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Talk:Talking animal

Link to talking animals (youtube)
what about these? http://www.youtube.com/watch?v=skE2dq3cm0A

aren't people really animals
Aren't people really animals?? 66.245.30.110 19:49, 25 May 2004 (UTC)

 * Can your read or only write? Try to track from animal. Mikkalai
 * Bad grammar war go Jhalkompwdr 21:05, 26 March 2007 (UTC)

There's probably a serious point here - humans are animals - but the article is about non-human animals. I feel like adding 'non-human' in places, but obviously it would be daft to say non-human at every step. Looking at the animal article is a start, but the pedant in me wants to do something. Stevebritgimp (talk) 20:31, 29 January 2010 (UTC)

"talking animal" and "furry" are the same thing
For over two decades, furry fandom has been defined as the appreciation, promotion, and production of stories and art about anthropomorphic animals, as well as the exploration, interpretation and examination of humanity and human values through anthropomorphic expression. There is no appreciable difference between "talking animal" and "furry."

Additional information and clarification can be found here and here. Xydexx 01:58, 7 May 2005 (UTC)

 * Not necessarily, there are different varieties of "talking animal" as the text of the article points out. Furry is a relavent link, because it has to do with talking animals, but there's definitely a difference. --Krishva 05:59, May 7, 2005 (UTC)

 * I've noticed both the links pointed out are created by people in the furry subculture, but not in the literature/animation/comic industries (for fictional talking animals) or anybody in animal research (for such cases as the parrot, and the dolphin's language). In addition to that I see no reference to the Furry subculture in this article, so it may be considred biased to say that Furry and Talking Animal are one and the same.

 * It can be said Furry has aspects of the Talking Animal, but the Talking Animal is definitely not the same as Furry, or a subset of it. -- Grumpyhan 07:11, 7 May 2005 (UTC)

 * Furry fandom is about animals with human characteristics. Talking animals are animals with human characteristics. It seems pretty obvious the furry fandom and literature/animation/comic industries (for fictional talking animals) are one and the same. —Xydexx 07:21, 7 May 2005 (UTC)

 * I quite doubt that; there is no supporting evidence that Talking Animals can be considered to be Furry just because both have animals which are anthropomorphized, because that would be saying English and Chinese are the same because both are languages. I see nothing obvious about talking animals in literature/animation/comic industries, as to call (as an example) the talking animals in Narnia furries is extremely inaccurate. -- Grumpyhan 07:31, 7 May 2005 (UTC)

 * Your analogy is invalid: It would be like saying English and Chinese are languages. Furries and talking animals are anthropomorphized. It's more like the difference between "Good Day" and "Guten Tag"— used by different people, but means the same thing. —Xydexx 17:57, 7 May 2005 (UTC)

 * It is an incorrect analogy because it was to point out your analogy is equally invalid, and Good Day and Guten Tag may mean the same but it does not mean both (if such an article exists) should share an article, but rather both should be included in Greetings along with "Good Day" in other languages.

 * I wrote on the Furry Talk Page how Furry and Talking/Funny Animal aren't considered the same; you may want to read that. -- Grumpyhan 00:17, 8 May 2005 (UTC)

 * Just because they aren't considered the same by you doesn't mean they aren't considered the same by anyone else. They've been considered the same by furry fandom for two decades. ("Funny animal" is sinply the outdated term for "furry".) Thus, I've taken the liberty of flagging this article as I believe (as Krishva will surely agree) all sides of an argument should be presented here. Since the issue of Furry and Talking/Funny Animal is debatable, it should be stated as such. This article presents a severely biased point of view, and the fact that you remove comments stating that an issue is debatable or some people do not agree with a certain point proves that. —Xydexx 23:48, 8 May 2005 (UTC)

 * ...What?

 * Not only have I not removed any comment stating that this issue is debatable, there wasn't even any! Funny animal has never been an outdated term for furry (most professionals in both arts and scientific fields I mentioned have never, ever called them furries), and how can you say this article's neurality is disputed just because it doesn't say "Talking Animal is actually Furry"?

 * I'm not sure what makes you so persistent in going everywhere (incl Funny Animal) to claim that Furry=a lot of terms, and while I admire your spirit in upholding your beliefs, making up things in order to show that you are right is not correct behaviour on Wikipedia. This may be jumping into conclusions, but I presume you took little time to read any supporting evidence I have mentioned, as all I have seen coming from your POV in the Talk pages is "furry=talking animal, period".

 * I have added a short category that is similar to the Funny Animal article, though I find it irrelevant and little to do with the article. -- Grumpyhan 00:07, 9 May 2005 (UTC)

 * I think a better question to ask might be why some people are so persistent in removing any references to furry from these articles.

 * I have been nothing but forthright in ensuring these articles remain NPOV, and have provided supporting evidence that funny animal was a term used for furry, which you deleted. When one considers the thriving genre or artwork and stories which has developed over the past twenty years as a direct result, it is patently ludicrous to claim anthropomorphized talking animals and furries have nothing at all to do with each other.

 * I'm sure many will agree with me that suppressing facts you don't agree with is not proper behavior on Wikipedia. —Xydexx 20:44, 15 May 2005 (UTC)

 * Excuse me, I was expecting an apology from you for making up facts about me removing things which never existed in the first point, not continuing to assert that I am persistent in removing them. The link you have given me was not only not removed, it was in funny animal, it wasn't removed by me (I deleted the incorrect description that it suggested that funny animal was an old term now used as furry, and no matter how much you try to say it is the other way round, I have given proof after proof that your view is erroneous), and it is the exact same link which I have pointed out in Funny Animal that it never suggested that furry was the new term for funny animal. Not only have I not even suppressed your (admittedly strange) opinion, I wrote a new category for it - only for you to write more lies about me on this talk page.

 * Also, this is Talking animal. It is not Funny Animal. These are two very different articles. The fact that you cannot distinguish this fact (and several others: including making up facts about me, personally attacking the user Krishva, having a lack of understanding of the Neurality tag (you were supposed to put the "cleanup" tag, if it was even necessary), not giving substantial proof other than a few weak - and disputed - urls to show your case) gives me doubts as to whether you actually care about wikipedia at a whole, but rather you only want to let it be known that furries are really interesting and important despite how the general populace have entirely no idea who they are. If my suspicions are correct, I would suggest that you make your own opinion-airing website (if you do have one) more popular and debated, rather than go into wikipedia and completely disregard its given etiquette. If not, please give me more proof that you are correct (not "my argument tactics are correct" - that is all you have been doing) and stop touting the three links you are throwing everywhere. -- Grumpyhan 04:05, 16 May 2005 (UTC)

 * Fred Patten, who documented the origins of furry fandom in A Chronology Of Furry Fandom, states it was around late 1983 or early 1984 that the fandom coalesced out of SF fandom and comics fandom. Mr. Patten is founding member of the Cartoon/Fantasy Organization, has written articles for Starlog and Animation Magazine, and was winner of the 2003 Ursa Major Award for Best in Show: Fifteen Years of Outstanding Furry Fiction. You can continue to trivialize Mr. Patten's accomplishments if it makes you feel better, but the connection between talking animals and furries is pretty ironclad at this juncture. Besides, if you're incapable of responding with anything but wild accusations and personal attacks against me, then there really is little reason to continue this discussion. —Xydexx 01:03, 18 May 2005 (UTC)

 * When did I trivalize his writing? I said this article does not support your assertions, not that the it is a bad one. If you bring up a Stephen Hawking article in a biology conference people will look at you funny (although this is an exaggeration of what you're doing here - you just gave me an article that suggests little to nothing that people, other than a select few, called talking and funny animals "furries"). And making up wild accusations about you? You made things up about my conduct here and tried to claim otherwise?

 * After observing that your inability to make a sound argument for your own case (and descending into making things up or about the other party or insulting them), and that you are the only one to assert that furry has anything to do with talking/funny animals, I'm convinced that the statement is POV and will remove them. -- Grumpyhan 05:00, 20 May 2005 (UTC)

 * He's certainly not the only one to "assert that furry has anything to do with talking animals". Nor was he the only one to object to furry and furry fandom being merged. But just like with that merging, you assumed there was consensus when there was not, and you took drastic action without that consensus. There is no reason to not link to furry fandom in this article, as the two have many similarities. 68.199.46.6 20:32, 3 August 2005 (UTC)

 * I think the reason that those links were not in the See Also was because all of them except kemono are linked in some portion of the main text. --Krishva 03:48, August 4, 2005 (UTC)

 * It is linked in the main article before your complaint. -- Grumpyhan 03:31, 12 August 2005 (UTC)

NPOV Categories & Content
I think "Anthropomorphism" and "Folklore" are relevant.

There are no "Speech" or "Animal psychology" categories, so I have removed them.

"Animal behaviour" seems to be a relevant category whatever one's POV. Nigosh 00:41, 12 Jun 2005 (UTC)

 * I didn't notice ContiE has added categories. Thanks! -- Grumpyhan 12:12, 12 Jun 2005 (UTC)

Archive
Personal argument-like discussions have been removed and archived at Talk:Talking animal/Archive1 -- Grumpyhan 00:21, 23 Jun 2005 (UTC)

Oh Long Johnson
The talking cat "Ole Long Johnson" is all over the Internet, but I am told we aren't allowed to post links to YouTube. Can anyone provide a citation for the footage? It's genuine, and if you go on Youtube and type "oh long johnson" the footage is easy to find. 68.146.47.196 15:25, 1 August 2007 (UTC)

Nazi Dogs
I read earlier in today's Metro (London free newspaper) that the Nazis were attempting to train dogs to talk during World War II. If anyone can find a copy of the article, it might be a good source for this article. Miyagawa  (talk)  20:32, 25 May 2011 (UTC)

Citations needed for internally linked items?
Why do Gef the talking mongoose and Kosik the elephant have "citation needed" next to their short descriptions, when they clearly link to full articles here on Wikipedia? That seems kind of lame. Cernansky (talk) 22:24, 5 December 2012 (UTC)

Should definition of talking animal include gestures
The definition of talking animal in this article includes gestures. Surely this makes the definition so broad it is (virtually) meaningless. "Gestures" would include every dog, cat, bear, bird, etc that has been trained or learned to raise its paw/claw for food. "Gestures" would include any animal that adopts a bi-pedal stance or locomotion. "Gestures" could even include scratching. I suggest the word "gestures" is deleted from the definition. __DrChrissy (talk) 10:08, 9 May 2014 (UTC)

Outdated source
Source 7 is no longer available. — Preceding unsigned comment added by 59.149.182.190 (talk) 09:11, 11 August 2014 (UTC)

Create a List of talking animals?
This article seems to be descending into a list of individual cases of animals that "talk". Several of these are inaccurate and/or poorly edited. WP prefers prose rather than lists, but there seems little effort by editors to do this here. Should we start a "List of talking animals" where these individual cases can be listed?__DrChrissy (talk) 14:16, 17 March 2015 (UTC)

External links modified
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title: Talk:Talking animal


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Paramount Fine Foods Centre

The Paramount Fine Foods Centre, formerly the Hershey Centre, is a multi-purpose sports and entertainment complex located in Mississauga, Ontario, Canada. Its current name was adopted on July 1, 2018, following a new naming rights agreement with Mississauga-based restaurant chain Paramount Fine Foods.

History

First opened in 1998 as the Hershey Centre, the complex is located on Rose Cherry Place, which was named after the late wife of Don Cherry, founder and former owner of the Mississauga IceDogs hockey team. The closest major intersection is Kennedy Road and Matheson Boulevard East. In 2007, a new multi-sport facility called SportZone opened just to the north of the main bowl. It houses a full-size indoor soccer field, a full size FIBA basketball court, a gymnastics facility, and two outdoor soccer fields.

The centre is currently the home arena for the Mississauga Steelheads of the Ontario Hockey League (ice hockey) and Raptors 905 of the NBA G League (basketball). It previously housed the Mississauga IceDogs (ice hockey) from 1998 to 2007, the Mississauga Power (basketball) from 2011 to 2015, the Toronto ThunderHawks of the National Professional Soccer League from 2000 to 2001, and the Mississauga MetroStars of the Major Arena Soccer League (indoor soccer) from 2018 to 2019. It has also been the venue for numerous musical acts, including The Tragically Hip, Green Day, The White Stripes, Hatebreed, and Chinese superstar Joker Xue.

Hockey
Along with being the home of Mississauga's OHL teams since its opening, it has hosted several hockey events. In the year 2000 the Hershey Centre hosted the OHL All-Star Classic as well as the IIHF Women's World Hockey Championship. The OHL Championship Series for the J. Ross Robertson Cup has been held at the facility in 2004, 2011 and 2017. In May 2011 the Mississauga St. Michael's Majors hosted the 2011 Memorial Cup. The Saint John Sea Dogs defeated Mississauga in the Final 3–1.

Basketball
The National Basketball League of Canada announced that the Oshawa Power would relocate to Mississauga and play as the Mississauga Power at the Hershey Centre starting in the 2013–14 season.

The Toronto Raptors announced that beginning in the 2015–16 season, they would have a team in the NBA Development League in Mississauga and play as the Raptors 905 at the Hershey Centre. The 905 displaced the Power and the NBLC team ceased operations. In 2017 and 2018 the Raptors 905 hosted both the NBA G League Showcase as well as the G League Finals at the arena.

Figure skating
The arena has hosted the Skate Canada International figure skating competition, part of the ISU Grand Prix of Figure Skating series in 2000, 2003, 2011 and in 2016. The venue is also host to this competition in October 2022.

It hosted the Canadian Figure Skating Championships for the first time in 2013 and again in 2020.

2015 Pan and Parapan American Games
During the 2015 Pan American Games, it hosted the four combative sports of judo, karate, taekwondo and wrestling. During that time the centre was temporarily renamed the Mississauga Sports Centre due to naming rights. The venue also hosted the parapan sports of goalball, powerlifting and it also featured the debut of wheelchair rugby.

Other events
It was the venue for the inaugural 2002 Heritage Cup, an international indoor lacrosse tournament. The North American Roller Hockey Championships finals were held at Hershey Centre in July 2006, 2009 and 2013. The centre hosted the 2009 World Cup of Curling. A funeral for Peel Regional Police officer James Ochakovsky took place at the arena on March 9, 2010. It has also hosted the FIRST Robotics Competition, an international high school robotics competition. On September 22, 2000, it was the site of the only ECW show in Canada before the promotion's demise in 2001. On February 14, 2023, the venue hosted the state funeral for former Mississauga mayor Hazel McCallion.

COVID-19 mass vaccination site
As of May 2021 the venue is being used as a mass COVID-19 vaccination site.

Mississauga and Iceland Fields
The grounds of the Paramount Fine Foods Centre are also home to two outdoor field facilities, known as the Mississauga Fields and Iceland Fields.

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

title: Paramount Fine Foods Centre


text:
Mara Wilson

Mara Wilson (born July 24, 1987) is an American actress. She rose to prominence as a child actress playing Natalie Hillard in the film Mrs. Doubtfire (1993) and went on to play Susan Walker in Miracle on 34th Street (1994), the title character in Matilda (1996), and Annabel Greening in A Simple Wish (1997). Following her role as Lily in Thomas and the Magic Railroad (2000), Wilson took a 12-year hiatus from acting to focus on writing. She returned to acting in 2012 and has predominantly worked in web series.

Early life
Mara Wilson was born in Burbank, California, the oldest daughter of Burbank PTA school volunteer Suzie and KTLA broadcast engineer Mike Wilson. Her mother was Jewish, while her father is half Irish.

Wilson's mother was diagnosed with breast cancer on March 10, 1995, and died on April 26, 1996. The film Matilda was dedicated to her memory. Wilson later recalled that this affected her passion for acting. At age 12, Wilson was diagnosed with obsessive–compulsive disorder. She has also been diagnosed with attention deficit hyperactivity disorder. She attended Idyllwild Arts Academy in Idyllwild, California. After graduation in 2005, Wilson relocated to New York City to continue her studies at New York University's Tisch School of the Arts, graduating in 2009. Wilson appeared in her own one-woman show called Weren't You That Girl? while in college.

Career
When Wilson was five, she became interested in acting after watching her older brother Danny appear in television commercials. Wilson’s parents were initially disinclined, but eventually appearing in several commercials for businesses, she was invited to audition for the 1993 comedy film Mrs. Doubtfire. Producers were impressed and awarded Wilson the role of Natalie Hillard. The following year, Wilson appeared in the remake of Miracle on 34th Street.

In 1993, Wilson was cast in a recurring role as Nikki Petrova on Melrose Place and played Barbara Barton in the 1994 television film A Time to Heal. She sang "Make 'Em Laugh" at the 67th Academy Awards broadcast on March 27, 1995, with Tim Curry and Kathy Najimy. In 1995, Wilson won the ShoWest Award for Young Star of the Year.

Wilson's film work caught the attention of Danny DeVito, and she was cast as the main protagonist Matilda Wormwood in the 1996 film Matilda. She was nine years old at the time. Wilson was nominated for three awards for her performance, winning the YoungStar Award for Best Performance by a Young Actress in a Comedy Film. In 1997, Wilson starred in A Simple Wish alongside Martin Short. Although she was nominated for three awards again, the film mostly received negative reviews by critics.

In 1997, Wilson went to a table reading for What Dreams May Come starring Robin Williams, but she did not get the part. A year later, Wilson unsuccessfully auditioned for the 1998 remake of Disney's The Parent Trap but the role was given to Lindsay Lohan after Wilson was deemed too young. In 1999, she portrayed Willow Johnson in the film for The Wonderful World of Disney titled Balloon Farm, based on a fiction book.

In 2000, Wilson appeared in the fantasy film Thomas and the Magic Railroad, which was her last film. The film was universally panned by critics and performed poorly at the box office. Wilson retired from film work shortly afterward. She received a script for the 2001 film Donnie Darko but declined to audition for the film. After retiring from film acting, Wilson began stage acting. Her theater credits include A Midsummer Night's Dream and Cinderella. Wilson starred in her own live shows Weren't You That Girl? and What Are You Afraid Of?

In 2012, Wilson appeared briefly in one episode of a web series called Missed Connection in the role of Bitty and made special appearances on internet review shows for That Guy with the Glasses—most notably a comedic turn playing an adult Matilda during a review of Matilda by The Nostalgia Chick, Lindsay Ellis. That year, Wilson explained why she quit film acting: "Film acting is not very fun. Doing the same thing over and over again until, in the director's eyes, you 'get it right', does not allow for very much creative freedom. The best times I had on film sets were the times the director let me express myself, but those were rare."

In May 2013, Wilson wrote an article for Cracked.com, offering her opinion of the delinquency of some former child stars. As of 2013, Wilson worked for Publicolor. Her play Sheeple was produced in 2013 for the New York International Fringe Festival. In an interview that December, Wilson stated that her film acting days are over, and that she is instead focusing on writing. Wilson’s book Where Am I Now?: True Stories of Girlhood and Accidental Fame was published on September 13, 2016.

Wilson has a recurring role on the podcast Welcome to Night Vale as "The Faceless Old Woman Who Secretly Lives in Your Home", as well as her own storytelling show called What Are You Afraid Of? In 2016, Wilson made a brief return to television in a Mrs. Doubtfire-inspired episode of Broad City, in which she played a waitress where the comical Heimlich scene from the film was re-enacted. That same year, Wilson voiced Jill Pill, a writer/director anthropomorphic spider, in season 3 of BoJack Horseman. Wilson voiced Liv Amara/Diane "Di" Amara in Big Hero 6: The Series.

In a 2017 NPR interview, The Simpsons voice actress Nancy Cartwright stated that a young Wilson was the inspiration for a character's voice on the episode "Bart Sells His Soul".

Charity work
In 2015, Wilson collaborated with Project UROK, a nonprofit organization whose mission is to aid teens with mental illness.

Personal life
Wilson has three older brothers: Danny, Jon, and Joel, and a younger sister, Anna. She is a cousin of political commentator and media host Ben Shapiro, whom she has disavowed due to his conservative views and her contrasting progressive beliefs; the two have no contact with each other. Wilson was raised Jewish, but became an atheist at the age of 15.

In 2015, Wilson appeared in a video by the mental health charity Project UROK in which she discussed the mental illnesses she has experienced, including anxiety, depression, and obsessive–compulsive disorder. Wilson discussed her history of mental illness on Paul Gilmartin's podcast The Mental Illness Happy Hour.

Wilson came out as bisexual during an interview with Medium in September 2017. In a 2017 op-ed in Elle magazine, she defended the then-13-year-old actress Millie Bobby Brown after commentators sexualized Brown's public image. In a 2021 op-ed in The New York Times, Wilson commented on the documentary Framing Britney Spears and the parallels between her own life as a child star and Britney Spears'. Wilson recalled an incident in which she was asked to comment on the burgeoning sexuality of an 18-year-old Spears when she herself was barely 13, and expressed relief at largely escaping oversexualization of her public image compared to Spears. Wilson described her disappointment when a reporter called her a "spoiled brat" after she stated that she wanted the day off on her 13th birthday instead of granting interviews.

As of 2013, Wilson resided in the Queens borough of New York City.

Stage roles

 * A Midsummer Night's Dream (2004)
 * Cinderella (2005)
 * Weren't You That Girl? (2009)
 * What Are You Afraid Of? (2014)

title: Mara Wilson


text:
WNBA Coach of the Year Award

The Women's National Basketball Association's Coach of the Year is an annual Women's National Basketball Association (WNBA) award given since the league's inaugural season. The winner is selected at the end of regular season by a panel of sportswriters from the United States, each of whom casts a vote for first, second and third place selections. Each first-place vote is worth five points; each second-place vote is worth three points; and each third-place vote is worth one point. The person with the highest point total, regardless of the number of first-place votes, wins the award.

Seven coaches have won both this award and the WNBA Finals in the same season: Van Chancellor (1997–1999), Bill Laimbeer (2003), John Whisenant (2005), Brian Agler (2010), Cheryl Reeve (2011), Sandy Brondello (2014), and Becky Hammon (2022).

Van Chancellor, Mike Thibault, and Cheryl Reeve have won the award the most times, with 3 selections each.

title: WNBA Coach of the Year Award


text:
Talk:Diagonal

Article fails to provide basic definition
I'm sorry I have to say this, but this article fails to answer even the basic question "what is a diagonal", moreover someone removed my stub for a section giving that defintion. As they didn't explain their action I'm reverting! --Mike 22:45, 30 October 2006 (UTC)
 * The objects in your son's homework are polygons. In the Polygon section, in the very first sentence you can read "a diagonal is a line segment joining any two non-consecutive vertices." Gogino 06:47, 31 October 2006 (UTC)

I think the (etymological) dictionary definition is more useful - it was far more useful than the article it said it derives from dia - "through" & gonal? - "angle" (related to knee & agony), therefore I believe it has the meaning of "bi-secting" the angle. I know diagonal also tends to be used for an upward sloping line (which is another use) as in a diagonal mark, or a diagonal brace in engineering (an entire subject in its own to do with strengthening structures), it may also be used in football for forward+side movement.

The use given in the article is such a small percentage of the use of the word that in my opinion it amounts to bias, but the real reason I don't like the article as currently written is that it fails to give a basic definition useable by a school child - who I believe would be the main audience using wikipedia.

As for your quote: "a diagonal is a line segment joining any two non-consecutive vertices." 1. If the line would be outside the angle, then by the common sense definition (through the angle) it cannot be a diagonal because it is not through the angle. 2. I did not spot it. 3. if you don't know what a diagonal is, you are hardly likely to know what a vertice is. 4. Please let me re-emphasis: this encyclopedia will be used by a large number of school children (and parents). Some of whom haven't a clue what a polygon or a matrix, or a polynomial. If they cannot find a sensible definition within the first few paragraphs the article is useless to the 95%? of humanity who aren't doing advanced upper-school or university maths.--Mike 08:31, 31 October 2006 (UTC)

PS. Sorry - I should also say that if I were still (forced to do/) doing advance maths it is a great article! --Mike 08:34, 31 October 2006 (UTC)

PPS. And .... why not put in the classic Harry potter (Diagnonally = Diagon Alley) --Mike 08:37, 31 October 2006 (UTC)

 * > I think the (etymological) dictionary definition is more useful
 * It might be so for many people. However, these kind of definitions should be in a dictionary. Luckily, there is wiki-dictionary and you can find there the definition you proposed: diagonal (dictionary entry). There is no etymology there. You can contribute by adding yours there. Here is an example of etymology entry: enemy (dictionary entry).

 * > it fails to give a basic definition useable by a school child - who
 * I have noticed this problem and suggested a solution here.
 * Would you like to help with it?

 * It wasn't my 11year old that was reading the article, it was me his father and I did mathematics and Universtity! Between us we must represent 99.9% of all wikipedia readers. As an engineer I never use diagonal except to mean: "from corner to corner of a rectangle", therefore I had no idea how to apply it to a rhombus or pentagon - I came to this article and it was useless! However I may have been a bit abrupt in previous comments - I know it is difficult to write an article for the many different readers and I got very annoyed when someone simply removed my request for a basic definition without comment. --Mike 09:51, 6 November 2006 (UTC)

 * > I believe would be the main audience using wikipedia.
 * I don't think so. And I, as an adult, don't want to spend time on reading kid's definitions since I have to take care of many things including my kids. I want concise and precise information. Besides, this article is at the level of high school geometry course. That is when you have first complete course of geometry. I understand your frustration. You want to help your son when current school system teaches bits and pieces of "everything at every grade". This is a known problem. Read, for example, here. And consequences of this are published, for example, here. Unfortunately, a solution will not come easily because there are too many opinions and too little research.

 * Please move what you added to the Wiktionary here after reconciling with what is already there.
 * --Gogino 02:51, 6 November 2006 (UTC)

 * You are quite a liberty to change it yourself, but if it is not suitable for the average reader, then I will simply change it back! --Mike 09:33, 6 November 2006 (UTC)

 * Finally, I found a basic definition of diagonal: Diagonal and Simple Wikipedia is the right place for it. Here should be only a link. The definition which, was here is good for high-school-geometry-class students. I think it is very appropriate. I can understand that the Wiktionary is not the best place, but the Simple Wikipedia was made with simplicity of understanding in mind and should be okay.
 * --Gogino 02:50, 9 November 2006 (UTC)

 * I'm sorry Gogino, you don't own this page. It is an encyclopedia not a maths text book. Diagonal is a common term used at all levels both inside and outside of mathematics you can't hog this page for the mathematical use and pretend other uses don't exist. Whether you like it or not the entry should reflect this. Take a look at other pages, this one ought to have sections like "fictonal use of diagonal" "sporting use of diagonal" the mathematics that currently dominates the page completely distorts the article and a short definition only goes a little way to addressing this. --Mike 21:20, 9 November 2006 (UTC)

 * Mike, I am not supposed to know about other uses. If you know you are free to contribute. I was discussing the basic or simple definition. The following are your statements:
 * "... a school child - who I believe would be the main audience using wikipedia."
 * "... I did mathematics and Universtity! Between us we must represent 99.9% of all wikipedia readers."
 * --Gogino 07:37, 23 November 2006 (UTC)

Proposed opening
"Diagonal an upward sloping line or a line crossing a shape that joins two nonadjacent corners. Originally from Greek: διαγωνιος (diagonios) used by both Strabo and Euclid for the longest line across a rhombus or from corner to corner through the middle of a cuboid . Formed from dia- ('through', 'across') and gonia ('angle' related to gony 'knee.') later taken into latin as: diagonus ('slanting line')."

This is a rare word in Greek with only with 3 greek references in Perseus (all Euclid Proposition 11.28 & propisiton 11.38 "diameter") However, although the greek is not available it is also used in strabo where he is arguing about whether a geographical area akin to a rhombus should be measured by its diagonal or its length:
 * Comment on proposed opening

"The fourth section Hipparchus certainly manages better, .... He properly objects to Eratosthenes giving as the length of this section a line drawn from Thapsacus to Egypt, as being similar to the case of a man who should tell us that the diagonal of a parallelogram was its length. ... and a line drawn from Thapsacus to Egypt would lie in a kind of diagonal or oblique direction between them"

From the evidence, it would appear the original definition relates to a line across/through a simple shape. Modern use is similar (e.g. in chess queens move diagonally). I've not seen any use outwith the narrow confines of theoretical geometry for it's definition to extend to line entirely outwith a shape so I think it would be wrong to give this as a general definition (although it clearly should be mentioned along with its more precise mathematical definition). --Mike 11:12, 31 October 2006 (UTC)

I've added the paragraph, shortened it a bit and although the greeks seem to use it for the longest length of a rhombus, I've left it as "a line" - not only does it show the origin but it also gives a good example for those who might wonder whether a rhombus can have a diagonal.

I've left in the line through a cuboid as I'm sure I've seen it used in this way in some engineering and it flags up the question of whether a diagonal can be 3-d (N-d?) --Mike 11:35, 31 October 2006 (UTC)

 * There is a difference between an encyclopedia and a dictionary. What you proposed should be in a dictionary. See my detailed response in section "Failed Article" above.
 * I invite others to express their opinions.
 * --Gogino 03:07, 6 November 2006 (UTC)

 * I might also say there is a difference between an encyclopedia and a mathemathics text book. Almost all articles start with a basic definition to scope the article. From your response, I can only assume I trod on someone's toes with my size 10 comments - sorry! Ok, lets start again. I don't expect a simple definition for polynonomial or Bessel function, but diagonal is a basic word mainly used outwith mathematics: in sports, literature, road markings, etc. it simply is not possible to have an encylopedic entry that only covers a very restriced use in advanced mathematics! --Mike 10:03, 6 November 2006 (UTC)

Challenging Question: 2 for a triangle, 5 for a square, 12 for a pentagon...
We know the pattern for the number of diagonals in an n-gon, but how about the number of regions determined by the number of diagonals??

To make sure you know what I mean, here are some examples:

 * A circle determines 2 regions, the inside and the outside.
 * A checkerboard determines 65 regions, the squares and the area outside the lines.

A regular hexagon has 25. A general hexagon, assumed to have no more than two diagonals intersecting at any point (other than a vertex) has 26. The general position is already done for us http://www.research.att.com/projects/OEIS?Anum=A027927. -- Smjg 11:08, 26 May 2004 (UTC)

POLYGON       DIAGONALS     REGIONS DETERMINED BY DIAGONALS 2 Digon         0             1 3 Triangle      0             2 4 Quadrilateral 2             5 (still 5 for a Square) 5 Pentagon      5            12 (still 12 for a regular pentagon) 6 Hexagon       9            26 (but only 25 for a regular hexagon) 7 Heptagon      14           51 8 Octagon       20           92 9 Enneagon      27          155 10 Decagon       35          247 11 Hendecagon    44          376 12 Dodecagon     54          551 13 Triskaidecagon 65         782 20 Icosagon      170       17876 30 Tricontagon   405 40 Tetracontagon 740 50 Pentacontagon 1175 60 Hexacontagon  1710 70 Heptacontagon 2345 80 Octacontagon  3080 90 Enneacontagon 3915 100 Hectagon      4850 1000 Chiliagon     498,500 10000 Myriagon      49,985,000 Uh-oh Googolgon     Extra credit

The numbers in this table come from "the On-Line Encyclopedia of Integer Sequences" http://www.research.att.com/projects/OEIS?Anum=A027927 which lists "a(n) = number of plane regions after drawing (general position) convex n-gon and all diagonals".

Note that this is the "general position convex n-gon", not the "regular n-gon".

The formula is a(n)= 1 + binomial(n,4) + binomial(n-1,2).

(By "binomial", I mean the binomial coefficient).

If there are any errors, *please* tell the people at "the On-Line Encyclopedia of Integer Sequences" so they can fix it. (Or tell me, and I'll forward it to them).

-- DavidCary 15:49, 26 Jun 2004 (UTC)

What are the number of plane regions after drawing the regular n-gon ?

 * The formula will depend on whether n is even or odd. We need to look at the number of common intersections of three or more diagonals.  Each point where three diagonals intersect loses one region, each point where four diagonals intersect loses three regions, and where d diagonal meet there are ½(d-1)(d-2) regions lost.  For the regular hexagon this is simple because the only multiple intersections (other than at the vertices) are the three diagonals in the centre, where just one region gets lost.  I'm trying to prove that when n is odd it is not possible for more than two diagonals to intersect at a point inside the polygon, and I'm thinking about a formula for bigger regular n-gons where n is even, but the situation gets more complicated as further symmetries emerge.  For example, I think 82 regions are lost for the regular dodecagon, but this reduces to 57 regions lost for a regular 14-sided shape because 14 has fewer factors than 12.  There are some experts on the Mathematics reference desk who will soon solve this if you wish to copy it there.    D b f i r s   10:02, 10 April 2011 (UTC)

split diagonal functors
I've made a new section on diagonal functors. These are not very related to other more geometrical notions of diagonals. If I could find enough stuff to write about them to fill an article, I wouldn't mind splitting to diagonal functor (currently a redirect to here). What you guys think? -lethe talk [ +] 23:01, 2 April 2006 (UTC)

I think you have enough for an article. Look at main diagonal - it is much shorter. And you can put diagonal functor under "See also." In your sense, "Diagonal" is an adjective. For example, there are all kinds of diagonal forms not listed here.--Gogino 08:22, 9 April 2006 (UTC)
 * Yeah, I think you're right. It doesn't belong in this article.  I've moved it to its own article, and left a "see also" link.  -lethe talk [ +] 04:21, 23 April 2006 (UTC)

Theatre
The following was removed wholesale. I thought some of it could be saved and put into the "non-mathematical" use, but I couldn't find a general quote that it was a term used by more than one eccentric director. If it is a term in general use in the theatre, then I think it would be worth listing under the "non-mathematical uses" Mike 10:20, 19 March 2007 (UTC)

"On the diagonal" is a term used by the well-known and notorious director Sue Kidd. It is a favourite positioning of hers for actors to be onstage, as she detests 'straight lines and semi-circles'. She regularly can be heard yelling at her poor, innocent AS Theatre Studies students "ON THE DIAGONAL, GIRLS!". A select few of these pupils have taken it into their own personal business to embrace the idea of diagonals into their lives. For instance, they particularly enjoy rearranging furniture diagonally and are also super smooth and incorporate the word 'diagonal' into many of their sentences.

Another favourite trick of the diagonal fans is to get Miss Kidd to use the phrase 'on the diagonal' daily. For instance, in their most recent meeting with her, the following conversation took place:

Amy: "Miss Kidd, how was the positioning of the mat in the birth scene?" Miss Kidd: "It was much better on the diagonal." Lauren: "Ooh Miss Kidd, you do like your diagonals don't you?" Jess: "Yeah Miss Kidd, would it not be better in a semi-circle?" Miss Kidd: "No Jess. For I hate semi-circles." Jess looks shocked and saddened

Naughty words need to be removed from first and third sentences of article. --anon 68.100.190.224 12:32, 3 April 2007 (UTC)

General Diagonal Formula
This user recently discovered the general use for the diagonal formula. It's pretty insane to think of streaming to dimensions above three.

http://www.mathhelpforum.com/math-help/f13/general-diagonal-formula-191707.html

Scroll down until you see proofs. Is this valid for the article? — Preceding unsigned comment added by Briandiaz (talk • contribs) 18:25, 13 November 2011 (UTC)

Nonsense reverted
I have reverted the following nonsense which was added to this article:

$$45^\circ\sum_{n=1}^346x\begin{array}{|c|c|c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array}\underbrace{ a+b+\cdots+z }_{10478}A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C\alpha\left ( \frac{1\! t}{2} \right )\textstyle \lim_{6 \to 103} \displaystyle\overbrace{ 1+2+\cdots+100 }^{5050}{}_pF_q\left({a_1, \ldots, a_p \atop b_1, \ldots, b_3}; z\right)\log_{13}(63)343\! 102\overbrace{ 1+2+\cdots+100 }^{\mu}f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}\phi$$

Samboy (talk) 06:59, 26 March 2022 (UTC)

Edits by AvrhUFfvr
User (talk · contribs) has recently made several edits to this article. They introduced at least one clear error: the article previously noted that the longest diagonals of a regular n-gon coincide at its circumcentre when n is even, but the edit removed this qualification.

I nearly reverted all of the edits, for this reason and for some issues with formatting (like using asterisks for multiplication), but then I thought that this might be a bit hasty, not to mention hostile to a relatively new editor. So instead I (re-)added a mention of n needing to be even, and I'm bringing the matter here for discussion.

It should perhaps be noted that other edits by this user to related articles (Face diagonal, Space diagonal) have been reverted, with reverter comments "WP:OR, nonstandard use of terms" and "Dubious, uncited, & very broken formatting". -- Perey (talk) 14:47, 1 July 2023 (UTC)

title: Talk:Diagonal


text:
Zaheer Khan

Zaheer Khan (born 8 October 1978) is an Indian former professional cricketer who played all forms of the game for the Indian national team from 2000 till 2014. He is a fast-medium left-arm bowler. He was the second-most successful Indian pace bowler in Test cricket, behind Kapil Dev. Zaheer Khan started his domestic career by playing for Baroda. In the early years of his career, Zaheer Khan was known for his hostile seam and pace bowling, especially fast inch-perfect yorkers.

With India, he was a member of the team that was one of the joint-winners of the 2002 ICC Champions Trophy, and one of the key members of the 2011 World Cup winning team, leading the pace attack with 21 wickets in just 9 games. In 2011 he was conferred with the Arjuna Award, India's second highest sporting award by the President of India. Zaheer Khan's career is also noted for recurring injuries, which often interrupted his progress at the international level. That is also the reason Zaheer khan has set up ProSport Fitness & Services, a special rehab & training center in association with Adrian Le Roux and Andrew Leipus. In 2020, the Government of India honoured him with the Padma Shri.

In a bid to improve his bowling, Zaheer Khan moved to England for a short stint with Worcestershire in 2006. A left-arm fast-medium bowler, he was best known for his ability to "move the ball both ways off the wicket and swing the old ball at some pace". Zaheer Khan excelled in reverse swing with the old ball.

He is praised for his performances on flat subcontinent pitches and the controlling of different types of cricket balls.

Zaheer Khan was selected as one of the Wisden Cricketers of the Year in 2008. Zaheer Khan announced his retirement from international cricket in October 2015. He also played for Worcestershire in County Cricket and played for Mumbai, Royal Challengers Bangalore, Delhi Daredevils and Mumbai Indians in Indian domestic cricket.

Only Muttiah Muralitharan (325) and Shaun Pollock (252) have dismissed more left-hand batsmen than Zaheer Khan, who has gotten the better of southpaws 237 times. He also has the distinct record of dismissing Graeme Smith, Kumar Sangakkara, Sanath Jayasuriya and Matthew Hayden – some of the game's most feared left-hand batsmen – over 10 times each in international cricket.

Early and personal life
He was born on 7 October 1978 in Shrirampur, Ahmednagar district, Maharashtra, India to parents Zakia and Bakhtiyar Khan. He was born in a Marathi Muslim family. He has an elder brother Zeeshan and younger brother Anees. He started his coaching under Utsav Yadav. Zaheer attended the New Marathi Primary school and the K.J. Somaiyya Secondary School in Shrirampur. He also played in the local Revenue Colony Cricket Club (RCC) in Shrirampur after which he started his career in Pune.

On 24 April 2017, he announced on his Twitter account that he was engaged to actress Sagarika Ghatge. The couple got married on 23 November 2017.

Domestic career
Khan came to Mumbai in 1996 and joined the National Cricket Club that played in Division A in the city. He played in competitions such as the Kanga Cricket League, Comrade Shield and the Purshottam Shield with the team. Sandeep Mahadkar, Khan's captain during the time, recalled the latter's ability with the ball with an instance where he reverse swung a ball that had been bowled 50 overs with, bowling ten maiden overs and helping his team win a Comrade Shield game. His ability with the bat was recalled by another former teammate with who Khan put together a 102-run stand for ninth wicket making an unbeaten 62 runs taking his team home. His "jaw-dropping spells in the Purshottam Shield" culminated with the 7/74 performance against Shivaji Park Gymkhana in January 1997. he was later sent to the MRF Pace Foundation in Chennai by Sudhir Naik, owner of the National Cricket Club. Impressed by his talent, the bowling coach there, T. A. Sekhar, pushed Khan to play for Baroda.

Khan quickly made his name playing for Baroda in the first-class level. In the final of the 2000–01 season of the Ranji Trophy against Railways, Khan received the man of the match award after he returned figures of 8/145 for the match, including a five-wicket haul in the second innings (5/16), helping his team lift the trophy for the fifth time and a first in 43 years.

Khan transferred to Mumbai at the start of the 2006–07 Indian cricket season his debut for Mumbai until the final of the Ranji Trophy in which he took 9 wickets as Mumbai defeated Bengal.

In 2005 Khan, signed for Worcestershire County Cricket Club in England as one of their two overseas players, replacing Shoaib Akhtar. Although Worcestershire went on to lose the match, Zaheer took ten wickets against Somerset on debut; in doing so he became the first Worcestershire player to take 10 wickets on debut for over 100 years. In June he took the first nine wickets to fall in the first innings against Essex, ending with 9–138; had wicket-keeper Steven Davies not dropped a catch offered by last man Darren Gough he would have become the first bowler ever to take all ten for the county.

Khan has played the Royal Challengers as well as Mumbai Indians before he was picked for the Delhi Daredevils in the 2015 auction. He has captained the Daredevils in 2016 and 2017. In 2017 season, Zaheer became the 10th bowler in the history and 8th Indian bowler, to pick 100 wickets in Indian Premier League. At the age of 38, he is the oldest player to achieve this feat.

International career
Zaheer was selected in 2000 for the first intake of the National Cricket Academy in Bangalore. He made his Test debut against Bangladesh and ODI debut against Kenya during the 2000 ICC KnockOut Trophy in the same year.

Struggling form
In late 2005 pacemen Sreesanth and R. P. Singh made their international debuts and became regular members of the Indian team making it difficult for Zaheer to retain his position in the playing eleven. The Board of Control for Cricket in India demoted Zaheer from a B-grade to a C-grade contract at the end of the year. He returned for the 2005 tour of Pakistan, where India fielded three left arm pacemen and had difficulty dismissing Pakistan with a lack of variety in the bowling attack.

Recall to team
Late in 2006, Zaheer was recalled to the Test and ODI team for the tour of South Africa, following Irfan Pathan's slump in form and an injury to Munaf Patel. After consistent performances on tour, his performance in early 2007 in home ODIs against the West Indies and Sri Lanka, including a career best 5/42, saw him named in the squad for the 2007 World Cup.

He won the Man of the Match award in the first Test between India and Australia in the 2008–2009 series in India for his all round performance with the bat and the ball.

ODI career
He has taken 282 ODI wickets at an average of just over 29 runs per wicket taking 4 wickets in a match 6 times (4 times against Zimbabwe) including 32 wickets against Zimbabwe at an average of 17.46 runs per dismissal. He, along with other seamers like Javagal Srinath and Ashish Nehra helped India to make it to the finals of the 2003 World Cup. Zaheer finished the tournament as fourth highest wicket-taker – 18 wickets from 11 matches at an average of 20 runs per wicket. He is also the fourth highest wicket-taker in ODIs for India with 282 scalps behind Anil Kumble (337), Javagal Srinath (315) and Ajit Agarkar (288).

Test career
Zaheer has taken 311 Test wickets at an average of just over 32 runs per wicket. South African star all-rounder Jacques Kallis was Zaheer's 300th test wicket. In 16 matches from the beginning of the tour of West Indies in April 2002 to the end of the 1st match against Australia in December 2003, Brisbane, Zaheer took 54 wickets from 16 matches at an average of 30 runs. It all turned downhill after the first Test against Australia in Brisbane in December 2003. Having taken 5 of the top 7 Australian batsmen in the first innings (5 for 95), he injured himself in the second during the opening spell. After missing the second Test he returned for the third, but was injured midway through the match and was forced to return home. The injury kept him from the early 2004 tour of Pakistan, India's first Test series victory in the country.

Earlier, Zaheer held the world record for the highest Test score by a number 11 when he scored 75 against Bangladesh in 2004. At the time he was batting with Sachin Tendulkar; the pair amassed 133 runs, a new record for India's tenth-wicket. This record was broken by Tino Best of the West Indies in 2012. The current record holder is Ashton Agar of the Australia on his debut match in 2013.

Knuckle Ball
In international cricket, Zaheer Khan was the first bowler to bowl knuckle ball. Zaheer Khan introduced the knuckle ball way back in 2011 world cup. He used that ball for great effect. He used that ball to get crucial wickets at crucial times like the wickets of Ian Bell and Paul Collingwood against England and the wicket of Devon Smith against the West Indies and the wicket of Michael Hussey in the Quarter Final against Australia.

In an interview he said : "The whole 2011 World Cup, I was looking forward to it, especially playing in front of the home crowd – even if it added that extra bit of pressure. I was preparing a new delivery that I wanted to use, which was the knuckle ball. I was working on it for a year leading up to the tournament. Even though I had perfected it, I was purposely not using it in any of the matches [before the tournament]. It got me a lot of success. When a plan like that works, it gives you extra satisfaction."

World Cup
Zaheer has 44 World Cup wickets, spanning from 2003 to 2011, putting him in ninth place behind Glenn McGrath (71), Muttiah Muralitharan (68), Mitchell Starc(65), Lasith Malinga (56), Wasim Akram (55), Trent Boult(53) and Chaminda Vaas (49) on the list of highest number of wickets by a bowler the marquee event. He is tied with Srinath in ninth but Srinath has played 34 games as opposed to Zaheer's 23.

Zaheer, who was one of India's trump cards during their World Cup triumph in 2011, finished as the joint highest wicket-taker along with Shahid Afridi with 21 scalps.

Later career
July 2011 India embarked on a tour of England. Having bowled 13.3 overs, Zaheer strained his hamstring and suffered an ankle injury in the first Test of the four-match series and as a result was ruled out of the rest of the tour. Zaheer came back in December and played a test match against Australia on Boxing day. He took two wickets in two consecutive deliveries, dismissing Michael Clarke for 31 and Mike Hussey for a duck. In the second test at Sydney, he took three wickets of the four to fall, Clarke scoring 329*; his were the best figures in both these innings. Zaheer Khan is ranked 22 in the ICC Player Rankings for Test bowlers. He toured South Africa in December 2013 and New Zealand in 2014.

Retirement
Zaheer Khan announced his retirement from international and first-class cricket on 15 October 2015 in a tweet saying "I bid adieu to my career in international cricket. I look forward to signing off with IPL 9."

Coaching career
Zaheer was appointed as bowling consultant for the India national cricket team in 2017

ProSport Fitness & Services
In 2014 Khan founded a fitness and sports company ProSport Fitness and Services in Mumbai, that offers fitness training and physiotherapy services. Involving personnel such as Andrew Leipus and Adrian Le Roux, the center aims to "maximize potential" of people and athletes by personally assisted fitness programs. Khan stated that the objective was to "bring in world class fitness program to India for sports injury management". It offers scientifically designed programs and treatment while conducting workshops and sessions for corporates and schools to spread awareness of physical fitness.

title: Zaheer Khan


text:
Talk:Vaira Vīķe-Freiberga

Stub?
I'm tempted to place a stub note here because there's zero information about the political work and/or views that caused the election and re-election for president. --Shallot 20:06, 25 May 2004 (UTC)

 * Good point. I extended it, although it may still need more work.Andris 21:27, May 25, 2004 (UTC)

The article says that criticisms of her for being uninvolved in domestic politics are "unfounded and speculative". POV much?

I agree on that. Therefore I made a minor modification of the sentence.--David

I'm unable to read the Latvian-language Wikipedia article, but concealed more information on Ms. Vike-Freiberga than the English-language article. I knew her political stance is in the center-right, note her diplomatic alliance to the US, and developed a friendship with US state secretary Condoleeza Rice in recent years. She's not a widely known female leader like Angela Merkel of Germany, but a small minority of women leaders aren't socialists like Margaret Thatcher of Great Britain and Kim Campbell of Canada are in the rightist spectrum. But I find more female leaders like Tarja Halonen of Finland, Hillary Rodham Clinton in the US (she may personally assisted Bill Clinton's presidency) and Michelle Bachelet of Chile are definitely in the leftist spectrum. -- G. Sageha

Quote on Salaspils - is this, as I suspect, incorrect?
I have, in several places, read claims that she has referred to the Salaspils concentration camp as an "educational institution". I suspect Russian nationalists to be behind this claim, and suspect it to be correspondingly empty. I just wondered .. have there been reports on a similar quote, however unreliable .. or is this *absolute* nonsense? ChiLlBeserker 01:43, 20 September 2006 (UTC)
 * She never said that. This name appeared in recently issued Latvian history book she granted to Russian president. Book was thoroughly screened for mistakes in Russia and they found that book provides also the official Nazi name of Salaspils death camp - "working educational camp". After all this is history book and it tries to provide more information. This was taken out of the context of book used to blow out one more PR campaign against Latvia. Come on, lots of Latvians themselves suffered and died in this camp...
 * Daarznieks 12:17, 18 October 2006 (UTC)

Canadian citizenship
Did she give up her Canadian citizenship to assume the presidency of Latvia? GAW

 * I can't find anything to describe if she's a dual-citizen of Canada, but I'm sure she returned to Latvia after independence and became involved in her homeland's political errands. I like for any wikipedian to do actual research on the issue. -- G. Sageha
 * Yes, she did around the time she was elected - according to Latvian law president can't have dual citizenship (acctualy no one can, but some apparently do...) -- Xil/talk 02:48, 9 December 2006 (UTC)

Rewrite
I've rewritten the article and included an honours section.

The article reads remarkably as if written by Mrs. Vike-Freiberga herself, or her PR agents. I've seen very few more obviously self-written entries on politicians. I suggest toning down the advertising language and leaning more towards impartiality and factuality. —Preceding unsigned comment added by 88.101.241.6 (talk) 14:10, 19 November 2009 (UTC)

Infobox?
Now that she is no longer president, shouldn't the infobox be removed from the article? Its continued presence may be confusing... — Zalktis 18:18, 5 September 2007 (UTC)
 * This box can be found in some articles not mentioned there, but if you think it's confusing, I think it can be removed - no other article on president has it, even Zatlers' didn't - I just placed it there  Xil/talk 13:52, 6 September 2007 (UTC)

Selected works?
VVF is an accomplished academic. Shouldn't there be a brief section listing some of here better known/more influential publications? The example I know best is Saules Dainas (1988). But there is also ''Linguistics and poetics of Latvian folk songs: essays in honour of the sesquicentennial of the birth of Kr. Barons'' (1989), and I assume there are also a number of good journal articles of hers out there. Anyone competent willing to take on this task? — Zalktis 15:32, 8 September 2007 (UTC)
 * Let's develop system, I looked trough FA quality biographies for ideas, so here are some ideas how TOC should look:

 * 1) Early life and education - her life until 1960
 * 2) Family and personal life - I noted that elsewhere this is in begining of article, placing it at end of article after "Honours", in my opinion, is inaproporite. She got married in 1960 so it fits here chronologicaly as well
 * 3) Studies of Latvian culture - I couldn't come up with a fully descriptive title for this section (any suggestions ?), I think this should include all her Latvia-related activities in exile and her research work on Latvian culture
 * 4) Professional life - this should concer her psychology-related activities. 3. and 4. sections could also be switched if needed
 * 5) Presidency - if needed this could be dived in two sections (one for each term). And posibly an section concerning her life after 1990 or after return to Latvia before this section or/and an a section on her leaving the office after this section.
 * 6) After presidency
 * 7) Selected works - the section you are asking for now, she has written some 150 works, here is a list, no way you can list all of them, I think up to ten most important should be enough - her books should be listed, rather then articles she has written.
 * 8) Honours
 * 9) See also
 * 10) References
 * 11) Further reading
 * 12) External links
 * Comments ? Xil/talk 13:57, 9 September 2007 (UTC)

 * I've now added a selection of her scholarly and other works, reflecting the span of years and interests. Perhaps you might consider re-naming the culture section something along the lines of "Engagement with issues of Latvian culture and identity". — Zalktis 15:13, 9 September 2007 (UTC)
 * I'd prefer something a bit shorter, like "Activities in Latvian diaspora", which might also be bad because it (kind of) partly excludes her research work -- Xil/talk 15:58, 9 September 2007 (UTC)

UN Secretary General postulation
At the begining of the article, it says that she was "oficcially" postulated to be the Sec. Gen. of the UN. This is completly contradicting the United Nations Secretary-General selection, 2006 article that, in the 'Background to the 2006 race' section states that evendoe there was a campaign for a women to be the Secretary General, there were no official postolations made. —Preceding unsigned comment added by 190.198.100.192 (talk) 03:53, 9 July 2010 (UTC)
 * No, it isn't, it seems you didn't bother to read everything the other article says Xil  (talk) 05:26, 9 July 2010 (UTC)

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title: Talk:Vaira Vīķe-Freiberga


text:
Talk:Plasma protein

The page previously redirected to Protein electrophoresis, which happened to use plasma proteins as an example, but which otherwise has nothing in particular to say about plasma proteins. -- Dominus 20:08, 25 May 2004 (UTC)

title: Talk:Plasma protein


text:
Northern Yan

Yan, known in historiography as the Northern Yan (407 or 409–436), Eastern Yan or Huanglong, was a dynastic state of China during the era of Sixteen Kingdoms. Some historians consider Gao Yun, a member of the Goguryeo royal family, to be the first Northern Yan monarch, while others consider Feng Ba of Han ethnicity to be the founder.

Background
Gao Yun was a descendant of the Goguryeo royal family. When the Former Yan captured the Goguryeo capital, Hwando in 342, they also captured several members of the royal family and moved them to Qingshan (青山, in modern Jinzhou, Liaoning), where Gao Yun was born and grew to become a minor general under the Later Yan. In 397, Gao Yun helped the Yan emperor, Murong Bao quell the rebellion of his son, Murong Hui. As a reward, Bao adopted him as his own son, changing his name to Murong Yun.

It was around this time when Murong Yun became friends with the general, Feng Ba. Feng Ba was a Han Chinese whose family was originally from Changle Commandery before his grandfather, Feng He (馮和) moved to Shangdang during the Disaster of Yongjia. Ba's father, Feng An (馮安) served as a military general under the Western Yan. After Later Yan conquered Western Yan in 394, the Feng clan resettled in Longcheng. Feng Ba appeared to have grew up under heavy Xianbei influence, as his nickname Qizhifa (乞直伐) suggests Xianbei origin.

In 401, Murong Yun's adoptive uncle, Murong Xi came to power, and he was described in records as a cruel and arbitrary ruler. Feng Ba and his brother, Feng Sufu were charged with crimes against Xi, forcing them to flee to the countryside where they were determined to overthrow him. In 407, as Murong Xi was holding a funeral for Empress Fu, Feng Ba and his conspirators took control of the capital Longcheng and acclaimed Murong Yun as their leader. Xi initially led an assault on Longcheng but then fled the battle alone in panic. After his forces collapsed, Xi was later found and executed by Yun.

Reign of Gao Yun and Feng Ba
The founding year of the Northern Yan is up to debate; some historians consider Feng Ba as the first ruler of Northern Yan while others assert that it was Gao Yun. The reason is that Gao Yun was a member of the Later Yan imperial family as Murong Bao's adopted son, and so he should be considered the last ruler of Later Yan. On the other hand, he was ethnically Goguryeo and reverted back to his old family name shortly after ascending. Thus, Northern Yan's founding year can either be 407 or 409.

Gao Yun took the title of Heavenly King. The Later Yan was previously at war with Goguryeo, but Yun managed to establish friendly relations between them and Northern Yan. However, conflict with the Northern Wei also began as the Yan Inspector of You Province, Murong Yi (慕容懿) defected to Wei. Worried by his lack of reputation, Yun attempted to protect himself by empowering his favourites, but in 409, two of them, Li Ban (離班) and Tao Ren (桃仁) assassinated him. Feng Ba's men then had the assassins killed, and the officials acclaimed him as the new Heavenly King.

The Northern Yan was relatively weak compared to Northern Wei, so Feng Ba formed good relations with the Eastern Jin, Hu Xia, Rouran, Khitan and Kumo Xi. He secured the support of his people by actively participating in politics, promoting agriculture and reducing tax burdens. However, he was also wary of handing out higher offices to his retainers, which led to a rebellion by his cousins in 410. On two occasions, Feng Ba had Wei envoys detained. In 416 and 418, Wei clashed with Yan, but due to pressure from stronger neighbours like the Hu Xia, they were unable to launch any substantial campaign throughout Feng Ba's reign. Northern Yan also continued Later Yan's dual administrative system between their Han Chinese and "Hu" subjects, as Feng Ba appointed his Crown Prince as the Grand Chanyu to supervise the tribes, along with introducing other offices to assist the Grand Chanyu.

Decline and fall
Feng Ba became deathly ill in 430. Conflict arose between his Crown Prince, Feng Yi (馮翼) and favourite concubine, Consort Song (宋夫人), who wanted her own son to inherit the throne. The situation soon leaked to Feng Ba's brother, the Prime Minister Feng Hong, who led his troops and took over the capital. Feng Ba died soon after, and Feng Hong took the throne for himself, slaughtering all of Feng Ba's sons including Feng Yi.

At the time, the Wei had dealt with the Hu Xia threat in the west and began focusing on conquering Northern Yan. From 432 onwards, Yan faced periodic attacks from Wei. In 433, a succession issue led to Feng Hong's sons handing over Liaoxi Commandery to Wei. Feng Hong refused to surrender and attempted to secure his position by allying with the Liu Song dynasty, even becoming a vassal to them in 435, but Wei continued their assault nonetheless. Finally, a major Wei invasion in 436 prompted Feng Hong to flee to Goguryeo for protection, ending the Northern Yan.

Feng Hong remained in Goguryeo until 438. While the Goguryeo king, Jangsu initially refused to hand him over to Wei, Feng Hong repeatedly offended him and tried to escape to Liu Song, resulting in Jangsu executing him and his sons. In Northern Wei, Feng Ba's granddaughter grew to become Empress Dowager Feng, an important figure in Wei's history. In 1965, the tomb of Feng Sufu was discovered in Beipiao, Liaoning, which contained the earliest extant of the double stirrup along with a unique duck-shaped glassware.

title: Northern Yan


text:
Doogie Howser, M.D.

Doogie Howser, M.D. is an American medical sitcom that ran for four seasons on ABC from September 19, 1989, to March 24, 1993, totaling 97 episodes. Created by Steven Bochco and David E. Kelley, the show stars a young Neil Patrick Harris in the title role as a teenage physician who balances the challenge of practicing medicine with the everyday problems of teenage life.

Plot
Dr. Douglas "Doogie" Howser (Harris) is the son of David (James B. Sikking) and Katherine Howser (Belinda Montgomery). As a child, he twice survived early-stage pediatric leukemia after his father—a family physician—discovered suspicious bruising. The experience contributed to the younger Howser's desire to enter medicine.

Possessing a genius intellect and a photographic memory, Howser participates in a longitudinal study of child prodigies until his 18th birthday. He earned a perfect score on the SAT at the age of six, completed high school in nine weeks, graduated from Princeton University in 1983 at age 10, and finished medical school four years later. At age 14, Howser was the youngest licensed doctor in the country. As a newspaper article (one of several noting some of Doogie's aforementioned accomplishments that are shown in the series' opening title sequence) stated, he "can't buy beer... [but] can prescribe drugs".

The series begins on Howser's 16th birthday; the cold open of the pilot episode shows him stopping his field test for his driver's license to help an injured person at the scene of a traffic accident. Howser is a second-year resident surgeon at Eastman Medical Center in Los Angeles, and still lives at home with his parents. His best friend and neighbor, Vinnie Delpino (Max Casella), is a more typical teenager—climbing through Howser's bedroom window to visit—and connects him to life outside of medicine. Howser has kept a diary on his computer since 1979; episodes typically end with him making an entry in it, making observations about the situations he had experienced or learned in the episode.

Howser seeks acceptance both from children his age and from his professional colleagues. Many episodes also deal with wider social problems: AIDS awareness, racism, antisemitism, homophobia, sexism, gang violence, access to quality medical care, and losing one's virginity are topics, along with aging, body issues, and friendship.

Howser initially has a girlfriend, Wanda Plenn (Lisa Dean Ryan), but they break up after she leaves for college; he also begins a trauma surgery fellowship and moves into his own apartment. Bochco intended to end the show with a "season-long story arc for Doogie where he becomes disaffected with the practice of medicine and quits medicine to become a writer". ABC abruptly canceled the show due to low ratings, preventing Bochco and the show's writers from implementing that storyline, other than Howser's resignation from Eastman and departure for Europe in the final episode.

Production
The weekly, half-hour dramedy was created by Steven Bochco. He originated the concept and asked David E. Kelley to help write the pilot, earning Kelley a "created by" credit. Harris was the first actor the show's staff had found that could convincingly play a teenage doctor, but ABC executives opposed his casting. Bochco's contract required that the network pay an "enormous" penalty if it canceled the project, so ABC was forced to let him film the pilot. The network still opposed Harris's casting and disliked the pilot, but after positive reception during test screenings, ABC greenlit the show.

Main cast

 * Neil Patrick Harris as Dr. Douglas "Doogie" Howser, the show's protagonist.
 * Max Casella as Vincent "Vinnie" Salvatore Delpino, Doogie's best friend since they were five years old. A typical girl-crazy teenager, Vinnie resists his father's demands to join the family business and instead attends film school to pursue a career as a film director.
 * Belinda Montgomery as Katherine Howser, Doogie Howser's mother. Originally a housewife, she later returns to work as a patient advocate at her son's hospital.
 * Lawrence Pressman as Dr. Benjamin Canfield, head of Eastman Medical. Canfield is an old friend and classmate of David Howser, and persuades him to join the hospital to run its family practice.
 * Mitchell Anderson (seasons 1–2) as Dr. Jack McGuire, a resident at Eastman and Doogie's friendly rival. A visit to rural Mexico inspires him to leave the hospital to serve the poor overseas.
 * Kathryn Layng as Mary Margaret "Curly" Spaulding, a nurse at Eastman. Spaulding occasionally dates McGuire and, briefly, both Canfield and Howser.
 * James B. Sikking as Dr. David Howser, Doogie Howser's father. He's a Vietnam War MASH veteran with a family practice.
 * Lisa Dean Ryan (seasons 1–2, recurring in season 3) as Wanda Plenn, Vinnie's high-school classmate and Doogie's girlfriend. After her mother dies in an automobile accident, Wanda's relationship with Doogie suffers. After she leaves for the School of the Art Institute of Chicago they end their relationship.
 * Lucy Boryer (seasons 1–3, two episodes in season 4) as Janine Stewart, Vinnie's girlfriend and Wanda's best friend. She drops out of college and becomes a buyer for a department store.
 * Markus Redmond (seasons 2–4, guest star in season 1) as Raymond Alexander, an orderly (and later an EMT) at Eastman. While he was a gang member, Alexander meets Doogie after taking him hostage during a convenience-store robbery; after finishing his sentence, Doogie helps him get a job at the hospital as an orderly.

Recurring cast

 * Rif Hutton as Dr. Ron Welch, a fellow doctor who is also friends with Howser.
 * Robyn Lively as Michele Faber (seasons 2 and 4), a nursing student. She becomes Howser's girlfriend shortly before he decides to leave Eastman and go to Europe.
 * Barry Livingston as Dr. Bob Rickett (seasons 2–4), a fellow doctor working at Eastman.

Syndication
In the United States, reruns of Doogie Howser, M.D. ran in syndication between September 1994 and September 1996. Repeats of the show aired on cable on the Odyssey Network (now Hallmark Channel) from 1999 to 2001. The Hub began airing reruns of the show on October 11, 2010 lasting until May 26, 2013.

Home media
Anchor Bay Entertainment released all four seasons of Doogie Howser, M.D. on DVD in Region 1 (United States and Canada) between 2005 and 2006. A Complete Collection release was announced on August 28, 2008, but was eventually canceled. All 4 seasons had been available to stream on Hulu, but expired on that service on June 27, 2023. The series was made available internationally on Star on Disney+ beginning March 15, 2023.

Critical reception
According to Metacritic, Marvin Kitman of Newsday gave season 1 of Doogie Howser, M.D. a 40/100 score and commented: "What a wasted childhood my kids have had, I got to thinking while watching this otherwise normal Doogie Howser. It makes you look at your kids differently. What lazy bums they must be, still in high school at 16." Scott Weinberg of DVD Talk recommended season two: "It's not high art, but it's a heckuva lot better than what generally passes for your average weeknight sitcom." Christopher Smith of the Bangor Daily News gave season three a "C" grade and commented: "No classic, this series. [...T]he show has become gratingly cute, particularly in the episodes “Doogiesomething,” “Double Doogie with Cheese,” and “Lonesome Doog.” Doog, I'm Dooged out."

Cultural influence

 * Neil Patrick Harris has satirized his years playing a teenage medical doctor several times:
 * In an episode of Roseanne, Roseanne Conner (Roseanne) has a dream after having undergone breast reduction surgery. She goes to the mirror and realizes that her breasts are comically larger than before. Doogie Howser (Harris) comes in and asks an upset Roseanne if they were supposed to be bigger than they are in the dream. Roseanne screams, but then is woken up by her husband Dan. To make sure she was dreaming, she looks under her bedsheet, sees the surgery went as planned, and sighs, "Way to go, Doogie!"
 * Barney Stinson (also played by Harris) writes in his computerized diary at the end of the How I Met Your Mother episode "The Bracket," while the Doogie Howser theme music plays. In the later episode "The Stinsons," he also comments, "Call me crazy but child actors were way better in the '80s".
 * In the 2004 comedy Harold & Kumar Go to White Castle, Harris – playing a fictionalized version of himself – claims to have "humped every piece of ass ever on that show" (except the hot nurse, over whom he expresses regret). Harris is referred to as "Doogie Howser" while stealing Harold (John Cho)'s car from the convenience store. In Harold & Kumar Escape from Guantanamo Bay, Harris remarks, after taking psychotropic mushrooms, "Dude, I was able to perform an appendectomy at 14, I think I can handle a few 'shrooms".
 * In 2008, Harris appeared in commercials for Old Spice deodorant, claiming to be an expert because he "used to be a doctor for pretends".
 * During the opening of the 2009 TV Land Awards, Harris, who hosted the show, travels through "The TV Land Zone" (a spoof of The Twilight Zone), where he finds himself the star of TV classics. At one point, Harris walks into a doctor's office, dressed as Doogie, while the Doogie Howser, M.D. theme plays. After realizing where he is, he storms out, saying, "No no no, not gonna happen! Check my contract!"
 * On the January 10, 2009 episode of Saturday Night Live, an "SNL Digital Short" featured Harris, the episode's guest host, leading a full orchestra version of the Doogie Howser theme. When the song concludes, he turns toward the camera and sheds a tear.
 * On the March 14, 2011 episode of Jimmy Kimmel Live!, a "real doctor" played by Harris endorses Kimmel's Jim-Miracle Diet, as the Doogie Howser theme plays.
 * Harris in 2017 joined other actors from medical television shows in Cigna's "TV Doctors of America" advertising campaign for annual checkups.
 * Neil Patrick Harris played Doogie Howser in The Earth Day Special in 1990. In the special, Doogie, along with two other doctors (played by Dana Delany and James Brolin), are informed by the Back to the Future trilogy scientist Emmett L. Brown (played by Christopher Lloyd) on how to save Mother Nature (played by Bette Midler).
 * In Anthony Bourdain's book Kitchen Confidential: Adventures in the Culinary Underbelly, any blond, good-looking waiter working in his restaurant is immediately nicknamed "Doogie Howser".
 * Smart mice obtained by genetic engineering have been named "Doogie mice" in honor of Harris's character.

Real life comparisons
Balamurali Ambati graduated from the Mount Sinai School of Medicine and obtained his medical license when he was only 17 years old, a Guinness World Record, and has been compared to the fictional Doogie Howser, though Ambati himself disliked the association.

Sho Yano, who became the youngest student to attain an M.D. from the University of Chicago at 21 years old, has also been called a real-life Doogie Howser.

Doogie Howser has been used as a moniker for several people involved in politics. In 2009, 13-year-old author and speaker Jonathan Krohn was nicknamed "Doogie Howser GOP". 17-year-old Evan Draim, the youngest delegate at the 2012 Republican National Convention, was referred to as a "Doogie Howser of the GOP". Republican congressman Aaron Schock has been referred to as a Doogie Howser for being the youngest member of Congress in 2009 at 27 years old. In 2015, Jon Stewart called Schock a "Doogie Howser wannabe" for his travel expenses and activities while still in office.

Some teenagers who have impersonated physicians are often referred to as Doogie Howser. Others who have excelled at a young age have been called Doogie Howser.

Reboot
In April 2020, it was announced that a reboot titled Doogie Kameāloha, M.D., was in development for Disney+ with Kourtney Kang writing and co-executive producing with Melvin Mar, Jake Kasdan, and Bochco's wife, Dayna Bochco and son, Jesse Bochco. The new series focuses on Lahela “Doogie” Kameāloha (Peyton Elizabeth Lee), a female 16-year-old doctor in Hawaii given her nickname by others who have seen Doogie Howser, M.D.. Disney+ gave the series a 10-episode straight-to-series order in September 2020.

title: Doogie Howser, M.D.


text:
Euclidean division

In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property    is that the quotient and the remainder exist and are unique, under some conditions. Because of this uniqueness, Euclidean division is often considered without referring to any method of computation, and without explicitly computing the quotient and the remainder. The methods of computation are called integer division algorithms, the best known of which being long division.

Euclidean division, and algorithms to compute it, are fundamental for many questions concerning integers, such as the Euclidean algorithm for finding the greatest common divisor of two integers, and modular arithmetic, for which only remainders are considered. The operation consisting of computing only the remainder is called the modulo operation, and is used often in both mathematics and computer science.

Division theorem
Euclidean division is based on the following result, which is sometimes called Euclid's division lemma.

Given two integers $a$ and $b$, with $b ≠ 0$, there exist unique integers $q$ and $r$ such that

and

where $a = bq + r$ denotes the absolute value of $0 ≤ r < |b|$.

In the above theorem, each of the four integers has a name of its own: $|b|$ is called the, $b$ is called the , $a$ is called the and $b$ is called the.

The computation of the quotient and the remainder from the dividend and the divisor is called, or in case of ambiguity,. The theorem is frequently referred to as the (although it is a theorem and not an algorithm), because its proof as given below lends itself to a simple division algorithm for computing $q$ and $r$ (see the section Proof for more).

Division is not defined in the case where $q$; see division by zero.

For the remainder and the modulo operation, there are conventions other than $r$, see.

Generalization
Although originally restricted to integers, Euclidean division and the division theorem can be generalized to univariate polynomials over a field and to Euclidean domains.

In the case of polynomials, the main difference is that the inequalities $$0\le r<|b|$$ are replaced with
 * $$\deg r < \deg b,$$

where $$\deg$$ denotes the polynomial degree.

In the generalization to Euclidean domains, the inequality becomes
 * $$f(r) < f(b),$$

where $$f$$ denote a specific function from the domain to the natural numbers called a "Euclidean function".

History
Although "Euclidean division" is named after Euclid, it seems that he did not know the existence and uniqueness theorem, and that the only computation method that he knew was the division by repeated subtraction.

Before the discovery of Hindu–Arabic numeral system, which was introduced in Europe during the 13th century by Fibonacci, division was extremely difficult, and only the best mathematicians were able to do it. Presently, most division algorithms, including long division, are based on this notation or its variants, such as binary numerals. A notable exception is Newton–Raphson division, which is independent from any numeral system.

The term "Euclidean division" was introduced during the 20th century as a shorthand for "division of Euclidean rings". It has been rapidly adopted by mathematicians for distinguishing this division from the other kinds of division of numbers.

Intuitive example
Suppose that a pie has 9 slices and they are to be divided evenly among 4 people. Using Euclidean division, 9 divided by 4 is 2 with remainder 1. In other words, each person receives 2 slices of pie, and there is 1 slice left over.

This can be confirmed using multiplication, the inverse of division: if each of the 4 people received 2 slices, then 4 × 2 = 8 slices were given out in total. Adding the 1 slice remaining, the result is 9 slices. In summary: 9 = 4 × 2 + 1.

In general, if the number of slices is denoted $$a$$ and the number of people is denoted $$b$$, then one can divide the pie evenly among the people such that each person receives $$q$$ slices (the quotient), with some number of slices $$r < b$$ being the leftover (the remainder). In which case, the equation $$a = bq + r$$ holds.

If 9 slices were divided among 3 people instead of 4, then each would receive 3 and no slice would be left over, which means that the remainder would be zero, leading to the conclusion that 3 evenly divides 9, or that 3 divides 9.

Euclidean division can also be extended to negative dividend (or negative divisor) using the same formula; for example −9 = 4 × (−3) + 3, which means that −9 divided by 4 is −3 with remainder 3.

Examples

 * If a = 7 and b = 3, then q = 2 and r = 1, since 7 = 3 × 2 + 1.
 * If a = 7 and b = −3, then q = −2 and r = 1, since 7 = −3 × (−2) + 1.
 * If a = −7 and b = 3, then q = −3 and r = 2, since −7 = 3 × (−3) + 2.
 * If a = −7 and b = −3, then q = 3 and r = 2, since −7 = −3 × 3 + 2.

Proof
The following proof of the division theorem relies on the fact that a decreasing sequence of non-negative integers stops eventually. It is separated into two parts: one for existence and another for uniqueness of $$q$$ and $$r$$. Other proofs use the well-ordering principle (i.e., the assertion that every non-empty set of non-negative integers has a smallest element) to make the reasoning simpler, but have the disadvantage of not providing directly an algorithm for solving the division (see for more).

Existence
For proving the existence of Euclidean division, one can suppose $$b > 0,$$ since, if $$b < 0,$$ the equality $$a=bq+r$$ can be rewritten $$a = (-b)(-q) + r.$$ So, if the latter equality is a Euclidean division with $$-b > 0,$$ the former is also a Euclidean division.

Given $$b > 0$$ and $$a,$$ there are integers $$q_1$$ and $$r_1 \ge 0$$ such that $$a = bq_1 + r_1;$$ for example, $$q_1 = 0$$ and $$r_1 = a$$ if $$a \ge 0,$$ and otherwise $$q_1 = a$$ and $$r_1 = a - ab.$$

Let $$q$$ and $$r$$ be such a pair of numbers for which $$r$$ is nonnegative and minimal. If $$r < b.$$ we have Euclidean division. Thus, we have to prove that, if $$r \ge b,$$ then $$r$$ is not minimal. Indeed, if $$r \ge b,$$ one has $$a = b(q+1) + (r-b),$$ with $$0 \le r-b < r,$$ and $$r$$ is not minimal

This proves the existence in all cases. This provides also an algorithm for computing the quotient and the remainder, by starting from $$q = 0$$ (if $$a \ge 0$$) and adding $$1$$ to it until $$a-bq < b.$$ However, this algorithm is not efficient, since its number of steps is of the order of $$a/b$$

Uniqueness
The pair of integers $b = 0$ and $0 ≤ r < |b|$ such that $r$ is unique, in the sense that there can be no other pair of integers that satisfy the same condition in the Euclidean division theorem. In other words, if we have another division of $q$ by $a = bq + r$, say $a$ with $b$, then we must have that

To prove this statement, we first start with the assumptions that

Subtracting the two equations yields

So $a = bq' + r'$ is a divisor of $0 ≤ r' < |b|$. As

by the above inequalities, one gets

and

Since $q' = q and r'  = r$, we get that $0 ≤ r < |b|$ and $0 ≤ r' < |b|$, which proves the uniqueness part of the Euclidean division theorem.

Effectiveness
In general, an existence proof does not provide an algorithm for computing the existing quotient and remainder, but the above proof does immediately provide an algorithm (see Division algorithm), even though it is not a very efficient one as it requires as many steps as the size of the quotient. This is related to the fact that it uses only additions, subtractions and comparisons of integers, without involving multiplication, nor any particular representation of the integers such as decimal notation.

In terms of decimal notation, long division provides a much more efficient algorithm for solving Euclidean divisions. Its generalization to binary and hexadecimal notation provides further flexibility and possibility for computer implementation. However, for large inputs, algorithms that reduce division to multiplication, such as Newton–Raphson, are usually preferred, because they only need a time which is proportional to the time of the multiplication needed to verify the result—independently of the multiplication algorithm which is used (for more, see Division algorithm).

Variants
The Euclidean division admits a number of variants, some of which are listed below.

Other intervals for the remainder
In Euclidean division with $d$ as divisor, the remainder is supposed to belong to the interval $a = bq + r$ of length $a = bq' + r'$. Any other interval of the same length may be used. More precisely, given integers $$m$$, $$a$$, $$d$$ with $$m>0$$, there exist unique integers $$q$$ and $$r$$ with $$d \le r < m+d $$ such that $$a = mq+r$$.

In particular, if $$ d=- \left\lfloor \frac{m}{2} \right\rfloor $$ then $$ - \left\lfloor \frac{m}{2} \right\rfloor \le r < m-\left\lfloor \frac{m}{2} \right\rfloor $$. This division is called the centered division, and its remainder $$r$$ is called the centered remainder or the least absolute remainder''.

This is used for approximating real numbers: Euclidean division defines truncation, and centered division defines rounding.

Montgomery division
Given integers $$a$$, $$m$$ and $$R,$$ with $$m >0$$ and $$\gcd(R,m) =1,$$ let $$R^{-1}$$ be the modular multiplicative inverse of $$R$$ (i.e., $$ 0<R^{-1}<m$$ with $$R^{-1}R-1$$ being a multiple of $$m$$), then there exist unique integers $$q$$ and $$r$$ with $$0 \le r < m $$ such that $$ a = mq+R^{-1} \cdot r $$. This result generalizes Hensel's odd division (1900).

The value $$r$$ is the $b(q – q) = r – r$-residue defined in Montgomery reduction.

In Euclidean domains
Euclidean domains (also known as Euclidean rings) are defined as integral domains which support the following generalization of Euclidean division:

 * Given an element $b$ and a non-zero element $r' – r$ in a Euclidean domain $|r' – r| < |b|$ equipped with a Euclidean function $r' – r = 0$ (also known as a Euclidean valuation or degree function ), there exist $b(q – q') = 0$ and $b ≠ 0$ in $r = r'$ such that $q = q'$ and either $[0, d)$ or $|d|$.

Uniqueness of $N$ and $a$ is not required. It occurs only in exceptional cases, typically for univariate polynomials, and for integers, if the further condition $b$ is added.

Examples of Euclidean domains include fields, polynomial rings in one variable over a field, and the Gaussian integers. The Euclidean division of polynomials has been the object of specific developments.

title: Euclidean division


text:
Synthetic crude

Synthetic crude is the output from a bitumen/extra heavy oil upgrader facility used in connection with oil sand production. It may also refer to shale oil, an output from an oil shale pyrolysis. The properties of the synthetic crude depend on the processes used in the upgrading. Typically, it is low in sulfur and has an API gravity of around 30. It is also known as "upgraded crude".

Synthetic crude is an intermediate product produced when an extra-heavy or unconventional oil source is upgraded into a transportable form. Synthetic crude is then shipped to oil refineries where it is refined into finished products. Synthetic crude may also be mixed, as a diluent, with heavy oil to create synbit. Synbit is more viscous than synthetic crude, but can also be a less expensive alternative for transporting heavy oil to a conventional refinery.

Syncrude Canada, Suncor Energy Inc., and Canadian Natural Resources Limited are the three largest worldwide producers of synthetic crude with a cumulative production of approximately 600000 oilbbl/d. The NewGrade Energy Upgrader became operational in 1988, and was the first upgrader in Canada, now part of the CCRL Refinery Complex.

"Synthetic crude" may also refer to crude-like hydrocarbon mixes generated from other processes. Examples are manure-derived synthetic crude oil and greencrude.

title: Synthetic crude


text: Talk:ARCH models

title: Talk:ARCH models


text:
Anglo-Swedish war of 1810–1812

During the Napoleonic Wars until 1810, Sweden and the United Kingdom of Great Britain and Ireland were allies in the war against Napoleon. As a result of Sweden's defeat in the Finnish War and the Pomeranian War, and the following Treaty of Fredrikshamn and Treaty of Paris, Sweden declared war on the UK. The bloodless war, however, existed only on paper, and the UK was still not hindered in stationing ships at the Swedish island of Hanö and trade with the Baltic states.

Background
The Treaty of Paris, concluded on 6 January 1810, forced Sweden to join the Continental System, a trade embargo against the UK. Since the UK was Sweden's biggest trade partner this caused economic difficulties, and trade continued to take place through smuggling. On 13 November that year, France delivered an ultimatum to the Swedish government demanding that within five days Sweden:
 * Declare war against the UK,
 * Confiscate all UK ships in Swedish ports,
 * Seize all UK products in Sweden.

France and its allies threatened to declare war against Sweden if it did not meet the French demands. On 17 November the same year, the Swedish government declared war against the UK.

War
No acts of war occurred during the conflict and the UK was even allowed to station boats in Hanö, thus "occupying" the island. Sweden did not try to hinder this as the UK used the island to continue trading with Sweden.

Aftermath
The elected crown prince of Sweden, Danish Prince Charles August, had died on 28 May 1810, and on 21 August 1810, the French Marshal Jean-Baptiste Bernadotte was elected crown prince of Sweden. Although Bernadotte was only the crown prince and technically subservient to King Charles XIII, the king's deteriorating health and disinterest made the crown prince the de facto ruler of Sweden. Under Bernadotte's rule, Sweden's relationship with Napoleonic France deteriorated. When France occupied Swedish Pomerania and the island of Rügen in 1812, Sweden sought peace with the UK.

After long negotiations, the Treaty of Örebro was signed on 18 July 1812. On the same day and at the same place, the UK and Russia signed a peace treaty to end the Anglo–Russian War (1807–1812).

Literature

 * Norie, John William (1827) – The naval gazetteer, biographer, and chronologist; containing a history of the late wars, from their commencement in 1793 to their final conclusion in 1815; and continued, as to the biographical part, to the present time(J. W. Norie & Co)
 * Sundberg, Ulf (1998) – Svenska krig, 1521–1814 (Hjalmarson & Högberg, Stockholm) ISBN 91-89080-14-9

title: Anglo-Swedish war of 1810–1812