PolyAgent/wiki_arabic_en_parallel_20231101 huggingface dataset:
فرانك ستولن

فرانك ستولن (و. 1913 – 2007 م) هو مهندس من الولايات المتحدة الأمريكية . ولد في ديترويت .
توفي في ترافيرس سيتي، عن عمر يناهز 94 عاماً.
جوائز
حصل على جوائز منها:
قلادة العلوم الوطنية الأمريكية في مجال التكنولوجيا والإبتكار.
مراجع
أشخاص من ديترويت (ميشيغان)
أشخاص من ديترويت
مهندسون
مواليد 1913
مواليد في ديترويت
وفيات 2007
وفيات في ترافيرس سيتي
هيو بيلي

هيو بيلي هو صحفي أمريكي، ولد في 23 أكتوبر 1890، وتوفي في 1 مارس 1966.
مراجع
وصلات خارجية
حرية الصحافة
صحفيون أمريكيون
صحفيون أمريكيون في القرن 20
مراسلون حربيون أمريكيون في الحرب العالمية الثانية
مواليد 1890
وفيات 1966
يونايتد برس إنترناشيونال
الكويكب 301580

الكويكب 301580، التعين المؤقت له الكويكب 2009UT94. وهو كويكب من كويكبات طروادة ينتمي إلى كويكبات معسكر الإغريق اكتشف في سنة 2009.
كباقي كويكبات معسكر الإغريق يقع مداره في النقطة L4 من نقاط لاغرانج وفق نظام الشمس - المشتري. يبلغ القدر المطلق لهذا الكويكب 12.9 ونصف المحور الرئيسي لمداره 5.159 وحدة فلكية. وقد تم رصده 6 مرة حتى شباط/فبراير 2013. الإشارة المرجعية له وفق الملحق الدوري لمدارات الكويكبات هي MPO227322
المراجع
كويكبات معسكر الإغريق
رابطة كرة القدم اليابانية 2002

رابطة كرة القدم اليابانية 2002 هو موسم من . فاز فيه هوندا إف سي.
نتائج الموسم
مراجع
دوريات كرة قدم يابانية في 2002
رابطة كرة القدم اليابانية
مواسم رابطة كرة القدم اليابانية
منشأة شلبي

منشأة شلبي
قرية منشأة شلبى هي إحدى القرى التابعة لمركز كفر صقر في محافظة الشرقية في جمهورية مصر العربية. حسب إحصاءات سنة 2006، بلغ إجمالي السكان في منشأة شلبى 1862 نسمة، منهم 989 رجل و873 امرأة.
التاريخ
قرية منشأة شلبي من القرى القديمة، واسمها الأصلي وقت الفتح الإسلامي لمصر «سيشنت» ، وقد وردت باسم «الأشانيط» في أعمال الشرقية ضمن قرى الروك الناصري التي أحصاها ابن الجيعان في كتاب «التحفة السنية بأسماء البلاد المصرية». وفي العصر العثماني ورد اسم «الأشانيط» في التربيع العثماني الذي أجراه الوالي العثماني سليمان باشا الخادم في عصر السلطان العثماني سليمان القانوني ضمن قرى ولاية الشرقية، وفي تاريخ 1228هـ/1813م الذي عدّ قرى مصر بعد المسح الذي قام به محمد علي باشا باسم «الأشانيط» ضمن قرى مديرية الشرقية. وفي سنة 1236هـ/1821م، قُسّمت «الأشانيط» إلى شنيط الحرابوة و«شنيط القرادنة». وفي سنة 1363هـ/1944م، تغيّر الاسم من «شنيط القرادنة» إلى «منشأة شلبي» بطلب من عمدتها.
طالع أيضا
محافظة الشرقية
قائمة قرى محافظة الشرقية
المصادر
قرى كفر صقر
Wellington Camargo

Wellington Camargo do Nascimento, also known as Tom (born 7 April 1990) is a Brazilian footballer who plays as a midfielder. He played for FK Rad in the 2012–13 Serbian SuperLiga.
Career
Born in Carlópolis, he started playing as senior with Campo Mourão. During the first half of 2010 he played with Campo Mourão U-20 team, having scored 10 goals in the Campeonato Paranaense U-20, and also for the senior team, having scored 5 goals. On September 20, 2010 he signed with Grêmio Maringá.
In the season 2011–12 he played with PFC Slavia Sofia in the Bulgarian A PFG.
In August 2013, Wellington Camargo signed with Serbian top-flight side FK Rad.
References
1990 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
PFC Slavia Sofia players
FK Rad players
Brazilian expatriate sportspeople in Bulgaria
Expatriate men's footballers in Bulgaria
Expatriate men's footballers in Serbia
Men's association football midfielders
قائمة مدن إنديانا

قائمة مدن إنديانا هذه قائمة بمدن ولاية إنديانا في الولايات المتحدة في 7 يوليو 2012.
مراجع
وصلات خارجية
Indiana Association of Cities & Towns
قوائم متعلقة بجغرافيا إنديانا
قوائم مدن الولايات المتحدة حسب الولاية
الجبب (إب)

الجبب (إب)
الجبب هي إحدى قرى عزلة بلادشار بمديرية إب التابعة لمحافظة إب، بلغ تعداد سكانها 230 نسمة حسب تعداد اليمن لعام 2004.
مراجع وروابط خارجية
World Gazetteer:Yemen
الجهاز المركزي للإحصاء بالجمهورية اليمنية
المركز الوطني للمعلومات باليمن
الجبب
مارتي ليونز

مارتي ليونز هو لاعب كرة قدم أمريكية ولاعب كرة قدم أمريكي في مراكز ، ولد في 15 يناير 1957 في تاكوما بارك في الولايات المتحدة. لعب مع نيويورك جتس.
مراجع
وصلات خارجية
أشخاص على قيد الحياة
أشخاص من بينيلاس بارك
أشخاص من تاكوما بارك
أعضاء قاعة مشاهير كرة القدم الأمريكية الجامعية
رياضيون من مقاطعة بينيلاس (فلوريدا)
لاعبو ألاباما كريمزون تايد فوتبول
لاعبو كرة القدم الأمريكية الجامعية من فئة أول-أمريكان
لاعبو نيويورك جتس
مذيعو الدوري الوطني لكرة القدم الأمريكية
مذيعو نيويورك جتس
مصطدمو دفاع كرة القدم الأمريكية
مواليد 1957
نهاية الدفاع كرة القدم الأمريكية
لاعبو كرة قدم أمريكية من مقاطعة مونغومري (ميريلاند)
لاعبو كرة قدم أمريكية من مقاطعة بينيلاس (فلوريدا)
هاينرش هيرتل

هاينرش هيرتل هو أستاذ جامعي ومهندس ألماني، ولد في 13 نوفمبر 1901 في دوسلدورف في ألمانيا، وتوفي في 5 ديسمبر 1982 في برلين في ألمانيا.
مراجع
وصلات خارجية
أشخاص من دوسلدورف
أعضاء هيئة تدريس معهد برلين للتكنولوجيا
خريجو جامعة ميونخ التقنية
ضباط الصلبان من وسام استحقاق جمهورية ألمانيا الاتحادية
علماء من دوسلدورف
مصممو طائرات
مهندسو فضاء ألمان
مهندسون من شمال الراين-وستفاليا
مواليد 1901
مواليد 1902
وفيات 1982
Alfred Murdoch

Alfred Murdoch
Alfred James (Fred) Murdoch (18 April 1877 – 1 June 1960) was a New Zealand politician, first as an Independent Liberal then of the United Party, and from 1943 the National Party. He was Minister of Agriculture and Minister of Mines from 1930 to 1931 in the United Government of New Zealand.
Biography
Early life
Murdoch was born in 1877 in Onehunga. He trained as a school teacher and taught at Onehunga, Northcote, Hikurangi, Mata, and Ruataka. He retired from teaching in 1919 and became a farmer, breeding Jersey cattle. For a time, he was the chairman of the New Zealand Dairy Board, and he belonged to the Chamber of Commerce in Whangārei.
Political career
Murdoch unsuccessfully contested the electorate in the as an independent Liberal against the incumbent from the Reform Party, Francis Mander. Mander retired at the , and Murdoch was elected. At the next election in , Murdoch was defeated by William Jones of the Reform Party, but he defeated Jones in turn in when he stood for the United Party. Murdoch was Minister of Agriculture, and Minister of Mines, in the United Government under George Forbes from May 1930 to September 1931.
After two parliamentary terms, Murdoch was defeated in by Jim Barclay of the Labour Party. In , Murdoch, now standing for the National Party, defeated Barclay and won the electorate back, and held it until he was deselected ahead of the .
In early 1954, the 77-year-old Murdoch was challenged for the National nomination by William Rodney Lewin Vallance, the deputy mayor of Whangarei. Vallance won a postal ballot of members, an outcome which split the Marsden National Party into two feuding factions. After it emerged that Vallance was in trouble with his taxes he was in turn deselected and replaced by Don McKay, the chairman of the Marsden electorate committee. Vallance ran as an independent candidate and split the vote, almost costing National the seat. Murdoch was only the second sitting National MP to not win reselection.
Murdoch died in 1960.
Notes
References
|-
|-
1877 births
1960 deaths
New Zealand National Party MPs
Members of the Cabinet of New Zealand
United Party (New Zealand) MPs
Independent MPs of New Zealand
Unsuccessful candidates in the 1919 New Zealand general election
Unsuccessful candidates in the 1925 New Zealand general election
Unsuccessful candidates in the 1938 New Zealand general election
Unsuccessful candidates in the 1935 New Zealand general election
Members of the New Zealand House of Representatives
New Zealand MPs for North Island electorates
Bob Beyer

Bob Beyer
Robert C. Beyer (born December 10, 1961) is an American professional basketball coach who serves as an assistant coach for the Charlotte Hornets of the National Basketball Association (NBA).
Early life and education
Beyer was born in LeRoy, New York and graduated from Alfred University in 1984 with a bachelor's degree in history with minors in coaching, writing, and secondary education. At Alfred, Beyer played three seasons on the basketball team before suffering a career-ending injury. Beyer served as assistant coach to the team as a senior in the 1983–84 season. Beyer then earned his master's degree in curriculum planning and development from the University of Albany in 1989.
Career
As a graduate student at Albany, Beyer was an assistant coach for the Albany Great Danes men's basketball team from 1985 to 1989. Beyer then was an assistant coach at Siena College from 1989 to 1993 and the University of Wisconsin from 1993 to 1994. Beyer returned to Siena to be head coach from 1994 to 1997. He returned to the assistant coaching ranks with Northwestern University from 1997 to 2000. Under Bob Knight, Beyer was an assistant coach at Texas Tech from 2001 to 2003. For the season, Beyer was an assistant coach with the Toronto Raptors of the NBA; he was an advance scout the next season.
On July 3, 2007, Beyer was one of four assistants hired to serve under head coach of the NBA's Orlando Magic, Stan Van Gundy, for the 2007–08 season.
The Golden State Warriors of the NBA hired Beyer on September 11, 2012.
On July 1, 2013, Beyer was hired by the Charlotte Bobcats as an assistant coach for the 2013–14 season.
On May 30, 2014, Beyer was one of three assistants hired to serve under new Detroit Pistons head coach Stan Van Gundy.
On August 20, 2018, Beyer was hired by the Oklahoma City Thunder as an assistant coach.
On June 14, 2019, Beyer was hired by the Sacramento Kings as an assistant coach.
On November 16, 2020, Beyer was hired as assistant coach by the New Orleans Pelicans.
On August 2, 2022, Beyer was hired by the Charlotte Hornets as an assistant coach.
Head coaching record
References
External links
NBA.com profile
1961 births
Living people
Albany Great Danes men's basketball coaches
Alfred Saxons men's basketball players
American men's basketball players
Basketball coaches from New York (state)
American expatriate basketball people in Canada
Basketball players from New York (state)
Charlotte Bobcats assistant coaches
College men's basketball head coaches in the United States
Dayton Flyers men's basketball coaches
Detroit Pistons assistant coaches
Golden State Warriors assistant coaches
New Orleans Pelicans assistant coaches
Northwestern Wildcats men's basketball coaches
Orlando Magic assistant coaches
Oklahoma City Thunder assistant coaches
People from Le Roy, New York
Sacramento Kings assistant coaches
Siena Saints men's basketball coaches
Texas Tech Red Raiders basketball coaches
Toronto Raptors assistant coaches
University at Albany, SUNY alumni
Wisconsin Badgers men's basketball coaches
بيتر تسيغلر

بيتر تسيغلر هو جيولوجي سويسري، ولد في 2 نوفمبر 1928 في فينترتور في سويسرا، وتوفي في 19 يوليو 2013 في في سويسرا.
مراجع
وصلات خارجية
جيولوجيون سويسريون في القرن 20
أشخاص من فينترتور
أعضاء الأكاديمية الأوروبية
أعضاء الأكاديمية الملكية الهولندية للفنون والعلوم
أعضاء هيئة تدريس جامعة بازل
جيولوجيون سويسريون
حاصلون على الدكتوراه الفخرية من جامعة دلفت للتكنولوجيا
خريجو جامعة زيورخ
مواليد 1928
وفيات 2013
Sultan Mosque

Sultan Mosque or Masjid Sultan is a mosque located at Muscat Street and North Bridge Road within the Kampong Glam precinct of the district of Rochor in Singapore. It was named after Sultan Hussain Shah. The mosque was inaugurated on 27 December 1936. In 1975, it was designated a national monument.
History
The mosque was two-thirds complete and was formally opened on 27 December 1929. The mosque was fully completed in 1932.
The first known installation of a microphone–loudspeaker set occurred in 1936 in the mosque; it was reported that the summons to prayer could 'carry more than a mile'. Some mosque attendees were sceptical of the new electric system, however most believed it was necessary to empower the muezzin's voice to transcend a modern city's noises.
The Sultan Mosque has stayed essentially unchanged since it was built, with only repairs carried out to the main hall in 1968 and an annex added in 1993. It was gazetted as a national monument on 8 March 1975.
The mosque is managed by its own board of trustees and management board.
Transportation
The mosque is accessible from Bugis MRT station and Jalan Besar MRT station.
See also
Islam in Singapore
List of mosques in Singapore
Gallery
References
National Heritage Board (2002), Singapore's 100 Historic Places, Archipelago Press,
External links
Sultan Mosque Facebook Page
Sultan Mosque Instagram Page
Sultan
Tourist attractions in Singapore
National monuments of Singapore
Mosques completed in 1928
Rochor
20th-century architecture in Singapore
Andrew Parsons (American politician)

Andrew Parsons (American politician)
Andrew Parsons (July 22, 1817 – June 6, 1855) was an American politician from the U.S. state of Michigan. He served as the 9th lieutenant governor of Michigan and as the 10th governor of Michigan.
Early life in New York
Parsons was born in Hoosick, New York. He was the son of John Parsons, and the grandson of Andrew Parsons, a Revolutionary soldier, who was the son of Phineas Parsons, the son of Samuel Parsons.
Life and politics in Michigan
Parsons moved to Michigan Territory in 1835 and spent the summer teaching in Ann Arbor. In the fall, he explored nearly the entire length of the Grand River valley by canoe, from Jackson to Lake Michigan. He spent the winter working as a store clerk in Ionia County and in the spring went to Marshall to live with his brother, Luke H. Parsons. In the fall of 1836, he moved to Corunna in what was to become Shiawassee County. This area at that time was mostly wilderness, and when it was organized into a county in 1837, Parsons was elected the county's first clerk at the age of nineteen.
Parsons became an attorney, and in 1840 was elected Register of Deeds, then reelected in 1842 and 1844. In 1846, he was elected to the Michigan State Senate from the sixth district and was appointed Prosecuting Attorney in 1848. He became a Regent of the University of Michigan in 1851 and was also elected as ninth lieutenant governor of Michigan in 1852.
Parsons became the tenth governor of Michigan when Robert McClelland resigned in March 1853 to become the Secretary of the Interior under U.S. President Franklin Pierce. During his twenty-two months as governor, tax laws were improved and the practice of depositing surplus state funds in banks was opposed. Parsons did not receive the Democratic Party's nomination for governor in 1854. This may have been due to the fact that the party was split by question of slavery and by the formation of the Republican Party (which held its first convention that year in Jackson, Michigan).
Retirement and death
In 1855, Parsons was elected to the Michigan House of Representatives from Shiawassee County district. He soon fell ill and retired to his farm in Corunna where he died at the age of 37, just five months after leaving office as governor. He is interred at Pinetree Cemetery in Corunna.
He was married to Marrietta Clason and had four children.
His brother, S. Titus Parsons, years later, was also a member of the state house from the same district from 1863 to 1864 and 1867–68, as well as a delegate to Michigan state constitutional convention in 1867.
References
1817 births
1855 deaths
Democratic Party governors of Michigan
Democratic Party Michigan state senators
Democratic Party members of the Michigan House of Representatives
Lieutenant Governors of Michigan
Regents of the University of Michigan
County officials in Michigan
People from Hoosick, New York
Burials in Michigan
People from Corunna, Michigan
19th-century American politicians
ديفيد براندون

ديفيد براندون هو ممثل أمريكي، ولد في 14 يناير 1940 ببالتيمور في الولايات المتحدة.
أعمال
أفلام
(1978) الأولاد من البرازيل
(2012) جزء مني
مراجع
وصلات خارجية
ممثلو أفلام أمريكيون
مواليد 1940
مواليد عقد 1950
غريغ وايزمان

غريغ وايزمان (ولد في 28 سبتمبر سنة 1963) روائي أمريكي وكاتب قصص مصورة شارك مع براندون فيتي في تأليف شباب العدالة
روابط خارجية
مراجع
كتاب تلفاز ذكور أمريكيون
أشخاص على قيد الحياة
كتاب تلفاز
كتاب تلفاز أمريكيون
كتاب سيناريو من كاليفورنيا
كتاب ومؤلفو قصص مصورة أمريكيون
مخرجو صوت
ممثلو أداء صوتي رجال أمريكيون
منتجو أفلام رسوم متحركة أمريكيون
منتجو تلفزيون من كاليفورنيا
مواليد 1963
مواليد في لوس أنجلوس
أشخاص من وودلاند هيلز
Lavinia Williams

Lavinia Williams (July 2, 1916 – July 19, 1989), who sometimes went by the married name Lavinia Williams Yarborough, was an American dancer and dance educator who founded national schools of dance in several Caribbean countries.
Biography
Grace Lavinia Poole Williams was born the second of six children in Philadelphia, Pennsylvania, in a family of west-indian descent. She grew up in Portsmouth, Virginia and Brooklyn, New York, and studied at Washington Irving High School and then the Art Students League of New York, where she joined the American Negro Ballet, beginning her career in a number of dance companies and stage productions.
Her work included classical ballet, folk, modern, musicals, and, most importantly, Caribbean dance, which she mastered in the 1940s while working with Katherine Dunham. She spent nearly the entirety of the years from 1953 through to the late 1980s teaching dance and founding and developing national schools of dance in Haiti, Guyana, and the Bahamas.
She spent most of the last years of her life teaching in New York City, but left the United States for Haiti in February 1984. The New York Times reported that she died of a heart attack in Port-au-Prince, although several other sources and Beryl Campbell reported it as "some kind of food poisoning". Diana Dunbar, Lavinia's friend and student, arranged her funeral service.
Marriages and children
Williams married Léon Theremin in the mid-1930s. In 1938, Theremin suddenly returned to the Soviet Union,
where he was imprisoned and later sent to a labor camp. Williams never saw him again.
She married Shannon Yarborough in the late 1940s and had two daughters, Sharron and Sara. The younger daughter, Sara Yarborough-Smith, followed in her mother's footsteps as a professional dancer with the Alvin Ailey American Dance Theater, the Dance Theater of Harlem and the Robert Joffrey Ballet, among others.
Lavinia visited Clara Rockmore in 1974 and expressed happiness in discovering that Theremin was still alive; shortly afterwards she and Theremin started corresponding, with Theremin even proposing remarriage.
Featured in
Aschenbrenner, Joyce. Katherine Dunham: reflections on the social and political contexts of Afro-American dance. New York: CORD: 1981.
Bibliography
She wrote the 49-page pamphlet Haiti Dance printed by Brönners Druckerei in 1959.
She wrote various other small pamphlets on dance, for example: Ballets d'Haïti: Bamboche creole, 24 pages, 1974; Dances of the Bahamas & Haiti, 1980, 12 pages.
Notes
References
Allen, Zita. Thirteen WNET New York. "Lavinia Williams." Dance In America: Free To Dance web companion. Online.
Kisselgoff, Anna. The New York Times. "Dance: For Alvin Ailey, 25th Anniversary Gala." December 2, 1983. Online.
1916 births
1989 deaths
American female dancers
Dancers from Pennsylvania
African-American female dancers
African-American dancers
20th-century American educators
American emigrants to Haiti
20th-century American dancers
20th-century African-American women
20th-century African-American educators
أيمن مكرم

أيمن مكرم مخرج مصري شاب، بدأ مشواره الفني كناقد سينمائي ثم كمساعد مخرج، ثم أعلن موهبته كمخرج عندما قدم فيلم «خليك في حالك» ثم «شيكامارا». تخرج في قسم الفلسفة في كلية الآداب جامعة المنيا دفعه حبه للفن للالتحاق بمعهد السينما ليدرس الإخراج ويتتلمذ على يد المخرج الكبير «علي بدرخان».
أعماله
أفلام من إخراجه
2007: خليك في حالك
2007: شيكامارا
2008: مناحي
2011: هالو كايرو
مسلسلات من إخراجه
2011: إحنا الطلبة
مراجع
وصلات خارجية
أيمن مكرم في قاعدة بيانات الأفلام العربية
مخرجون سينمائيون مصريون
مواليد 1387 هـ
Julia Bell (author)

Julia Bell (author)
Julia Bell (born 1971) is a British novelist and poet living in North London. She is Senior Lecturer at Birkbeck and the founder and Project Director of the annual publication the Mechanics’ Institute Review and the website "Writers Hub" .
She has published two novels for young adults – Massive and Dirty Work – and the bestselling Creative Writing Coursebook, as well as poetry and short stories in various magazines and anthologies. She is an alumna of the University of East Anglia MA programme and a member of the Birmingham-based Tindal Street Fiction Group.
Works
Massive
Her first novel, Massive, was published in the UK in 2002 (Macmillan) and the US in 2005 (Simon and Schuster). The novel is set in Birmingham and deals with a mother-daughter relationship in which the mother is suffering from anorexia. Imogen Russell Williams describes the book in The Guardian:
"Julia Bell's 2002 novel Massive focuses on Carmen, the unlucky teenage daughter of rail-thin, glamorous, ambitious Maria, who oscillates between anorexia and bulimia like a nightmarish pinball, calling Carmen "Miss Piggy" and castigating her for hoarding sweet wrappers behind her headboard. Eventually, Maria inculcates Carmen with the seductive delusion that mastery of food equals mastery of fate, and the book culminates in a dreadful duel between mother and daughter, both desperate to prove themselves stronger, more powerful and more in control of their fabulous destiny by refusing to cave in and eat." According to WorldCat, the book is in over 430 libraries.
Dirty Work
Her second novel, Dirty Work, published in the UK (Macmillan) and US (Simon & Schuster) in 2007, deals with issues of human trafficking, especially for the sex trade. The book was well-received, with Stephanie Merritt describing it in The Observer as:
"Julia Bell's gritty second novel […} follows two teenage girls through the brutality of Europe's sex trade. Hope, the wealthy English teenager mistakenly kidnapped by traffickers, makes explicit the comparison with slavery: 'No one buys people any more, they banned that, we did it in history. And anyway, it was only people from Africa, it wasn't, like, white people. William Wilberry or something.' Bell's dual narrative, divided between spoilt but resourceful Hope and fierce, broken Oksana from Russia, is pitch-perfect and the careful research is worn lightly." According to WorldCat, the book is in over 343 libraries
The Creative Writing Coursebook
Published in 2001 (Macmillan), the book was created while Bell was teaching an undergraduate creative writing course at the University of East Anglia. It is devised as a series of lesson plans with contributions from 40 authors including David Lodge, Malcolm Bradbury, Ali Smith, Vicki Feaver.
Bell's teaching is also available online on the Writers Hub website. She gives an annual lecture to the MA students at Birkbeck. Her most recent on "Territory and the work of Damon Galgut."
References
1971 births
Living people
Alumni of the University of East Anglia
21st-century English novelists
Academics of Birkbeck, University of London
قاسم مشترك أكبر

قاسم مشترك أكبر
في الرياضيات، القاسم المشترك الأكبر لعددين كما يدل على ذلك اسمه هو أكبر عدد يقسم في نفس الوقت العددين معاً بدون أي باقي قسمة، فمثلاً القاسم المشترك الأكبر للعددين 48 و 60 هو 12.
يمدد هذا المفهوم إلى متعددات الحدود (من أجل ذلك انظر القاسم المشترك الأكبر لمتعددتي حدود) وإلى حلقات تبادلية أخرى.
نظرة شاملة
القاسم المشترك الأكبر (GCD) لعددين صحيحين غير صفريين و هو أكبر عدد صحيح موجب بحيث يكون قاسمًا لكل من و; أي أن هناك أعدادًا صحيحة و بحيث تكون و، و هو أكبر عدد صحيح من هذا القبيل. يعرف GCD لـ و عمومًا بـ .
اختزال الكسور
يستعمل القاسم المشترك الأكبر في اختزال الكسور. على سبيل المثال، القاسم المشترك الأكبر ل 42 و 56 هو 14، إذن :
عددان هما أوليان فيما بينهما إذا كان قاسمهما المشترك الأكبر مساويا ل1. على سبيل المثال، 9 و 28 هما عددان أوليان فيما بينهما.
نظرة هندسية
طريقة الحساب
استعمال التعميل إلى جداء أعداد أولية
يمكن حساب القاسم المشترك الأكبر لعددين كما في المثال التالي:
نأخذ كمثال العددين 6 و3 ونبحث عن قاسمهما المشترك الأكبر.
نكتب العددان على شكل جداء عوامل أولية.
3=1x3
6=2x3
نختار الآن العوامل المشتركة (لأنه قاسم سوف نختار الأعداد المشتركة ) ذات الأس الأصغر (لأنه أكبر * قاسم مشترك أكبر ) .
العوامل المشتركة ذات الأس الأصغر هي 3 . إذا ق.م.أ (6,3 ) = 3
استعمال خوارزمية اقليدس
نقسم العدد الأكبر على الأصغر ثم نأخذ باقي القسمة مع العدد الأصغر الناتج ونعيد العملية مع هذين العددين الجديدين حتى نحصل على باقي هو الصفر فيكون العدد الأصغر هو القاسم المشترك الأكبر
خصائص
كل قاسم مشترك لعددين a وb هو قاسم لقاسمهما المشترك الأكبر .
إذا كان a يقسم جداء b·c، وكان ، عندها a/d يكون قاسم للعدد c.
انظر أيضًا
مضاعف مشترك أصغر
خوارزمية إقليدس
أعداد أولية فيما بينها
مراجع
حسابيات ابتدائية
دوال جدائية
نظرية جبرية للأعداد