[edit]
Chinese Zhusuan
Chisanbop
Logical abacus
Mental abacus
Napier's bones
Sand table
Slide rule
Soroban
Suanpan
Notes[edit]
Jump up ^ Both C. J. Gadd, a keeper of the Egyptian and Assyrian Antiquities at the British Museum, and Jacob Levy, a Jewish Historian who wrote Neuhebräisches und chaldäisches wörterbuch über die Talmudim und Midraschim [Neuhebräisches and Chaldean dictionary on the Talmuds and Midrashi] disagree with the "dust table" theory.[7]
Footnotes[edit]
^ Jump up to: a b c Boyer & Merzbach 1991, pp. 252–253
Jump up ^ de Stefani 1909, p. 2
Jump up ^ Gaisford 1962, p. 2
Jump up ^ Lasserre & Livadaras 1976, p. 4
Jump up ^ Klein 1966, p. 1
Jump up ^ Onions, Friedrichsen & Burchfield 1967, p. 2
^ Jump up to: a b Pullan 1968, p. 17
Jump up ^ Huehnergard 2011, p. 2
^ Jump up to: a b Brown 1993, p. 2
Jump up ^ Gove 1976, p. 1
Jump up ^ Ifrah 2001, p. 11
Jump up ^ Crump 1992, p. 188
Jump up ^ Melville 2001
Jump up ^ Carruccio 2006, p. 14
Jump up ^ Smith 1958, pp. 157–160
Jump up ^ Carr 2014
Jump up ^ Ifrah 2001, p. 15
^ Jump up to: a b c Williams 1997, p. 55
^ Jump up to: a b Pullan 1968, p. 16
Jump up ^ Williams 1997, pp. 55–56
Jump up ^ Ifrah 2001, p. 17
Jump up ^ Fernandes 2003
Jump up ^ Pullan 1968, p. 18
Jump up ^ Brown 2010, pp. 81–82
Jump up ^ Brown 2011
Jump up ^ Huff 1993, p. 50
Jump up ^ Ifrah 2001, p. 18
Jump up ^ Rowlett, Russ (2004-07-04), Roman and "Arabic" Numerals, University of North Carolina at Chapel Hill, retrieved 2009-06-22
Jump up ^ Körner 1996, p. 232
Jump up ^ Mollin 1998, p. 3
Jump up ^ Gullberg 1997, p. 169
Jump up ^ Williams 1997, p. 65
Jump up ^ Murray 1982
Jump up ^ Anon 2002
Jump up ^ Jami 1998, p. 4
Jump up ^ Anon 2013
Jump up ^ Sanyal 2008
Jump up ^ Anon 2004
Jump up ^ Hidalgo 1977, p. 94
Jump up ^ Hidalgo 1977, pp. 94–101
Jump up ^ Albree 2000, p. 42
Jump up ^ Aimi & De Pasquale 2005
Jump up ^ Burnett & Ryan 1998, p. 7
Jump up ^ Hudgins 2004, p. 219
Jump up ^ Leushina 1991, p. 427
Jump up ^ Trogeman & Ernst 2001, p. 24
Jump up ^ Flegg 1983, p. 72
Jump up ^ Williams 1997, p. 64
Jump up ^ West 2011, p. 49
^ Jump up to: a b Terlau & Gissoni 2006
Jump up ^ Presley & D'Andrea 2009
Jump up ^ Good Jr. 1985, p. 34
References[edit]
Aimi, Antonio; De Pasquale, Nicolino (2005). "Andean Calculators" (PDF). translated by Del Bianco, Franca. Archived (PDF) from the original on August 1, 2014. Retrieved July 31, 2014.
Albree, Joe (2000). Hessenbruch, Arne, ed. Reader's Guide to the History of Science. London, UK: Fitzroy Dearborn Publishers. ISBN 1-884964-29-X.
Anon (September 12, 2002). "Abacus middle ages, region of origin Middle East". The History of Computing Project. Archived from the original on July 31, 2014. Retrieved July 31, 2014.
Anon (2004). "Nepohualtzintzin, The Pre Hispanic Computer". Iberamia 2004. Archived from the original on August 1, 2014. Retrieved July 31, 2014.
Anon (2013). 주판 [Abacus]. enc.daum.net (in Korean). Archived from the original on July 31, 2014. Retrieved July 31, 2014.
Boyer, Carl B.; Merzbach, Uta C. (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.
Brown, Lesley, ed. (1993). "abacus". Shorter Oxford English Dictionary on Historical Principles. 2: A-K (5th ed.). Oxford, UK: Oxford University Press. ISBN 978-0-19-860575-1.
Brown, Nancy Marie (2010). The Abacus and the Cross: The Story of the Pope Who Brought the Light of Science to the Dark Ages. Philadelphia, PA: Basic Books. ISBN 978-0-465-00950-3.
Brown, Nancy Marie (January 2, 2011). "Everything You Think You Know About the Dark Ages is Wrong". rd magazine (Interview). USC Annenberg. Archived from the original on July 31, 2014.
Burnett, Charles; Ryan, W. F. (1998). "Abacus (Western)". In Bud, Robert; Warner, Deborah Jean. Instruments of Science: An Historical Encyclopedia. Garland Encyclopedias in the History of Science. New York, NY: Garland Publishing, Inc. pp. 5–7. ISBN 978-0-8153-1561-2.
Carr, Karen (2014). "West Asian Mathematics". Kidipede. History for Kids!. Archived from the original on June 19, 2014. Retrieved Jun 19, 2014.
Carruccio, Ettore (2006). Mathematics and Logic In History and In Contemporary Thought. translated by Quigly, Isabel. Aldine Transaction. ISBN 978-0-202-30850-0.
Crump, Thomas (1992). The Japanese Numbers Game: The Use and Understanding of Numbers in Modern Japan. The Nissan Institute/Routledge Japanese Studies Series. Routledge. ISBN 978-0-415-05609-0.
de Stefani, Aloysius, ed. (1909). Etymologicum Gudianum quod vocatur; recensuit et apparatum criticum indicesque adiecit. I. Leipzig, Germany: Teubner. LCCN 23016143.
Fernandes, Luis (November 27, 2003). "A Brief Introduction to the Abacus". ee.ryerson.ca. Retrieved July 31, 2014.
Flegg, Graham (1983). Numbers: Their History and Meaning. Dover Books on Mathematics. Mineola, NY: Courier Dover Publications. ISBN 978-0-233-97516-0.
Gaisford, Thomas, ed. (1962) [1848]. Etymologicon Magnum seu verius Lexicon Saepissime vocabulorum origines indagans ex pluribus lexicis scholiastis et grammaticis anonymi cuiusdam opera concinnatum [The Great Etymologicon: Which Contains the Origins of the Lexicon of Words from a Large Number or Rather with a Great Amount of Research Lexicis Scholiastis and Connected Together by the Works of Anonymous Grammarians] (in Latin). Amsterdam, The Netherlands: Adolf M. Hakkert.
Good Jr., Robert C. (Fall 1985). "The Binary Abacus: A Useful Tool for Explaining Computer Operations". Journal of Computers in Mathematics and Science Teaching. 5 (1): 34–37.
Gove, Philip Babcock, ed. (1976). "abacist". Websters Third New International Dictionary (17th ed.). Springfield, MA: G. & C. Merriam Company. ISBN 0-87779-101-5.
Gullberg, Jan (1997). Mathematics: From the Birth of Numbers. Illustrated by Pär Gullberg. New York, NY: W. W. Norton & Company. ISBN 0-393-04002-X.
Hidalgo, David Esparza (1977). Nepohualtzintzin: Computador Prehispánico en Vigencia [The Nepohualtzintzin: An Effective Pre-Hispanic Computer] (in Spanish). Tlacoquemécatl, Mexico: Editorial Diana.
Hudgins, Sharon (2004). The Other Side of Russia: A Slice of Life in Siberia and the Russian Far East. Eugenia & Hugh M. Stewart '26 Series on Eastern Europe. Texas A&M University Press. ISBN 978-1-58544-404-5.
Huehnergard, John, ed. (2011). "Appendix of Semitic Roots, under the root ʾbq.". American Heritage Dictionary of the English Language (5th ed.). Houghton Mifflin Harcourt Trade. ISBN 978-0-547-04101-8.
Huff, Toby E. (1993). The Rise of Early Modern Science: Islam, China and the West (1st ed.). Cambridge, UK: Cambridge University Press. ISBN 978-0-521-43496-6.
Ifrah, Georges (2001). The Universal History of Computing: From the Abacus to the Quantum Computer. New York, NY: John Wiley & Sons, Inc. ISBN 978-0-471-39671-0.
Jami, Catherine (1998). "Abacus (Eastern)". In Bud, Robert; Warner, Deborah Jean. Instruments of Science: An Historical Encyclopedia. New York, NY: Garland Publishing, Inc. ISBN 0-8153-1561-9.
Klein, Ernest, ed. (1966). "abacus". A Comprehensive Etymological Dictionary of the English Language. I: A-K. Amsterdam: Elsevier Publishing Company.
Körner, Thomas William (1996). The Pleasures of Counting. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-56823-4.
Lasserre, Franciscus; Livadaras, Nicolaus, eds. (1976). Etymologicum Magnum Genuinum: Symeonis Etymologicum: Una Cum Magna Grammatica (in Greek and Latin). Primum: α — άμωσϒέπωϛ. Rome, Italy: Edizioni dell'Ateneo. LCCN 77467964.
Leushina, A. M. (1991). The development of elementary mathematical concepts in preschool children. National Council of Teachers of Mathematics. ISBN 978-0-87353-299-0.
Melville, Duncan J. (May 30, 2001). "Chronology of Mesopotamian Mathematics". St. Lawrence University. It.stlawu.edu. Archived from the original on June 19, 2014. Retrieved Jun 19, 2014.
Mish, Frederick C., ed. (2003). "abacus". Merriam-Webster's Collegiate Dictionary (11th ed.). Merriam-Webster, Inc. ISBN 0-87779-809-5.
Mollin, Richard Anthony (September 1998). Fundamental Number Theory with Applications. Discrete Mathematics and its Applications. Boca Raton, FL: CRC Press. ISBN 978-0-8493-3987-5.
Murray, Geoffrey (July 20, 1982). "Ancient calculator is a hit with Japan's newest generation". The Christian Science Monitor. CSMonitor.com. Archived from the original on July 31, 2014. Retrieved July 31, 2014.
Onions, C. T.; Friedrichsen, G. W. S.; Burchfield, R. W., eds. (1967). "abacus". The Oxford Dictionary of English Etytmology. Oxford, UK: Oxford at the Clarendon Press.
Presley, Ike; D'Andrea, Frances Mary (2009). Assistive Technology for Students who are Blind Or Visually Impaired: A Guide to Assessment. American Foundation for the Blind. p. 61. ISBN 978-0-89128-890-9.
Pullan, J. M. (1968). The History of the Abacus. New York, NY: Frederick A. Praeger, Inc., Publishers. ISBN 978-0-09-089410-9. LCCN 72075113.
Reilly, Edwin D., ed. (2004). Concise Encyclopedia of Computer Science. New York, NY: John Wiley and Sons, Inc. ISBN 978-0-470-09095-4.
Sanyal, Amitava (July 6, 2008). "Learning by Beads". Hindustan Times.
Smith, David Eugene (1958). History of Mathematics. Dover Books on Mathematics. 2: Special Topics of Elementary Mathematics. Courier Dover Publications. ISBN 978-0-486-20430-7.
Stearns, Peter N.; Langer, William Leonard, eds. (2001). The Encyclopedia of World History (6th ed.). New York, NY: Houghton Mifflin Harcourt. ISBN 978-0-395-65237-4.
Terlau, Terrie; Gissoni, Fred (July 20, 2006). "Abacus: Position Paper". APH.org. Archived from the original on August 1, 2014. Retrieved July 31, 2014.
Trogeman, Georg; Ernst, Wolfgang (2001). Trogeman, Georg; Nitussov, Alexander Y.; Ernst, Wolfgang, eds. Computing in Russia: The History of Computer Devices and Information Technology Revealed. Braunschweig/Wiesbaden: Vieweg+Teubner Verlag. ISBN 978-3-528-05757-2.
West, Jessica F. (2011). Number sense routines : building numerical literacy every day in grades K-3. Portland, Me.: Stenhouse Publishers. ISBN 978-1-57110-790-9.
Williams, Michael R. (1997). Baltes, Cheryl, ed. A History of Computing technology (2nd ed.). Los Alamitos, CA: IEEE Computer Society Press. ISBN 0-8186-7739-2. LCCN 96045232.
Yoke, Ho Peng (2000). Li, Qi and Shu: An Introduction to Science and Civilization in China. Dover Science Books. Courier Dover Publications. ISBN 978-0-486-41445-4.
Further reading[edit]
Fernandes, Luis (2013). "The Abacus: A Brief History". ee.ryerson.ca. Archived from the original on July 31, 2014. Retrieved July 31, 2014.
Menninger, Karl W. (1969), Number Words and Number Symbols: A Cultural History of Numbers, MIT Press, ISBN 0-262-13040-8
Kojima, Takashi (1954), The Japanese Abacus: its Use and Theory, Tokyo: Charles E. Tuttle Co., Inc., ISBN 0-8048-0278-5
Kojima, Takashi (1963), Advanced Abacus: Japanese Theory and Practice, Tokyo: Charles E. Tuttle Co., Inc., ISBN 0-8048-0003-0
Stephenson, Stephen Kent (July 7, 2010), Ancient Computers, IEEE Global History Network, arXiv:1206.4349  , retrieved 2011-07-02
Stephenson, Stephen Kent (2013), Ancient Computers, Part I - Rediscovery, Edition 2, ISBN 1-4909-6437-1
External links[edit]
Look up abacus in Wiktionary, the free dictionary.
Wikimedia Commons has media related to Abacus.
Texts on Wikisource:
"Abacus". Encyclopædia Britannica (11th ed.). 1911.
"Abacus", from A Dictionary of Greek and Roman Antiquities, 3rd ed., 1890.
Tutorials[edit]
Heffelfinger, Totton & Gary Flom, Abacus: Mystery of the Bead - an Abacus Manual
Min Multimedia
Stephenson, Stephen Kent (2009), How to use a Counting Board Abacus
Abacus curiosities[edit]
Schreiber, Michael (2007), Abacus, The Wolfram Demonstrations Project
Abacus in Various Number Systems at cut-the-knot
Java applet of Chinese, Japanese and Russian abaci
An atomic-scale abacus
Examples of Abaci
Aztex Abacus
Authority control
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