text:
List of guest stars in 3rd Rock from the Sun
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This is a list of notable guest stars who appeared in the American television sitcom 3rd Rock from the Sun throughout its six season run.
Contents
1 Guest stars
1.1 Season 1
1.2 Season 2
1.3 Season 3
1.4 Season 4
1.5 Season 5
1.6 Season 6
2 References
3 See also
Guest stars[edit]
Season 1[edit]
Harry Morgan - (3 episodes, seasons 1 & 2) playing Professor Suter, an elderly colleague of Dick and Mary
Martha Stewart - playing herself[1]
Phil Hartman - (seasons 1 & 3) playing a camp cosmetics store worker[2] and Randy, Vicki Dubcek's ex-lover[3]
Jane Lynch - playing Tommy's science teacher, Ms. Koppel
John Mahoney - playing Leonard Hamlin, a rude, sexist professor[4]
Lauren Graham - playing Laurie Ives
John Raitt - playing Singing Truck Driver
Marla Sokoloff - playing Dina, Tommy's lab partner and love interest[1]
Season 2[edit]
Dennis Rodman - playing himself; it is revealed that he is actually another alien[5][6]
George Takei - playing himself at a sci-fi convention[7]
Al Franken - playing Harry's opponent in the City Council election[7]
Mike Ditka - playing Coach Mafferty; coach for Pendelton Badgers[8][9]
Mark Hamill - playing himself[10]
Christine Baranski - playing Sonja Umdahl
Randy Newman - playing himself[11]
Dick Martin-playing sociology professor Dr. Ben Littmeyer[12]
Greg Proops
Season 3[edit]
Roseanne Barr - playing Dick's forced-wife Janet[13][14]
Leigh McCloskey - playing Matthew, a yoga instructor
Elaine Stritch - (seasons 3 & 6) playing Martha Albright, Mary's mother[15][16]
George Grizzard - (seasons 3 & 4) playing George Albright, Mary's Father[15][16]
Cindy Crawford - playing Mascha, a Venusian woman[17][17]
Angie Everhart - playing Chloe, A Venusian woman dating Tommy
Dom DeLuise - playing the father of Dick's student Bug[18]
Peter DeLuise - playing Franky
John Cleese - (seasons 3 & 6) playing Professor Liam Neesam, a hostile alien[19][20][21][21]
Sam Lloyd - playing Eddie, a man Dick helps.
Season 4[edit]
Laurie Metcalf - playing Jennifer Ravelli, a teacher of comparative literature[22][23][24]
Kathy Bates - playing Charlotte Everley, an alien hunter[25]
Gil Christner - playing Carl, a Nobel Laureate[26]
William Shatner - (seasons 4 & 5) playing The Big Giant Head (a.k.a. Stone Phillips)[27][27][28][29][29]
Aaron Paul - (Season 4) Playing the Junior Prom King & Queen announcer[27]
Kurtwood Smith (Season 4) Playing Dick's "cousin" Jacob when they attend a Solomon family reunion
Bryan Cranston - Plays a Neil Diamond Impersonator (whom Sally kisses) Season 4 Episode 14[30]
Season 5[edit]
Billy Connolly - playing an actor who is playing the part of Inspector McAffrey[31]
David Hasselhoff - playing a plastic surgeon[32]
Jonathan Frakes - playing Larry McMichael, the husband of Mary's friend Gwen[33]
Genie Francis - playing Gwen McMichael, the wife of Larry McMichael[33]
Chyna - playing Janice, a police officer[34][28][28]
Miguel Ferrer - playing Jack McMannus, a government agent[35]
Alan Cumming - playing Angus 'The Hole' McDuff, a hole expert[36]
Enrico Colantoni - playing Frank, an ex-student of Mary's[37]
Bob Odenkirk - plays as Gary Parkinson an insurance salesman in "The Fifth Solomon" (episode 3 season 5)[38]
Season 6[edit]
Megan Mullally - playing Renata Albright, Mary's sister[39]
Elvis Costello - playing himself[40]
Mark McKinney - Playing a new alien that stumbled through the Solomon's closet door.
Andrea Speyer - Guest Star as Claire Volk [41]
References[edit]
^ Jump up to: a b "Post-Nasal Dick". 3rd Rock from the Sun. Season 1. Episode 2. 1996-01-16. NBC.
Jump up ^ "Lonely Dick". 3rd Rock from the Sun. Season 1. Episode 7. 1996-02-20. NBC.
Jump up ^ "Eat, Drink, Dick, Mary". 3rd Rock from the Sun. Season 3. Episode 27. 1998-05-20. NBC.
Jump up ^ "Body and Soul and Dick". 3rd Rock from the Sun. Season 1. Episode 8. 1996-02-27. NBC.
Jump up ^ "See Dick Continue to Run - Part I". 3rd Rock from the Sun. Season 2. Episode 1. 1996-09-22. NBC.
Jump up ^ "See Dick Continue to Run - Part II". 3rd Rock from the Sun. Season 2. Episode 2. 1996-09-22. NBC.
^ Jump up to: a b "Hotel Dick". 3rd Rock from the Sun. Season 2. Episode 3. 1996-09-29. NBC. Cite error: Invalid <ref> tag; name "HD" defined multiple times with different content (see the help page).
Jump up ^ "Fourth and Dick". 3rd Rock from the Sun. Season 2. Episode 7. 1996-11-03. NBC.
Jump up ^ "Romeo and Juliet and Dick". 3rd Rock from the Sun. Season 2. Episode 14. 1997-01-12. NBC.
Jump up ^ "Fifteen Minutes of Dick". 3rd Rock from the Sun. Season 2. Episode 23. 1997-05-11. NBC.
Jump up ^ "A Nightmare on Dick Street". 3rd Rock from the Sun. Season 2. Episode 26. 1997-05-18. NBC.
Jump up ^ "Dick Jokes". 3rd Rock from the Sun. Season 2. Episode 11. 1996-06-12. NBC.
Jump up ^ "Fun with Dick and Janet - Part I". 3rd Rock from the Sun. Season 3. Episode 1. 1997-09-24. NBC.
Jump up ^ "Fun with Dick and Janet - Part II". 3rd Rock from the Sun. Season 3. Episode 2. 1997-09-24. NBC.
^ Jump up to: a b "Dick-In-Law". 3rd Rock from the Sun. Season 3. Episode 4. 1997-10-15. NBC.
^ Jump up to: a b "My Mother, My Dick". 3rd Rock from the Sun. Season 6. Episode 14. 2001-02-20. NBC.
^ Jump up to: a b "36! 24! 36! Dick - Part I". 3rd Rock from the Sun. Season 3. Episode 14. 1998-01-25. NBC. Cite error: Invalid <ref> tag; name "362426D" defined multiple times with different content (see the help page).
Jump up ^ "Auto Eurodicka". 3rd Rock from the Sun. Season 3. Episode 17. 1998-02-04. NBC.
Jump up ^ "Just Your Average Dick". 3rd Rock from the Sun. Season 3. Episode 22. 1998-04-28. NBC.
Jump up ^ "Dick and the Other Guy". 3rd Rock from the Sun. Season 3. Episode 23. 1998-04-28. NBC.
^ Jump up to: a b "Mary Loves Scoochie - Part I". 3rd Rock from the Sun. Season 6. Episode 17. 2001-05-08. NBC. Cite error: Invalid <ref> tag; name "MLS" defined multiple times with different content (see the help page).
Jump up ^ "What's Love Got to Do, Got to Do with Dick?". 3rd Rock from the Sun. Season 4. Episode 5. 1998-10-28. NBC.
Jump up ^ "I Am Dick Pentameter!". 3rd Rock from the Sun. Season 4. Episode 6. 1998-11-04. NBC.
Jump up ^ "DIII: Judgement Day". 3rd Rock from the Sun. Season 4. Episode 7. 1998-11-11. NBC.
Jump up ^ "Alien Hunter". 3rd Rock from the Sun. Season 4. Episode 20. 1999-05-04. NBC.
Jump up ^ "Dick vs. Strudwick". 3rd Rock from the Sun. Season 4. Episode 21. 1999-05-11. NBC.
^ Jump up to: a b c "Dick's Big Giant Headache - Part I". 3rd Rock from the Sun. Season 4. Episode 23. 1999-05-25. NBC. Cite error: Invalid <ref> tag; name "DBGH" defined multiple times with different content (see the help page). Cite error: Invalid <ref> tag; name "DBGH" defined multiple times with different content (see the help page).
^ Jump up to: a b c "The Big Giant Head Returns". 3rd Rock from the Sun. Season 5. Episode 12. 2000-02-22. NBC. Cite error: Invalid <ref> tag; name "TBGHR" defined multiple times with different content (see the help page). Cite error: Invalid <ref> tag; name "TBGHR" defined multiple times with different content (see the help page).
^ Jump up to: a b "The Big Giant Head Returns Again - Part I". 3rd Rock from the Sun. Season 5. Episode 21. 2000-05-23. NBC. Cite error: Invalid <ref> tag; name "TBGHRA" defined multiple times with different content (see the help page).
Jump up ^ https://www.imdb.com/title/tt0502700/
Jump up ^ "Dial M For Dick". 3rd Rock from the Sun. Season 5. Episode 4. 1999-11-09. NBC.
Jump up ^ "Dick and Tuck". 3rd Rock from the Sun. Season 5. Episode 5. 1999-11-16. NBC.
^ Jump up to: a b "Gwen, Larry, Dick and Mary". 3rd Rock from the Sun. Season 5. Episode 10. 2000-01-05. NBC.
Jump up ^ "This Little Dick went to Market". 3rd Rock from the Sun. Season 5. Episode 14. 2000-03-14. NBC.
Jump up ^ "Youth is Wasted on the Dick". 3rd Rock from the Sun. Season 5. Episode 15. 2000-03-21. NBC.
Jump up ^ "Dick and Harry Fall in a Hole". 3rd Rock from the Sun. Season 5. Episode 18. 2000-05-02. NBC.
Jump up ^ "Frankie Goes to Rutherford". 3rd Rock from the Sun. Season 5. Episode 19. 2000-05-09. NBC.
Jump up ^ https://www.imdb.com/title/tt0502729/
Jump up ^ "Les Liaisons Dickereuses". 3rd Rock from the Sun. Season 6. Episode 1. 2000-10-24. NBC.
Jump up ^ "The Thing That Wouldn't Die - Part II". 3rd Rock from the Sun. Season 6. Episode 20. 2001-05-22. NBC.
Jump up ^ "Dick Soup For The Soul". 3rd Rock from the Sun. Season 6. Episode 16. 2001-05-01. NBC.
See also[edit]
3rd Rock from the Sun episodes
3rd Rock from the Sun
hide
v
t
e
3rd Rock from the Sun
Characters
Dick Solomon
Sally Solomon
Harry Solomon
Tommy Solomon
Nina Campbell
Mamie Dubcek
Don Orville
Mary Albright
Big Giant Head
Seasons
1
"Brains and Eggs"
2
3
4
5
"The Loud Solomon Family: A Dickumentary"
6
"The Thing That Wouldn't Die"
Other
Awards and nominations
Guest stars
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text:
Rice production in the United States
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Left:US rice production states. Right: Varieties of Rice grown
Rice production is important to the economy of the United States. Of the country's row crop farms, rice farms are the most capital-intensive, and have the highest national land rental rate average. In the US, all rice acreage requires irrigation. In 2000-09 approximately 3.1 million acres in the US were under rice production, while an increase is expected in the next decade to approximately 3.3 million acres.[1] US Rice represents rice producers in the six largest rice-producing states of Arkansas, California, Louisiana, Mississippi, Missouri, and Texas.[2][3]
Contents
1 History
1.1 Early history
1.2 19th century
1.3 20th century to present
2 Production
3 Types of rice
4 Milling process
5 Exports
6 Culture
7 See also
8 References
History[edit]
Early history[edit]
Wooden mortar and pestle found in the rice loft on Briars Plantation, John's Island (Charleston County), South Carolina. It is believed to have been used in husking and/or polishing rice which was grown on the plantation. The age is unknown.
Winnowing barn at the Mansfield Rice Plantation, Georgetown, South Carolina.
African rice (a separate species from Asian rice, originally domesticated in the inland delta of the Upper Niger River[4][5]) was introduced to the United States in the 17th century. It is mentioned to have been under cultivation in Virginia as far back as 1609, although it is reported that one bushel of rice had been sent to the colony later, in the summer of 1671, on the cargo vessel William and Ralph. In 1685, a bag of Madagascar rice known as "Gold Seede" was given to Dr. Henry Woodward. A tax law of 26 September 1691 had permitted payment of taxes by the colonists by way of rice and other commodities.[6] [7]
The colonies of South Carolina and Georgia prospered and amassed great wealth from rice planting, based on the slave labor obtained from the Senegambia area of West Africa and from coastal Sierra Leone. One batch of slaves was advertised as "a choice cargo of Windward and Gold Coast Negroes, who have been accustomed to the planting of rice". At the port of Charleston, through which 40% of all American slave imports passed, slaves from Africa brought the highest prices in recognition of their prior knowledge of rice culture, which was put to use on the many rice plantations around Georgetown, Charleston, and Savannah.[6]
Dikes are used to protect the rice paddy fields from the channels of saltwater which overflow during high tide. Karabane, Senegal, 2008; similar delta cultivation techniques were used in West Africa back to at least the 15th century[8]
Similar dike, used to grow rice in the early United States, now abandoned and reclaimed by woodland[8]
Enslaved Africans cleared the land, diked the marshes and built the irrigation system, skimming the freshwater layer off the high tide, flushing the fields, and adjusting the water level to the development stage of the rice. Rice was planted, hoed, and harvested with hand tools; plows and harvest wains could be pulled by mules or oxen wearing special shoes.[6] At first rice was milled by hand with wooden paddles, then winnowed in sweetgrass baskets (the making of which was another skill brought by slaves from Africa). The invention of the rice mill increased profitability of the crop, and the addition of water power for the mills in 1787 by American millwright Jonathan Lucas was another step forward.
Rice production was not merely unhealthy but lethal. One 18th-century writer wrote:[6]
If a work could be imagined peculiarly unwholesome and even fatal to health, it must be that of standing like the negroes, ankle and mid-leg deep in water which floats an ouzy mud, and exposed all the while to a burning sun which makes the air they breathe hotter than the human blood; these poor wretches are then in a furness of stinking putrid effluvia.
Inadequate food, housing, and clothing, malaria, yellow fever, venomous snakes, alligators, hard labour, and brutal treatment killed up to a third of Low Country slaves within a year. Not one child in ten lived to age sixteen. However, in the 1770s, a slave could produce rice worth more than six times his or her own market value in a year, so this high death rate was not uneconomical for their owners. Rice plantations could produce profits of up to 26 percent per year. Runaways, on the other hand, were a problem:[6]
I gave them a hundred lashes more than a dozen times; but they never quit running away, till I chained them together, with iron collars round their necks, and chained them to spades, and made them do nothing but dig ditches to drain the rice swamps. They could not run away then, unless they went together, and carried their chains and spades with them. I kept them in this way two years....
— one overseer's method of controlling slaves, reported by fugitive slave Charles Ball
Most plantations were run on the task system, where a slave was given one or more tasks, estimated at ten hours' hard work, each day. After they had finished the tasks to the overseer's satisfaction, they could spend the remainder of the day as they chose, often on growing their food, spinning, sewing their clothes, or building their houses (slaves were typically supplied with nails and five yards of cloth per year). The task system, and the unwillingness of free people to live in rice-growing areas, may have led to the greater survival of African culture among the Gullah.[6]
In the country's early years, rice production was limited to the South Atlantic and Gulf states. For almost the first 190 years of rice production in the US, the principal producers were South Carolina and Georgia. Limited amounts were grown in North Carolina, Florida, Alabama, Mississippi and Louisiana.[9]
19th century[edit]
Plantation workers carrying sheaves of rice, South Carolina, circa 1895
Rice was introduced into the southern states of Louisiana and east Texas in the mid-19th century.[10] Meanwhile, soil fertility in the east fell, especially for inland rice.[6]
Emancipation in 1863 freed rice workers. East-coast rice farming required hard, skilled work under extremely unhealthy conditions, and without slave labour, profits fell. Increasing automation in response came too late, and a series of hurricanes that hit Carolina in the late 1800s and damaged levees put an end to the industry. Production shifted to the Deep South,[11] where the geography was more favourable to mechanization.[9]
These events can be seen in rice production statistics. In 1839, the total production was 80,841,422 pounds, of which 60,590,861 pounds were grown in South Carolina and 12,384,732 pounds in Georgia. In 1849, cultivation reached 215,313,497 pounds.[12] Between 1846 and 1861, annual rice production in North Carolina, South Carolina, and Georgia averaged more than 105 million pounds of cleaned rice, with South Carolina producing more than 75 percent.
A Civil War era rice barn on a plantation along the Pee Dee River.
At the census of 1870, after emancipation, the production of rice decreased to 73,635,021 pounds. In 1879, the total area devoted to rice was 174,173 acres, and the total production of clean rice was up again to 110,131,373 pounds. A decade later, the total area devoted to rice cultivation was 161,312 acres, and the total production of clean rice equaled 128,590,934 pounds; this represented a 16.76 percent increase in the amount produced, with a decrease of 7.38 percent in the area under cultivation.[12]
Between 1890 and 1900, Louisiana and Texas increased rice crop acreage to such an extent that they produced almost 75 percent of the country's product. Between 1866 and 1880, the annual production of the three States averaged just under 41 million pounds, of which South Carolina produced more than 50 percent. After 1880, their average annual production approximated 46 million pounds of cleaned rice, of which North Carolina produced 5.5 million, South Carolina 27 million and Georgia 13.5 million pounds.[9]
The rice industry in Louisiana began around the time of the Civil War. For a number of years, production was small, but during the 1870s the industry began to assume large proportions, averaging nearly 30 million pounds for the decade and exceeding 51 million pounds in 1880. In 1885, the production reached 100 million pounds, and in 1892, 182 million pounds. The great development of the rice industry in Louisiana after 1884 resulted from the opening up of a prairie region in the southwestern part of the state, and the development of a system of irrigation and culture which made possible the use of harvesting machinery similar to that used in the wheat fields of the Northwest, greatly reducing the costs of production. In 1896, yield from the Louisiana rice fields, where harvesting machinery was used, was good. However the milling process was not successful commercially in some rice varieties. The loss due to the milling process was considerable, particularly of the unbroken rice in the "head rice" variety.[9]
20th century to present[edit]
Hauling rice in South Texas, 1909
Rice was established in Arkansas in 1904, California in 1912, and the Mississippi Delta in 1942.[3] Rice cultivation in California in particular started during the California Gold Rush. It was introduced primarily for the consumption of about 40,000 Chinese laborers who were brought as immigrants to the state; only a small area was under rice cultivation to meet this requirement. However, commercial production began only in 1912 in the town of Richvale in Butte County.[13] Since then, California has cultivated rice in a big way, and as of 2006, its production of rice was the second largest in the United States.[14]
Production[edit]
Rice dryer and storage building in Arkansas County, Arkansas
Rice culture in the southeastern U.S. became less profitable with the loss of slave labor after the American Civil War, and it finally died out just after the turn of the 20th century. Today, people can visit the historic Mansfield Plantation in Georgetown, South Carolina, the state's only remaining rice plantation with the original mid-19th century winnowing barn and rice mill. The predominant strain of rice in the Carolinas was from Africa and was known as "Carolina Gold". The cultivar has been preserved and there are current attempts to reintroduce it as a commercially grown crop.[15]
In 1900, the annual production of rice in the US was approximately half the annual consumption. The two principal varieties of lowland rice which were cultivated in the Atlantic States were the "gold seed rice" and white rice, which were the original rice varieties introduced into the US. Gold seed rice was notable for the larger yield of the grain. It thus practically superseded white rice which was cultivated in the earlier years. Experiments with upland rice demonstrated that it could grow over large areas of the country but the crop's yield and quality are inferior to lowland rice produced by irrigation methods.[9]
Geese flying over a rice field in the Sacramento Valley, California.
Since then, California has cultivated rice on a large scale, and as of 2006 its production was the second largest in the United States,[14] after Arkansas, with production concentrated in six counties north of Sacramento.[16]
During 2012, the estimated rice production was 199 million cwt, or 19.9 billion lbs. This was a rise of 8% over the production of 2011. The harvested area also recorded a rise from 2.68 million ha in 2012 to 2.7 million ha in 2013. Another record was of the yield during 2012 recorded at 7,449 pounds per acre, higher than the 2011 yield by 382 pounds per acre.[17]
Six states now account for over 99% of all rice grown in the US. These are Arkansas, California, Louisiana, Mississippi, Missouri and Texas. As of 2003, Arkansas topped the list with a production level of 213 million bushels against a total production of 443 million bushels in the country, and the annual per capita consumption reported is in excess of 28 pounds.[18]
Types of rice[edit]
Oryza sativa, commonly known as Asian rice
The earliest types grown in Carolina were the African Oryza glaberrima, the prized "Carolina Gold". Asian Oryza sativa was "Carolina White".[citation needed]
After the total decline of rice cultivation in Carolina, "Carolina Gold" is now cultivated in Texas, Arkansas and Louisiana.[6]
In California, production is dominated by short and medium grain japonica varieties, including cultivars developed for the local climate such as Calrose, which makes up as much as 85% of the state's crop. The broad classification of rice grown includes Long Grain Rice, Medium Grain Rice and Short Grain Rice.[19]
While now more than 100 varieties of rice are grown in the world, in the US 20 varieties of rice are commercially produced, primarily in the states of Arkansas, Texas, Louisiana, Mississippi, Missouri, and California. Primary classification of rice grown are the long, medium or short grain type. The Long Grain Rice is slender and long, the Medium Grain Rice is plump but not round, and the Short Grain Rice is round. The forms of rice are Brown Rice, Parboiled Rice and Regular-Milled White Rice.[18][20]
The domestic utilization of rice in the US is food use (58%), while 16% is used in food and beer processing and 10% is used in pet food.[20]
Special varieties of rice such as jasmine rice and basmati rice which are of the aromatic variety are imported from Thailand, India, and Pakistan, as such varieties have not been evolved in the US; this demand for import is quite substantial and largely to meet the increasing population of the rice-eating ethnic community.[21]
Milling process[edit]
Harvested rice is subject to milling to remove the husk, which encloses the kernel. Before this process is started, the rice from the field is subject to a cleaning process to remove stalks and any extraneous material by means of special machinery. In the case of parboiled rice, a steam pressure process is adopted for milling. After drying, the rice is subjected to further processing to remove the hull and then polished. Brown rice is processed through a shelling machine which removes the hull. The resulting brown rice retains the brawn layer around the kernel. In the case of white rice, the hull and the brawn are removed and polished in a polishing machine, producing a polished kernel.[18]
Exports[edit]
The first export of rice from Carolina was 5 tons in 1698, which rose to 330 tons by 1700 and jumped to 42,000 tons in 1770. However, as a result of the abolition of slave labour, export from Carolina eventually ceased.[6]
While the rice production in the US accounts for about 2% of world production, its exports account for about 10% of all exports. The export is mostly of high-quality rice of the long and combined medium/short-grain varieties of rice. The type of rice exported is rough or unmilled rice, parboiled rice, brown rice, and fully milled rice. Exports to Mexico and Central America are mostly of the rough rice variety. Other countries to which the US exports rice include Mexico, Central America, Northeast Asia, the Caribbean, and the Middle East, Canada, the European Union (EU-27), and Sub-Saharan Africa.[21]
The exported variety is free of genetically enhanced (GE) rice. The World Trade Organization (WTO) and the North American Free Trade Agreement (NAFTA) are the agreements under which the US exports its rice and this has resulted in an increase of exports from the country since the 1990s.[21]
Culture[edit]
"Rice Is King" parade float at the National Rice Festival in Crowley, Louisiana, (1938).
A popular festival observed on New Year's Day, by many Americans (mostly from the southern states) is the preparation and consuming of a rice cuisine called the "Hoppin' John". Since rice is associated with slave labour as their staple diet (with horse-beans[clarification needed] made in to a pulp by boiling; boiled yams and occasionally a small amount of beef or pork) it is eaten in the US on New Year's Day in the belief that it brings good luck since people who "eat poor New Year's Day, eat rich the rest of the year."[6]
The International Rice Festival is held every year in Crowley, Louisiana on Friday and Saturday of the third weekend in October. It is the largest and oldest agricultural festival of Louisiana. The festival is a celebration of rice as a staple food and its economic importance in the world.[22] The tradition was set in 1927 as a Rice Carnival by Sal Right, a pioneer of the rice industry. However, the celebration of this festival in Crowley is also attributed to Harry D Wilson, Commissioner of Agriculture. It is also said that the festival was the idea of the Governor to celebrate the festival on the occasion of the silver jubilee of establishment of the city of Crowley on 25 October 1937.[23]
See also[edit]
African rice
Wild rice
References[edit]
Jump up ^ Baldwin, Katherine (April 2011). Consolidation and Structural Change in the U.S. Rice Sector. DIANE Publishing. pp. front cover, 11–. ISBN 978-1-4379-8478-1.
Jump up ^ "USA Rice". USA Rice. Retrieved 22 June 2013.
^ Jump up to: a b Kulp, Karel; Ponte, Jr., Joseph G. (2000). Handbook of Cereal Science and Technology. Marcel Dekker. pp. 203–. ISBN 978-0-8247-8294-8.
Jump up ^ Linares, Olga F. (2002-12-10). "African rice (Oryza glaberrima): History and future potential". Proceedings of the National Academy of Sciences. 99 (25): 16360–16365. doi:10.1073/pnas.252604599. ISSN 1091-6490. PMC 138616  . PMID 12461173. Retrieved 2016-08-09.
Jump up ^ Wang, Muhua; Yu, Yeisoo; Haberer, Georg; Marri, Pradeep Reddy; Fan, Chuanzhu; Goicoechea, Jose Luis; Zuccolo, Andrea; Song, Xiang; Kudrna, Dave; Ammiraju, Jetty S. S.; Cossu, Rosa Maria; Maldonado, Carlos; Chen, Jinfeng; Lee, Seunghee; Sisneros, Nick; de Baynast, Kristi; Golser, Wolfgang; Wissotski, Marina; Kim, Woojin; Sanchez, Paul; Ndjiondjop, Marie-Noelle; Sanni, Kayode; Long, Manyuan; Carney, Judith; Panaud, Olivier; Wicker, Thomas; Machado, Carlos A.; Chen, Mingsheng; Mayer, Klaus F. X.; Rounsley, Steve; Wing, Rod A. (2014-07-27). "The genome sequence of African rice (Oryza glaberrima) and evidence for independent domestication". Nature Genetics. 46 (9): 982–988. doi:10.1038/ng.3044. ISSN 1061-4036. Retrieved 2016-08-09.
^ Jump up to: a b c d e f g h i j "Rice and Slavery in America". Slavery in America Organization. Archived from the original on January 1, 2007. Retrieved 24 June 2013.
Jump up ^ "The History of U.S. Rice Production - Part 1". Luisiana State University Ag Center. November 29, 2012.
^ Jump up to: a b https://ricediversity.org/outreach/educatorscorner/documents/Carolina-Gold-Student-handout.pdf
^ Jump up to: a b c d e Knapp, Seaman Ashahel (1900). Rice culture in the United States (Public domain ed.). U.S. Department of Agriculture. pp. 6–.
Jump up ^ "Farm Raised Crawfish". Crawfish.com. Retrieved 24 June 2013.
Jump up ^ http://www.learnnc.org/lp/editions/nchist-colonial/1875
^ Jump up to: a b United States. Census Office (1895). Reports on the statistics of agriculture in the United States: agriculture by irrigation in the western part of the United States, and statistics of fisheries in the United States at the eleventh census: 1890 (Public domain ed.). Government Printing Office. pp. 72–.
Jump up ^ Lee, Ching (2005). "Historic Richvale – the birthplace of California rice". California Farm Bureau Federation. Archived from the original on October 11, 2007. Retrieved 10 June 2013.
^ Jump up to: a b "California's Rice Growing Region". California Rice Commission. Archived from the original on February 10, 2006. Retrieved 27 June 2013.
Jump up ^ "Carolina Gold Rice Foundation". Carolina Gold Rice Foundation. Retrieved 24 June 2013.
Jump up ^ Sumner, Daniel A. & Brunke, Henrich (September 2003). "The economic contributions of the California rice industry". California Rice Commission. Archived from the original on April 26, 2006. Retrieved 25 June 2013.
Jump up ^ "Crop Production: 2012 Summary" (pdf). United States Department of Agriculture National Agricultural Statistics Service. Retrieved 25 June 2013.
^ Jump up to: a b c "U.S. Rice Production". Riceland.com. Retrieved 25 June 2013.
Jump up ^ "Medium Grain Varieties". California Rice Commission. Archived from the original on May 8, 2006. Retrieved 25 June 2013.
^ Jump up to: a b "United States Department of Agriculture:Release No. 0306.06". U.S. RICE STATISTICS. August 2006.
^ Jump up to: a b c "Trade". Rice exports. USDA Economic Research Service. Retrieved 25 June 2013.
Jump up ^ "About the Festival". Rice Festival.Com. Archived from the original on 8 February 2012. Retrieved 25 June 2013.
Jump up ^ "Festival History". Rice Festival.com. Retrieved 25 June 2013.
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List of Family Guy cast members
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Family Guy creator Seth MacFarlane also provides the voices of Peter Griffin, Stewie Griffin, Brian Griffin, and Glenn Quagmire.
Family Guy is an American animated sitcom that features five main voice actors, and numerous regular cast and recurring guest stars. The principal voice cast consists of show creator Seth MacFarlane, Alex Borstein, Mila Kunis (who replaced Lacey Chabert after the first season), Seth Green, and Mike Henry. Recurring voice actors include Patrick Warburton, Adam West, John G. Brennan, Nicole Sullivan and Jennifer Tilly, and repeat guest stars include Phyllis Diller, Charles Durning, Rush Limbaugh, and Phil LaMarr.
Many cast members provide voices for multiple characters. The voice actors, in portraying the various character personalities on the show, draw inspiration from celebrities and pop culture. Family Guy characters have been played by more than one actor, after members of the show left the series or had conflicting obligations.
Kunis was nominated for an Annie Award for voicing Meg Griffin in the season 5 episode "Barely Legal" and MacFarlane has also won an Emmy Award for Outstanding Voice-Over Performance and an Annie Award for Best Voice Acting in an Animated Television Production, though no other cast member has won an award for their work on the series.
Contents
[hide]
1 Current cast
1.1 Seth MacFarlane
1.2 Alex Borstein
1.3 Mila Kunis
1.4 Seth Green
1.5 Mike Henry
2 Recurring cast
3 Recurring guest voices
4 Casting changes
5 Awards and nominations
6 References
Current cast[edit]
Seth Green provides the voice of Chris Griffin.
Mike Henry voices various characters in the series.
Mila Kunis provides the voice of Meg Griffin.
Alex Borstein provides the voice of Lois Griffin.
Patrick Warburton provides the voice of Joe Swanson.
The real Adam West provided the voice of Mayor Adam West.
From seasons 1 to 4, Family Guy had four main cast members. Since season 5, there have been five main cast members. The casting of Meg Griffin changed after season 1.
Seth MacFarlane[edit]
Seth MacFarlane voices four of the show's main characters: Peter Griffin, Brian Griffin, Stewie Griffin, and Glenn Quagmire.[1] MacFarlane chose to voice these characters himself, believing it would be easier to portray the voices he had already envisioned than for someone else to attempt it.[2] MacFarlane drew inspiration for the voice of Peter from a security guard he overheard talking while attending the Rhode Island School of Design.[3] Stewie's voice was based on the voice of English actor Rex Harrison,[4] especially his performance in the 1964 musical drama film My Fair Lady.[5] MacFarlane uses his own voice while portraying Brian.[2]
MacFarlane also provides the voices for various other recurring and one-time only characters, most prominently those of news anchor Tom Tucker, Lois' father Carter Pewterschmidt and Dr. Hartman.[6] He is the only voice to be in every episode.
Alex Borstein[edit]
Alex Borstein voices Lois Griffin, Asian correspondent Tricia Takanawa, Loretta Brown and Lois' mother Barbara Pewterschmidt.[7] Borstein was asked to provide a voice for the pilot while she was working on MADtv. She had not met MacFarlane or seen any of his artwork and said it was "really sight unseen".[8] At the time, Borstein performed in a stage show in Los Angeles, in which she played a redhead mother whose voice she had based on one of her cousins.[7][8] The voice was originally slower (and deeper for the original series), but when MacFarlane heard it, he replied "Make it a little less fucking annoying ... and speed it up, or every episode will last four hours."[7]
Mila Kunis[edit]
Mila Kunis is the voice of the character named Meg Griffin.[6] Kunis won the role after auditions and a slight rewrite of the character, in part due to her performance on That '70s Show.[9] MacFarlane called Kunis back after her first audition, instructing her to speak slower, and then told her to come back another time and enunciate more. Once she claimed that she had it under control, MacFarlane hired her.[9] Kunis described her character as "the scapegoat". She further explained, "Meg gets picked on a lot. But it's funny. It's like the middle child. She is constantly in the state of being an awkward 14-year-old, when you're kind of going through puberty and what-not. She's just in a perpetual mode of humiliation. And it's fun."[10]
Seth Green[edit]
Seth Green primarily plays Chris Griffin and Neil Goldman.[6][11] Green stated that he did an impression of the "Buffalo Bill" character from the thriller film The Silence of the Lambs during his audition.[12] His main inspiration for Chris' voice came from envisioning how "Buffalo Bill" would sound if he were speaking through a public address system at a McDonald's.[13]
Mike Henry[edit]
Mike Henry is the voice of Cleveland Brown, John Herbert The Pervert and other various characters. A Family Guy writer and producer, he began acting on the show as part of the recurring cast repertory (see below) but was promoted to main cast member in 2005. Since the cancellation of The Cleveland Show, he also voices Cleveland's step-son Rallo Tubbs on Family Guy.
Recurring cast[edit]
In addition to both its main cast and guest stars, Family Guy utilizes a deep bench of regularly appearing supporting voice actors. Some appear in nearly every episode each season, while others appear less frequently. Some of these actors specifically play recurring characters, while others mainly play background citizens of Quahog or characters in cutaway gags.
The current supporting cast repertory includes the following actors:
Actor
Character(s)
No. of Episodes
(Out of 245 produced)
Notes
Benjamin, H. JonH. Jon Benjamin Carl 14 Since 2005
Breckenridge, AlexandraAlexandra Breckenridge Various 57 Since 2005. Currently voices most female “extras” not voiced by Alex Borstein.
Brennan, JohnnyJohnny Brennan Goldman, MortMort Goldman, Horace the bartender 77
Callaghan, SteveSteve Callaghan Various 37 Also the current showrunner and executive producer of Family Guy and former showrunner/EP of American Dad!. [14]
Garman, RalphRalph Garman Various 138
Lakin, ChristineChristine Lakin Kinney, JoyceJoyce Kinney 23 Since 2010.
LaMarr, PhilPhil LaMarr Williams, OllieOllie Williams and the Quahog judge 56
MacFarlane, RachaelRachael MacFarlane Olivia and various women 54 Formerly one of the most frequent female voices. She reduced her number of appearances per season after joining American Dad! in 2005 but still appears several times per season. Seth MacFarlane's sister.
Osment, EmilyEmily Osment Various 14 Since 2012.
Richardson, Kevin MichaelKevin Michael Richardson Jerome and Cleveland Jr. 30 Since 2009.
Sheridan, ChrisChris Sheridan Various 33 Also a Family Guy writer.
Smith, DannyDanny Smith Various, including Evil Monkey, Al Harrington and Ernie, the Giant Chicken 189 Also a Family Guy writer.
Sulkin, AlecAlec Sulkin Christ, JesusJesus Christ and various others 147 Also a Family Guy writer.
Tatasciore, FredFred Tatasciore Various 36
Tilly, JenniferJennifer Tilly Swanson, BonnieBonnie Swanson 42 Has recurred as the Griffin's neighbor since the first season.
Viener, JohnJohn Viener Various 182 Since 2005, he has been one of the most frequently heard male voices aside from Seth MacFarlane. Also a Family Guy writer.
Warburton, PatrickPatrick Warburton Swanson, JoeJoe Swanson 163 Has appeared as the Griffins' neighbor since the first season, and usually appears in most episodes each season. Warburton is the most frequently appearing one-character actor in the supporting repertory.
Wingert, WallyWally Wingert Various 41

In addition to the above, the following actors were formerly regularly recurring voice actors in the series:
Actor
Character(s)
No. of Episodes
Notes
Alan, LoriLori Alan Simmons, DianeDiane Simmons 63 Left the show in season nine when her character was killed off. Was replaced in the series' context by Christine Lakin's Joyce Kinney
Alazraqui, CarlosCarlos Alazraqui Weed, Mr.Mr. Weed 10 Peter's first boss, Mr. Weed, was killed off early in the series' run.
Barrymore, DrewDrew Barrymore Russell, JillianJillian Russell 12 Played Jillian, Brian's former girlfriend. The character still appears in background roles
Cole, GaryGary Cole Various 38 Cole appeared frequently in the earlier seasons, but still pops up now and then to play Meg and Chris' principal, Mr. Shepherd.
Hartman, ButchButch Hartman Various 8
Henry, MikeMike Henry Cleveland Brown, Herbert, Bruce, Consuela, and various others Was promoted to main cast in 2005. Also a Family Guy writer.
Hentemann, MarkMark Hentemann Opie and various others 45 Recently left Family Guy to work on another Seth MacFarlane project. Also a Family Guy writer.
Fisher, CarrieCarrie Fisher Angela 19 Has recurred as Peter's boss several times per season since 2005. Died in 2016.
Strong, TaraTara Strong Various, as well as Meg's singing voice 21 Appeared frequently in the first four seasons. Returned briefly in 2010-2011 and again for one episode in 2014.
Sullivan, NicoleNicole Sullivan Goldman, MurielMuriel Goldman 27 Muriel was killed off in season nine.
Whitman, MaeMae Whitman Various 10 Was a recurring younger female voice for several seasons between 2007-2010.
Wild, WellesleyWellesley Wild Various 14 No longer a recurring voice (since 2013). He was a producer, but left the show.
Wilhoit, LisaLisa Wilhoit D'Amico, ConnieConnie D'Amico 15 Meg's bully Connie has not appeared in the series since 2013.
West, AdamAdam West Mayor West, AdamAdam West 93 Played a warped version of himself as the mayor of Quahog. Died in 2017.
Recurring guest voices[edit]
Main article: List of Family Guy guest stars
The recurring guest voices include Adam Carolla as Death, Patrick Stewart as Susie Swanson, Scott Grimes as Kevin Swanson and Sanaa Lathan as Donna Tubbs Brown. Previous recurring guests included Phyllis Diller in three episodes as Peter's Mother, Thelma, and Charles Durning as Peter's father, Francis. Both characters have since died, but Durning returned once to play Francis as a ghost. Early in the show's run, Fred Willard and Jane Lynch had a recurring role as a family of nudists. James Woods as James Woods.
Casting changes[edit]
Lacey Chabert voiced Meg for the first production season (14 episodes), but, because of a contractual agreement, was never credited.[15] Chabert left the series due to time constraints with her acting role in Party of Five, as well as schoolwork.[16]
Norm Macdonald voiced the character of Death in a second season episode of Family Guy. He was subsequently replaced by Adam Carolla in all other appearances.
Jon Cryer originally voiced Kevin Swanson in his first appearance, before the role was passed temporarily onto Seth MacFarlane. The character was written out of the series for several years, with Scott Grimes taking over the voice when the character returned.
Fairuza Balk was the original voice of high school bully Connie D'Amico until Lisa Wilhoit took over the character in the third season.
Awards and nominations[edit]
Year
Actor
Award
Category
Role
Result
Ref.
2000 Seth MacFarlane Primetime Emmy Award Outstanding Voice-Over Performance Stewie Griffin Won [17]
2009 Seth MacFarlane Primetime Emmy Award Outstanding Voice-Over Performance Peter Griffin Won [18]
2006 Seth MacFarlane Annie Award Best Voice Acting in an Animated Television Production Stewie Griffin Won [19]
2007 Mila Kunis Annie Award Voice Acting in an Animated Television Production Meg Griffin Won [20]
References[edit]
Notes
Jump up ^ Graham, Jefferson (January 29, 1999). "Cartoonist MacFarlane funny guy of Fox's 'Family' Subversive voice of series is his". USA Today. p. E7.
^ Jump up to: a b Cruz, Gilbert (September 26, 2008). "Family Guy's Seth MacFarlane". Time. Retrieved August 28, 2009.
Jump up ^ Smith, Andy (April 30, 2005). "A Real Family Reunion". Providence Journal TV. Archived from the original on July 22, 2011. Retrieved August 28, 2009.
Jump up ^ Dean, John (November 1, 2008). "Seth MacFarlane's $2 Billion Family Guy Empire". Fox Business. Archived from the original on September 23, 2010. Retrieved August 24, 2009.
Jump up ^ Franklin, Nancy (January 16, 2006). "American Idiots". The New Yorker.
^ Jump up to: a b c "Family Guy Cast and Details". TV Guide. Retrieved August 24, 2009.
^ Jump up to: a b c Miller, Kirk (November 19, 2008). "Q&A: Alex Borstein". Metromix. Archived from the original on February 18, 2012. Retrieved August 28, 2009.
^ Jump up to: a b "Alex Borstein (Lois) Laughs at the Once-Dead Family Guy's Longevity". TV Guide. November 13, 2006. Retrieved August 24, 2009.
^ Jump up to: a b Family Guy – Casting Mila Kunis. The Paley Center for Media. Retrieved September 20, 2010.
Jump up ^ De Leon, Kris (September 25, 2007). "Mila Kunis Talks About Working on Family Guy and Her Upcoming Movie". BuddyTV. Retrieved September 3, 2009.
Jump up ^ Graham, Jefferson (April 9, 1999). "Seth Green fits right in with new Family". USA Today.
Jump up ^ "Fans help 'Family Guy' return to Fox". Observer-Reporter. April 29, 2005. p. E5.
Jump up ^ Green, Seth (September 27, 2005). Stewie Griffin: The Untold Story: Audio Commentary (DVD).
Jump up ^ "Steve Callaghan Named 'American Dad' Showrunner".
Jump up ^ Epstein, Daniel Robert. "Interview with Seth MacFarlane, creator of The Family Guy". UGO Networks. Archived from the original on June 11, 2007. Retrieved November 23, 2008.
Jump up ^ "Sonic the Horndog". GameSpy. Retrieved 2009-10-03.
Jump up ^ Brian Lowry (2000-08-28). "NBC Leads Tally of Early Emmys, Boosted by 'West Wing'". Los Angeles Times. Retrieved 2008-08-20.
Jump up ^ "The 61st Primetime Emmy Awards and 2009 Creative Arts Emmy Awards Nominees are...". Academy of Television Arts & Sciences. 2009-07-16. Archived from the original on 2009-07-18. Retrieved 2009-07-16.
Jump up ^ "Annie Award Winners". Annie Awards. Archived from the original on 2007-07-01. Retrieved 2007-12-21.
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Congruence (geometry)
From Wikipedia, the free encyclopedia
Jump to: navigation, search
An example of congruence. The two triangles on the left are congruent, while the third is similar to them. The last triangle is neither similar nor congruent to any of the others. Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distance and angles. The unchanged properties are called invariants.
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.[1]
More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted.
In elementary geometry the word congruent is often used as follows.[2] The word equal is often used in place of congruent for these objects.
Two line segments are congruent if they have the same length.
Two angles are congruent if they have the same measure.
Two circles are congruent if they have the same diameter.
In this sense, two plane figures are congruent implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters and areas.
The related concept of similarity applies if the objects have the same shape but do not necessarily have the same size. (Most definitions consider congruence to be a form of similarity, although a minority require that the objects have different sizes in order to qualify as similar.)
Contents
[hide]
1 Determining congruence of polygons
2 Congruence of triangles
2.1 Determining congruence
2.1.1 Side-side-angle
2.1.2 Angle-angle-angle
3 Definition of congruence in analytic geometry
4 Congruent conic sections
5 Congruent polyhedra
6 Congruent triangles on a sphere
7 Notation
8 See also
9 References
10 External links
Determining congruence of polygons
The orange and green quadrilaterals are congruent; the blue is not congruent to them. All three have the same perimeter and area. (The ordering of the sides of the blue quadrilateral is "mixed" which results in two of the interior angles and one of the diagonals not being congruent.)
For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with n sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for n sides and n angles.
Congruence of polygons can be established graphically as follows:
First, match and label the corresponding vertices of the two figures.
Second, draw a vector from one of the vertices of the one of the figures to the corresponding vertex of the other figure. Translate the first figure by this vector so that these two vertices match.
Third, rotate the translated figure about the matched vertex until one pair of corresponding sides matches.
Fourth, reflect the rotated figure about this matched side until the figures match.
If at any time the step cannot be completed, the polygons are not congruent.
Congruence of triangles
See also: Solution of triangles
Two triangles are congruent if their corresponding sides are equal in length, in which case their corresponding angles are equal in measure.
If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as:
△ A B C ≅ △ D E F {\displaystyle \triangle \mathrm {ABC} \cong \triangle \mathrm {DEF} }
In many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two triangles.
The shape of a triangle is determined up to congruence by specifying two sides and the angle between them (SAS), two angles and the side between them (ASA) or two angles and a corresponding adjacent side (AAS). Specifying two sides and an adjacent angle (SSA), however, can yield two distinct possible triangles.
Determining congruence
Sufficient evidence for congruence between two triangles in Euclidean space can be shown through the following comparisons:
SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
SSS (Side-Side-Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.
ASA (Angle-Side-Angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.
The ASA Postulate was contributed by Thales of Miletus (Greek). In most systems of axioms, the three criteria – SAS, SSS and ASA – are established as theorems. In the School Mathematics Study Group system SAS is taken as one (#15) of 22 postulates.
AAS (Angle-Angle-Side): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent. AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should be 180°. ASA and AAS are sometimes combined into a single condition, AAcorrS – any two angles and a corresponding side.[3]
RHS (Right-angle-Hypotenuse-Side), also known as HL (Hypotenuse-Leg): If two right-angled triangles have their hypotenuses equal in length, and a pair of shorter sides are equal in length, then the triangles are congruent.
Side-side-angle
The SSA condition (Side-Side-Angle) which specifies two sides and a non-included angle (also known as ASS, or Angle-Side-Side) does not by itself prove congruence. In order to show congruence, additional information is required such as the measure of the corresponding angles and in some cases the lengths of the two pairs of corresponding sides. There are a few possible cases:
If two triangles satisfy the SSA condition and the length of the side opposite the angle is greater than or equal to the length of the adjacent side (SsA, or long side-short side-angle), then the two triangles are congruent. The opposite side is sometimes longer when the corresponding angles are acute, but it is always longer when the corresponding angles are right or obtuse. Where the angle is a right angle, also known as the Hypotenuse-Leg (HL) postulate or the Right-angle-Hypotenuse-Side (RHS) condition, the third side can be calculated using the Pythagorean Theorem thus allowing the SSS postulate to be applied.
If two triangles satisfy the SSA condition and the corresponding angles are acute and the length of the side opposite the angle is equal to the length of the adjacent side multiplied by the sine of the angle, then the two triangles are congruent.
If two triangles satisfy the SSA condition and the corresponding angles are acute and the length of the side opposite the angle is greater than the length of the adjacent side multiplied by the sine of the angle (but less than the length of the adjacent side), then the two triangles cannot be shown to be congruent. This is the ambiguous case and two different triangles can be formed from the given information, but further information distinguishing them can lead to a proof of congruence.
Angle-angle-angle
In Euclidean geometry, AAA (Angle-Angle-Angle) (or just AA, since in Euclidean geometry the angles of a triangle add up to 180°) does not provide information regarding the size of the two triangles and hence proves only similarity and not congruence in Euclidean space.
However, in spherical geometry and hyperbolic geometry (where the sum of the angles of a triangle varies with size) AAA is sufficient for congruence on a given curvature of surface.[4]
Definition of congruence in analytic geometry
In a Euclidean system, congruence is fundamental; it is the counterpart of equality for numbers. In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the Euclidean distance between them is equal to the Euclidean distance between the corresponding points in the second mapping.
A more formal definition states that two subsets A and B of Euclidean space Rn are called congruent if there exists an isometry f : Rn → Rn (an element of the Euclidean group E(n)) with f(A) = B. Congruence is an equivalence relation.
Congruent conic sections
Two conic sections are congruent if their eccentricities and one other distinct parameter characterizing them are equal. Their eccentricities establish their shapes, equality of which is sufficient to establish similarity, and the second parameter then establishes size. Since two circles, parabolas, or rectangular hyperbolas always have the same eccentricity (specifically 0 in the case of circles, 1 in the case of parabolas, and 2 {\displaystyle {\sqrt {2}}} in the case of rectangular hyperbolas), two circles, parabolas, or rectangular hyperbolas need to have only one other common parameter value, establishing their size, for them to be congruent.
Congruent polyhedra
For two polyhedra with the same number E of edges, the same number of faces, and the same number of sides on corresponding faces, there exists a set of at most E measurements that can establish whether or not the polyhedra are congruent.[5][6] For cubes, which have 12 edges, only 9 measurements are necessary.
Congruent triangles on a sphere
Main articles: Solving triangles § Solving spherical triangles, and Spherical trigonometry § Solution of triangles
As with plane triangles, on a sphere two triangles sharing the same sequence of angle-side-angle (ASA) are necessarily congruent (that is, they have three identical sides and three identical angles).[7] This can be seen as follows: One can situate one of the vertices with a given angle at the south pole and run the side with given length up the prime meridian. Knowing both angles at either end of the segment of fixed length ensures that the other two sides emanate with a uniquely determined trajectory, and thus will meet each other at a uniquely determined point; thus ASA is valid.
The congruence theorems side-angle-side (SAS) and side-side-side (SSS) also hold on a sphere; in addition, if two spherical triangles have an identical angle-angle-angle (AAA) sequence, they are congruent (unlike for plane triangles).[7]
The plane-triangle congruence theorem angle-angle-side (AAS) does not hold for spherical triangles.[8] As in plane geometry, side-side-angle (SSA) does not imply congruence.
Notation
A symbol commonly used for congruence is an equals symbol with a tilde above it, ≅, corresponding to the Unicode character 'approximately equal to' (U+2245). In the UK, the three-bar equal sign ≡ (U+2261) is sometimes used.
See also
CPCTC (Corresponding parts of congruent triangles are congruent)
Euclidean plane isometry
Isometry
References
Jump up ^ Clapham, C.; Nicholson, J. (2009). "Oxford Concise Dictionary of Mathematics, Congruent Figures" (PDF). Addison-Wesley. p. 167. Archived from the original on 29 October 2013. Retrieved 2 June 2017. CS1 maint: BOT: original-url status unknown (link)
Jump up ^ "Congruence". Math Open Reference. 2009. Retrieved 2 June 2017.
Jump up ^ Parr, H. E. (1970). Revision Course in School mathematics. Mathematics Textbooks Second Edition. G Bell and Sons Ltd. ISBN 0-7135-1717-4.
Jump up ^ Cornel, Antonio (2002). Geometry for Secondary Schools. Mathematics Textbooks Second Edition. Bookmark Inc. ISBN 971-569-441-1.
Jump up ^ Alexander Borisov, Mark Dickinson, and Stuart Hastings, "A congruence problem for polyhedra", American Mathematical Monthly 117, March 2010, pp. 232-249. [1]
Jump up ^ Alexa Creech, "A congruence problem" http://146.163.152.131/teaching/projects/creech_final.pdf Archived November 11, 2013, at the Wayback Machine.
^ Jump up to: a b Michael Bolin, "Exploration of Spherical Geometry", September 9, 2003, pp.6-7. http://math.iit.edu/~mccomic/420/notes/Bolin_spherical.pdf
Jump up ^ Hollyer, L., http://www.uh.edu/~hollyer/Module6/m6ppt/sld089.htm
External links
Wikimedia Commons has media related to Congruence.
The SSS at Cut-the-Knot
The SSA at Cut-the-Knot
Interactive animations demonstrating Congruent polygons, Congruent angles, Congruent line segments, Congruent triangles at Math Open Reference
Retrieved from "https://en.wikipedia.org/w/index.php?title=Congruence_(geometry)&oldid=805558264"
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