title: Huey, Dewey, and Louie

text: Huey, Dewey, and Louie are the sons of Donald's sister Della Duck; in "Donald's Nephews", their mother is instead named Dumbella. In the original theatrical shorts, they were originally sent to visit Donald for only one day; in the comics, the three were sent to stay with Donald on a temporary basis, until their father came back from the hospital (the boys ended up sending him there after a practical joke of putting firecrackers under his chair). In both the comics and animated shorts, the boys' parents were never heard from or mentioned again after these instances, with the boys ending up permanently living with Donald. All four of them live in the fictional city of Duckburg, in the fictional state of Calisota.


title: Huey, Dewey, and Louie

text: In the theatrical shorts, Huey, Dewey, and Louie often behave in a rambunctious and mischievous manner, and they sometimes commit retaliation or revenge on Donald. In the early Barks comics, the ducklings were still wild and unruly, but their character improved considerably due to their membership in the Junior Woodchucks and the good influence of Grandma Duck. As the boys mature, they prefer to assist Donald and Scrooge in the adventure at hand.


title: Huey, Dewey, and Louie

text: In early comic books and shorts, the caps of Huey, Dewey, and Louie were colored randomly, depending on the whim of the colorist. On few occasions until 1945 and most cartoons shortly afterward, all three nephews wore identical outfits (most commonly red).


title: Huey, Dewey, and Louie

text: It was not until the 1980s when it became established that Huey is dressed in red, Dewey in blue, and Louie in green. Disney's archivist Dave Smith, in "Disney A to Z", said, "Note that the brightest hue of the three is red (Huey), the color of water, dew, is blue (Dewey), and that leaves Louie, and leaves are green (Louie)."


title: Huey, Dewey, and Louie

text: A few random combinations appear in early Disney merchandise and books, such as orange and yellow. Another combination that shows up from time to time is Huey in blue, Dewey in green, and Louie in red. In-story, this inconsistency is explained away as a result of the ducklings borrowing each other's clothes. The trio have often been depicted wearing indistinguishable black shirts (or the same dark color).


title: Huey, Dewey, and Louie

text: The Don Rosa story "An Eye for Detail" was based around Donald spending so much time trying to tell his three nephews apart that he developed a heightened sense of sight.


title: Huey, Dewey, and Louie

text: Clarence Nash, Donald's voice actor, voiced the nephews in the cartoon shorts, making their voices just as duck-like (and thereby difficult to understand) as Donald's. Huey, Dewey, and Louie were all voiced by Russi Taylor in "DuckTales". In "Quack Pack", they were voiced by Jeannie Elias, Pamela Segall, and Elizabeth Daily, respectively. Tony Anselmo voiced the characters in "Down and Out with Donald Duck" (1987), "Mickey Mouse Works", "House of Mouse", and the "Have a Laugh!" shorts, while Taylor continued voicing the trio in other projects, such as the video games, "" and "Mickey's Speedway USA", and the direct-to-video films "Mickey's Once" and "Twice Upon a Christmas". Taylor also reprised her role as the nephews in the "" video game and the post-2013 "Mickey Mouse" shorts until her death in 2019. Danny Pudi, Ben Schwartz, and Bobby Moynihan voiced the trio in the 2017 "DuckTales" reboot.


title: Huey, Dewey, and Louie

text: On a few occasions, an artist by error drew four nephews and the error was published. This fourth nephew has been named Phooey Duck by Disney comic editor Bob Foster.


title: Huey, Dewey, and Louie

text: The six-page Danish Egmont-licensed Disney comic "Much Ado About Phooey" (1999), plotted by Lars Jensen, written by Jack Sutter and drawn by Tino Santanach Hernandez, used Phooey as a character and explained Phooey's sporadic appearances as a freak incident of nature. (The text in the two speech balloons says "It is a fourth nephew! An exact copy of the others! / Yes, it's probably best that I explain".) Phooey also made a cameo appearance in the 2017 "DuckTales" animated series episode, "A Nightmare on Killmotor Hill!", during a dream sequence.


title: Huey, Dewey, and Louie

text: In the comics, Huey, Dewey, and Louie often play a major role in most stories involving either their "Unca Donald" or great-uncle Scrooge McDuck, accompanying them on most of their adventures. Originating in the comics is the boys' membership in the Boy Scouts of America-like organization, the Junior Woodchucks, including their use of the Junior Woodchucks Guidebook, a fantastically exhaustive field guide containing information on science, history and survival skills. This youth organization, which has twin goals of preserving knowledge and protecting the environment, was instrumental in transforming the three brothers from "little hellions" to upstanding young ducks.


title: Huey, Dewey, and Louie

text: In Disney comic writer Don Rosa's continuity, Huey, Dewey, and Louie Duck were born around 1940 in Duckburg. In his award-winning epic series, "Life and Times of Scrooge McDuck", Rosa reveals the domestic pain felt by the boys' loss of their parents. When Scrooge first meets Donald and his nephews, he says: "I'm not used to relatives, either! The few I had seem to have... disappeared!" Huey, Dewey, and Louie respond: "We know how "that" feels, Unca Scrooge!"


title: Huey, Dewey, and Louie

text: In "Some Heir Over the Rainbow" by Carl Barks, Huey, Dewey, and Louie, along with Donald Duck and Gladstone Gander, are tested by Scrooge McDuck, who wants to pick an heir to his fortune. Using the legend of a pot of gold at the end of a rainbow, Scrooge secretly gives the nephews, Donald and their cousin each $1,000 to invest. Donald uses his money for a down payment of a new car, now being $1,000 in debt. Gladstone, considering himself too lucky to need the money this soon, hides the money for when and if he needs it, causing Scrooge to consider him a better option than Donald. Huey, Dewey, and Louie lend their money to a man who claims to need the money to search for a treasure. Initially thinking they were tricked out of the money, Scrooge actually considers leaving his fortune to Gladstone, even though he sees that as "an awful injustice to the world", but the man actually finds the treasure and pays the kids back. Scrooge makes Huey, Dewey, and Louie his heirs. It seems to be the most solidly canon indication of Scrooge's plans.


title: Huey, Dewey, and Louie

text: In a 1994 interview, Erik Svane asked Barks who would inherit Scrooge's money. Barks' response was "Probably Donald's nephews." Svane further queried, "Why would Huey, Dewey and Louie receive it?" Barks: "Oh, well, because they are so much more practical than Donald. In the later stories, as I developed those duck people and the whole community of Duckburg and all of its problems, I began giving those kids much more intelligence than anybody else in Duckburg. And so, I guess that when Uncle Scrooge passes on, he will leave all of his money to his three nephews. And I'm sure they will do a lot of good in the world, their Junior Woodchucks organization. They will save all the birds and all the whales."


title: Huey, Dewey, and Louie

text: Huey, Dewey, and Louie starred in the 1987 animated television series "DuckTales", in which they went on adventures with their great-uncle, Scrooge McDuck, after their "Unca Donald" left them with him to enlist in the U.S. Navy. The boys' personalities in this series were mainly based on their comic book appearances versus the theatrical shorts. In the 1996 series "Quack Pack", the three were portrayed as teenagers and given distinct personalities, with Huey serving as the group's leader, Dewey as a computer whiz, and Louie as a sports enthusiast. After "Quack Pack", the boys were reverted to their original ages for most appearances, including the 1999 series "Mickey Mouse Works". An exception was the 2001 series "House of Mouse", in which they served as the house band in a variety of different styles (most commonly as "The Quackstreet Boys"). They were also featured in a segment of the computer-animated film, "Mickey's Twice Upon a Christmas" from 2004.


title: Huey, Dewey, and Louie

text: In the 2017 "DuckTales" series, the brothers are once again given distinct designs, voices, and personalities: Huey is intelligent and logical, Dewey is adventurous and excitable, and Louie is laid-back and cunning. The boys move to Scrooge's mansion with Donald after Dewey accidentally destroys their houseboat and travel the world on adventures with their uncles. They also have different roles: Huey is a Junior Woodchuck, Dewey likes to go on adventures, and Louie wants to be wealthy like Scrooge, except that he likes to do everything the easy way. This iteration also changed Dewey's real name to Dewford, while making Dingus his middle name, and Louie's real name to Llewellyn. In the second season, the boys are reunited with their long-lost mother Della, who reveals she intended to name them "Jet, Turbo, and Rebel" before she disappeared, after which Donald named them instead.


title: Huey, Dewey, and Louie

text: Huey, Dewey and Louie have been given many appearances in video games over the years, starting with "DuckTales" (1989), a popular NES game based on the show, wherein they aid their Uncle Scrooge in finding treasure.


title: Huey, Dewey, and Louie

text: In "The Lucky Dime Caper" (1991) for Sega's Game Gear and Master System, the nephews are kidnapped by Magica De Spell. Donald must find Scrooge's lucky dime and barter for their safety. The trio also appear in the Sega Genesis and Sega Saturn game,"Quackshot" (1991), piloting Donald's plane as he travels the world in search of a lost treasure. The object of Disney's Magical Quest 3 Starring Mickey & Donald (1995), for Super Famicom (Japan) and Game Boy Advance, is to rescue the nephews from the clutches of the villainous King Pete.


title: Huey, Dewey, and Louie

text: "" (2000) was released for many gaming systems. The boys aid Donald to bat Gladstone in rescuing Daisy, while he also rescues their hexed play toys. The nephews appear as unlockable playable characters in "Mickey's Speedway USA" (2000) for Nintendo 64. In "" (2000), that premiered as an arcade game in Japan and afterward on PlayStation and as a Plug-and-Play handheld TV game, they appear as DJ's for certain music tracks. They are playable characters in "Disney Magic Kingdoms" (2016), a Disney Parks themed game for ios, Android and Windows.


title: Huey, Dewey, and Louie

text: Huey, Dewey, and Louie have recurring roles as shopkeepers in the "Kingdom Hearts" video game series. In the first entry (2002), the trio work in the item shop in the First District of Traverse Town. In "Kingdom Hearts II" (2005), they individually run an item shop (Huey), an accessory shop (Dewey), and a weapon shop (Louie) in Hollow Bastion/Radiant Garden. In both games' endings, they are seen returning to Disney Castle.


title: Huey, Dewey, and Louie

text: "" (2010) features the nephews in Disney Town, recreating Ice Cream flavors, this time with a speaking role. In "Kingdom Hearts χ" (2013), they are displayed on special Support medals that grant the player's other medals a set number of experience points based on the medal's star value. They appear in the Tram Common area of Twilight Town in "Kingdom Hearts III" (2019), where they each take turns running the gummi shop. In all of their "Kingdom Hearts" appearances, the nephews look similar to their appearance in the original "DuckTales".


title: Huey, Dewey, and Louie

text: The nephews appeared in seasonal parades during Easter, Halloween and Christmas 2011 after a long absence. They also appeared in the Countdown Party Parade 2011.


title: Huey, Dewey, and Louie

text: Huey, Dewey and Louie appear regularly in Paris. They appeared during the Christmas season 2010 in their daytime and nighttime Parades at ""Disneyland Paris's Magic Kingdom"", Disney's Once Upon a Dream Parade and in the Disney's Fantillusion Parade in glittery outfits. They made another appearance at Disneyland Paris for meet-and-greet at the Disneyland Hotel on April 2, 2011, the day of the Press Event for the launch of the "Magical Moments Festival". They also appeared at Disney's Once Upon a Dream Parade at the Disneyland Park in special outfits for the parade and at the Disney's Stars 'n' Cars Parade at the Walt Disney Studios Park in directors outfits.


title: Huey, Dewey, and Louie

text: The nephews appeared at Disneyland Paris's Halloween season 2011. They have their own show during "Mickey's Not-So-Scary Halloween Parties" at the Disneyland Park in Disneyland Paris, titled "Huey, Dewey and Louie's Trick or Treat Party". They also made an appearance for meet-and-greet at Disneyland Paris's "Disney's Halloween Party" on October 31, 2011. They were also part of the Christmas Eve and New Year's Eve 2011–2012 celebrations at the Disneyland Hotel.


title: Iron(II) sulfate

text: Iron(II) sulfate (British English: iron(II) sulphate) or ferrous sulfate denotes a range of salts with the formula Fe SO·"x"HO. These compounds exist most commonly as the heptahydrate ("x" = 7) but several values for x are known. The hydrated form is used medically to treat iron deficiency, and also for industrial applications. Known since ancient times as copperas and as green vitriol (vitriol is an archaic name for sulfate), the blue-green heptahydrate (hydrate with 7 molecules of water) is the most common form of this material. All the iron(II) sulfates dissolve in water to give the same aquo complex [Fe(HO)], which has octahedral molecular geometry and is paramagnetic. The name copperas dates from times when the copper(II) sulfate was known as blue copperas, and perhaps in analogy, iron(II) and zinc sulfate were known respectively as green and white copperas.


title: Iron(II) sulfate

text: It is on the World Health Organization's List of Essential Medicines. In 2020, it was the 116th most commonly prescribed medication in the United States, with more than 5million prescriptions.


title: Iron(II) sulfate

text: Industrially, ferrous sulfate is mainly used as a precursor to other iron compounds. It is a reducing agent, and as such is useful for the reduction of chromate in cement to less toxic Cr(III) compounds. Historically ferrous sulfate was used in the textile industry for centuries as a dye fixative. It is used historically to blacken leather and as a constituent of iron gall ink. The preparation of sulfuric acid ('oil of vitriol') by the distillation of green vitriol (Iron(II) sulfate) has been known for at least 700 years.


title: Iron(II) sulfate

text: Iron(II) sulfate is sold as ferrous sulfate, a soil amendment for lowering the pH of a high alkaline soil so that plants can access the soil's nutrients.


title: Iron(II) sulfate

text: In horticulture it is used for treating iron chlorosis. Although not as rapid-acting as ferric EDTA, its effects are longer-lasting. It can be mixed with compost and dug into the soil to create a store which can last for years. Ferrous sulfate can be used as a lawn conditioner. It can also be used to eliminate silvery thread moss in golf course putting greens.


title: Iron(II) sulfate

text: Ferrous sulfate can be used to stain concrete and some limestones and sandstones a yellowish rust color.


title: Iron(II) sulfate

text: Ferrous sulfate was used in the manufacture of inks, most notably iron gall ink, which was used from the middle ages until the end of the 18th century. Chemical tests made on the Lachish letters () showed the possible presence of iron. It is thought that oak galls and copperas may have been used in making the ink on those letters. It also finds use in wool dyeing as a mordant. Harewood, a material used in marquetry and parquetry since the 17th century, is also made using ferrous sulfate.


title: Iron(II) sulfate

text: Two different methods for the direct application of indigo dye were developed in England in the 18th century and remained in use well into the 19th century. One of these, known as "china blue", involved iron(II) sulfate. After printing an insoluble form of indigo onto the fabric, the indigo was reduced to "leuco"-indigo in a sequence of baths of ferrous sulfate (with reoxidation to indigo in air between immersions). The china blue process could make sharp designs, but it could not produce the dark hues of other methods.


title: Iron(II) sulfate

text: In the second half of the 1850s ferrous sulfate was used as a photographic developer for collodion process images.


title: Iron(II) sulfate

text: Iron(II) sulfate can be found in various states of hydration, and several of these forms exist in nature or were created synthetically.


title: Iron(II) sulfate

text: The tetrahydrate is stabilized when the temperature of aqueous solutions reaches . At these solutions form both the tetrahydrate and monohydrate.


title: Iron(II) sulfate

text: Mineral forms are found in oxidation zones of iron-bearing ore beds, e.g. pyrite, marcasite, chalcopyrite, etc. They are also found in related environments, like coal fire sites. Many rapidly dehydrate and sometimes oxidize. Numerous other, more complex (either basic, hydrated, and/or containing additional cations) Fe(II)-bearing sulfates exist in such environments, with copiapite being a common example.


title: Iron(II) sulfate

text: In the finishing of steel prior to plating or coating, the steel sheet or rod is passed through pickling baths of sulfuric acid. This treatment produces large quantities of iron(II) sulfate as a by-product.


title: Iron(II) sulfate

text: Another source of large amounts results from the production of titanium dioxide from ilmenite via the sulfate process.


title: Iron(II) sulfate

text: It can be produced by displacement of metals less reactive than Iron from solutions of their sulfate:


title: Iron(II) sulfate

text: Upon dissolving in water, ferrous sulfates form the metal aquo complex [Fe(HO)], which is an almost colorless, paramagnetic ion.


title: Iron(II) sulfate

text: On heating, iron(II) sulfate first loses its water of crystallization and the original green crystals are converted into a white anhydrous solid. When further heated, the anhydrous material decomposes into sulfur dioxide and sulfur trioxide, leaving a reddish-brown iron(III) oxide. Thermolysis of iron(II) sulfate begins at about .


title: Iron(II) sulfate

text: Like other iron(II) salts, iron(II) sulfate is a reducing agent. For example, it reduces nitric acid to nitrogen monoxide and chlorine to chloride:


title: Iron(II) sulfate

text: Its mild reducing power is of value in organic synthesis. It is used as the iron catalyst component of Fenton's reagent.


title: Iron(II) sulfate

text: Ferrous sulfate can be detected by the cerimetric method, which is the official method of the Indian Pharmacopoeia. This method includes the use of ferroin solution showing a red to light green colour change during titration.


title: Michael Wittmann

text: Michael Wittmann (22 April 19148 August 1944) was a German Waffen-SS tank commander during the Second World War. He is known for his ambush of elements of the British 7th Armored Division during the Battle of Villers-Bocage on 13 June 1944. While in command of a Tiger I tank, Wittmann destroyed up to 14 tanks, 15 personnel carriers and two anti-tank guns within 15 minutes for the loss of his own tank. The news was disseminated by Nazi propaganda and added to Wittmann's reputation.


title: Michael Wittmann

text: Wittmann became a cult figure after the war thanks to his accomplishments as a "panzer ace" (a highly decorated tank commander), part of the portrayal of the Waffen-SS in popular culture. Historians have mixed opinions about his tactical performance in battle. Some praised his actions at Villers-Bocage, while others found his abilities lacking, and the praise for his tank kills overstated. He is also known as the Black Baron.


title: Michael Wittmann

text: Michael Wittmann was born in the village of Vogelthal, near Dietfurt in Bavaria's Upper Palatinate on 22 April 1914. He enlisted in the German Army ("Heer") in 1934 after the Nazi seizure of power. Wittmann joined the Schutzstaffel (SS) in October 1936 and was assigned to the regiment, later division, Leibstandarte SS Adolf Hitler (LSSAH) on 5 April 1937. A year later, he participated in the annexation of Austria, the occupation of Sudetenland, and joined the Nazi Party.


title: Michael Wittmann

text: Wittmann's unit was transferred to the Eastern Front in the spring of 1941 for Operation Barbarossa, the planned invasion of the Soviet Union. He was assigned to SS Panzer Regiment 1, a tank unit, where he commanded a StuG III assault gun/tank destroyer as well as a Panzer III medium tank. By 1943, he commanded a Tiger I tank, and had become a platoon leader in the heavy company by the time Operation Citadel and the Battle of Kursk took place. Attached to the LSSAH, Wittmann's platoon of four Tigers reinforced the division's reconnaissance battalion to screen the division's left flank. On their first day in battle at Kursk, Wittmann and his crew scored eight tanks and seven anti-tank guns destroyed. At one point, his tank survived a collision with a burning T-34.


title: Michael Wittmann

text: In November 1943, Wittmann, still serving in Leibstandarte’s heavy company, was involved in armored counterattacks against the Russians around Zhitomir. On their first day in action against the Soviets, Wittman’s crew destroyed ten T-34s and five anti-tank guns. “By early January 1944 his combined total of destroyed tanks would rise to sixty-six.”


title: Michael Wittmann

text: On 14 January 1944, Wittmann was awarded the Knight's Cross of the Iron Cross. The presentation was made by his divisional commander, SS-"Oberführer" Theodor Wisch, who nominated him for the Knight's Cross of the Iron Cross with Oak Leaves. Wittmann was awarded the Oak Leaves on 30 January for the destruction of 117 tanks, making him the 380th member of the German armed forces to receive it. He received the award from Adolf Hitler, who presented it to him at the Wolf's Lair, his headquarters in Rastenburg, on 2 February 1944.


title: Michael Wittmann

text: In April 1944, the LSSAH's Tiger Company was transferred to SS Heavy Panzer Battalion 101. This battalion was assigned to the I SS Panzer Corps as a corps asset, and was never permanently attached to any division or regiment. Wittmann was appointed commander of the battalion's second company, and held the rank of SS-"Obersturmführer". On 7 June, the day after the Allied Invasion of Normandy began, the battalion was ordered to move from Beauvais to Normandy. The move, covering 165 km (105 miles), took five days to complete.


title: Michael Wittmann

text: Due to the Anglo-American advance south from Gold and Omaha Beaches, the German 352nd Infantry Division began to buckle. As the division withdrew south, it opened a 12 km (a 7.5-mile) gap in the front line near Caumont-l'Éventé. Sepp Dietrich, commander of 1st SS Panzer Corps, ordered Heavy SS-Panzer Battalion 101, his only reserve, to position itself behind the Panzer Lehr Division and SS Division Hitlerjugend. From this position, the battalion could protect the developing open left flank. Anticipating the importance the British would assign to the high ground near Villers-Bocage, Wittmann's company was positioned near the town. It arrived late on 12 June. Nominally composed of 12 tanks, his company was 50 per cent understrength due to losses and mechanical failures.


title: Michael Wittmann

text: The next morning, lead elements of the British 7th Armoured Division entered Villers-Bocage. Their objective was to exploit the gap in the front line, seize Villers-Bocage, and capture the nearby ridge (Point 213) in an attempt to force a German withdrawal. Wittman had not expected them to arrive so soon and had no time to assemble his company. "Instead I had to act quickly, as I had to assume that the enemy had already spotted me and would destroy me where I stood." Having ordered the rest of the company to hold its ground, he set off with one tank.


title: Michael Wittmann

text: At approximately 09:00, Wittmann's Tiger emerged from cover onto the main road, Route Nationale 175, and engaged the rearmost British tanks positioned on Point 213, destroying them. Wittmann then moved towards Villers-Bocage, engaging several transport vehicles parked along the roadside; the carriers burst into flames as their fuel tanks were ruptured by machine gun and high explosive fire. Moving into the eastern end of the town, he engaged several light tanks, followed by medium tanks. Alerted to Wittmann's actions, light tanks in the middle of the town quickly got off the road, while medium tanks were brought forward. Wittmann, meanwhile, had destroyed another British tank, two artillery observation post (OP) tanks, followed by a scout car and a half-track.


title: Michael Wittmann

text: Accounts differ as to what happened next. Historians record that, after destroying the OP tanks, Wittmann duelled briefly without success with a Sherman Firefly before withdrawing. His Tiger is then reported to have continued eastwards to the outskirts of the town before being disabled by an anti-tank gun. However, Wittmann said his tank was disabled by an anti-tank gun in the town centre.


title: Michael Wittmann

text: In less than 15 minutes, 13 or 14 tanks, two anti-tank guns, and 13 to 15 transport vehicles had been destroyed by Heavy SS-Panzer Battalion 101, the majority attributed to Wittmann. He played no further role in the Battle of Villers-Bocage. For his actions during the battle, Wittmann was promoted to SS-"Hauptsturmführer", and awarded the Knight's Cross of the Iron Cross with Oak Leaves and Swords.


title: Michael Wittmann

text: The German propaganda machine swiftly credited Wittmann, by then a household name in Germany, with all the British tanks destroyed at Villers-Bocage. He recorded a radio message on the evening of 13 June, describing the battle and claiming that later counter-attacks had destroyed a British armoured regiment and an infantry battalion. Doctored images were produced; three joined-together photographs, published in the German army magazine "Signal", gave a false impression of the scale of destruction in the town. The propaganda campaign was given credence in Germany and abroad, leaving the British convinced that the Battle of Villers-Bocage had been a disaster. In fact, its results were less clear-cut. The Waffen-SS may have fought with distinction during the Battle of Kursk but could not match the army's success, hence Sepp Dietrich's attempts to manufacture a hero out of Wittmann.


title: Michael Wittmann

text: On 8 August 1944, Anglo-Canadian forces launched Operation Totalize. Under the cover of darkness, British and Canadian tanks and troops seized the tactically important high ground near the town of Saint-Aignan-de-Cramesnil. Here they paused, awaiting an aerial bombardment that would signal the next phase of the attack. Unaware of the reason the Allied forces had halted, SS Hitlerjugend Division Commander Kurt Meyer ordered a counterattack to recapture the high ground.


title: Michael Wittmann

text: Wittmann led a group of seven Tiger tanks from Heavy SS-Panzer Battalion 101, supported by additional tanks and infantry. His group of Tigers crossed open terrain towards the high ground. They were ambushed by Allied tanks from two sides. On the right or northeast, British tanks from "A" Squadron 1st Northamptonshire Yeomanry and "B" Squadron 144th Regiment Royal Armoured Corps were positioned in woods. To the left or west, "A" Squadron Sherbrooke Fusilier Regiment was located at a chateau courtyard broadside to the attack, where they had knocked firing positions through the stone walls. The attack collapsed as the Canadian tanks destroyed two Tiger tanks, two Panzer IVs and two self-propelled guns in Wittman's force, while British tank fire destroyed three other Tigers. During the ambush, anti-tank shells—fired from either the British or Canadian tanks—penetrated the upper hull of Wittmann's tank, igniting the ammunition. The resulting fire engulfed the tank and blew off the turret. The destroyed tank's dead crew members were buried in an unmarked grave. In 1983, the German war graves commission located the burial site. Wittmann and his crew were reinterred together at the La Cambe German war cemetery in France.


title: Michael Wittmann

text: In 2008 a documentary in the "Battlefield Mysteries" series examined the final battle. A historian, Norm Christie, interviewed participants; Rad Walters, Joe Ekins and Ken Tout, and from their testimony and the two German accounts pieced the final battle together. The Tigers left the cover of a hedge near Cintheaux at 12:30 in two prongs; one in the middle of the field with the other—including Wittman—moving slower on the right. The British 75mm armed tanks engaged the lead Tiger (Iriohn) hitting it in the transmission, bogies or track and it started going in circles trying to withdraw. Joe Ekins' tank hit the second Tiger on the right side and knocked it out. As the crew escaped and brought out their wounded, they watched another Tiger north of them go up in flames (Kisters). Iriohn partly withdrew but could not get away and was hit by Ekins—"the one that was mulling around." Wittmann signalled "Pull back!" He did not realize that a group of the Sherbrookes were immediately to his right, and in a volley they knocked out the two Tigers beside the road. The commander of the second Tiger recalled the position of Wittmann's tank and specifically the skewed turret. The tank blew up shortly afterwards. Survivors from Dollinger's tank passed by the wreck of Wittmann's tank shortly afterwards.


title: Michael Wittmann

text: For such a junior officer, an unusual amount of speculation has surrounded Wittmann's death, both as to its cause and the party responsible. Agte states that "the English" could have possibly placed a bounty on him. This is contradicted by Allied records and the testimony of Allied troops involved that he was not singled out during the battle.


title: Michael Wittmann

text: After the war, claims were made by or for the following units as being responsible for Wittmann's death: the 1st Polish Armoured Division, the 4th Canadian Armoured Division, the 144th Regiment Royal Armoured Corps, and the RAF Second Tactical Air Force.


title: Michael Wittmann

text: Nazi propaganda reported that Allied aircraft struck Wittmann's tank, stating that he had fallen in combat to the "dreaded fighter-bombers". In a post-war account, French civilian Serge Varin, who took the only known photograph of the destroyed tank, claimed that he found an unexploded rocket nearby and that he saw no other penetration holes in the tank. Historian Brian Reid dismisses this contention as relevant RAF logs make no claim of engaging tanks in the area at that time. This position is supported by the men of Wittmann's unit who stated they did not come under air attack, and by British and Canadian tank crews who also dismissed any involvement by aircraft.


title: Michael Wittmann

text: In a 1985 issue of "After the Battle Magazine", Les Taylor, a wartime member of the 1st Northamptonshire Yeomanry, claimed that fellow yeoman Joe Ekins was responsible for the destruction of Wittmann's tank. Veteran and historian Ken Tout, a member of the same unit, published a similar account crediting Ekins. This became, for a time, the widely accepted version of events. According to Hart, Ekin's unit was positioned in a wood on the right flank of the advancing Tiger tanks. At approximately 12:47, they engaged them, halting the attack, and killing Wittmann.


title: Michael Wittmann

text: Reid discusses the possibility that A Squadron of the Sherbrooke Fusilier Regiment, 2nd Canadian Armoured Brigade, positioned on the left flank of the advancing German tanks, was responsible instead. Commanded by Sydney Valpy Radley-Walters, the squadron's six 75 mm Shermans and two 17-pounder Sherman Fireflies were situated on the grounds of a chateau at Gaumesnil. The unit had created firing holes in the property's walls and, based on verbal testimony, engaged the advancing German tanks, including Tigers. The British tanks were between and away from the German line of advance, whereas the Canadian squadron was less than 150 m (500 feet) away behind a stone wall. Reid argues that due to the Canadians' proximity to the Germans, and the firing angle which precisely coincides with the tank round's entry hole in the Tiger, their troops more than likely destroyed Wittmann's tank. Reid supports this with H. Holfinger's account of the engagement. Holfinger was in a Tiger approximately behind Wittmann and he said Wittmann's Tiger was destroyed at 12:55. Ekin's crew was credited with the destruction of 3 Tigers at 12:40, 12:47 and 12:52, Wittmann's tank being allegedly the one destroyed at 12:47. Considering Holfinger's account, Reid concludes that the Tiger destroyed at 12:47 could not be that of Wittmann; he also notes that the circumstances surrounding the fate of the Tiger destroyed at 12:52 exclude the possibility that it could have been Wittmann's.


title: Michael Wittmann

text: Some historians and authors of the late twentieth-century found Wittmann's actions at Villers-Bocage impressive, describing his attack as "one of the most amazing engagements in the history of armoured warfare", "one of the most devastating single-handed actions of the war", and "one of the most devastating ambushes in British military history". Historian Stephen Badsey has stated that the ambush Wittmann launched has cast a shadow over the period between D-Day and 13 June in historical accounts.


title: Michael Wittmann

text: With a record of 130 tanks destroyed, Wittman was Germany's top tank ace. Claims by Franz Kurowski over Kurt Knispel having a greater number are disputed.


title: Michael Wittmann

text: Jim Stor, writing in "The Human Face of War" notes that Wittman's attack on the British regiment at Bocage went beyond just a bad day of tanks losses for the British. He states that the shock of losses to the British regiment had operational and strategic effect for the operation.


title: Michael Wittmann

text: German tank commander and historian is not as impressed. In analyzing Wittmann's actions at Villers-Bocage, he called into question his tactical ability. Schneider states: "a competent tank company commander does not accumulate so many serious mistakes". He highlights how Wittmann dispersed his forces in a sunken lane with a broken down tank at the head of the column, thereby hampering his unit's mobility. The solitary advance into Villers-Bocage was heavily criticized as it breached "all the rules". No intelligence was gathered, and there was no "centre of gravity" or "concentration of forces" in the attack. Schneider argues that due to Wittmann's rash actions: "the bulk of the 2nd Company and Mobius 1st Company came up against an enemy who had gone onto the defensive". He calls Wittmann's "carefree" advance into British-occupied positions "pure folly", and says "such over hastiness was uncalled for." He concludes that had a properly prepared assault been launched involving the rest of his company, and the 1st Company, far greater results could have been achieved. Finally, Schneider opines that: "thoughtlessness of this kind was to cost [Wittmann] his life ... during an attack casually launched in open country with an exposed flank."


title: Michael Wittmann

text: Historian Sönke Neitzel describes Wittmann as the "supposedly successful" tank commander of World War II and attests to "hero worshiping" around Wittmann. According to Neitzel, numbers of successes, by highly decorated tank commanders, should be read with caution as it is rarely possible to determine reliably, in the heat of battle, how many tanks were destroyed by whom.


title: Michael Wittmann

text: Historian Steven Zaloga credits Wittmann with around 135 tank kills and points out that he achieved 120 of these in 1943, operating a Tiger I tank on the Eastern Front. Having advantages both in firepower and in armor, the Tiger I was "nearly invulnerable in a frontal engagement" against any of the Soviet tanks of that time, and Wittmann thus could destroy opposing tanks from a safe distance. Zaloga concludes that "Most of the 'tank aces' of World War II were simply lucky enough to have an invulnerable tank with a powerful gun." German documents from 1944 state that Allied technology had caught up with the Tiger I and "no longer can it prance around, oblivious to the laws of tank tactics". Zaloga believes that Wittmann's fate reflected that new reality: after his transfer to France, his crew only lasted two months, and was destroyed either by a British medium tank, the up-gunned Sherman Firefly, or a standard 75mm-equipped Sherman. The 75mm's armour piercing round was more than enough to have penetrated his Tiger's thin rear upper deck armour from less than 150 m (500 feet) and all of the Sherbrooke-Fusilier's records were lost shortly after the battle when an American aircraft dropped a bomb on the vehicle that contained these documents.


title: Michael Wittmann

text: Writing in 2013, British historian John Buckley criticised the accounts which many historians continue to provide of the fighting around Villers-Bocage. Buckley argued that by wrongly attributing the entire German success to Wittmann, "many historians through to today continue to repackage unquestioningly Nazi propaganda".


title: Michael Wittmann

text: Wittmann is often featured in books on the battles in Normandy. Several websites are dedicated to him, along with books by authors such as Patrick Agte and Franz Kurowski. The former is an author and publisher affiliated with the pro-Waffen-SS revisionist history group HIAG, while the latter is a prolific author who lauded decorated Waffen-SS men.


title: Michael Wittmann

text: Wittmann became a cult figure after the war thanks to his accomplishments as a "panzer ace" (a highly decorated tank commander) in the portrayal of the Waffen-SS in popular culture. Historian Stephen Hart said that "the Wittmann legend [has] become well-established" and "continues to stimulate huge public interest". Military historian Steven Zaloga refers to Wittmann as "the hero of all Nazi fanboys". He discusses the popular perception of a tank-versus-tank engagement as an "armoured joust"—two opponents facing each other—with the "more valiant or better-armed the eventual victor". Zaloga contends that the perception is nothing but "romantic nonsense". According to him, most successful tank commanders were "bushwackers", having a battlefield advantage rather than a technical one: a tank crew that could engage its opponent before the latter spotted it often came out on top.


title: Michael Wittmann

text: Wittmann is featured by Kurowski in his 1992 book "Panzer Aces", an ahistorical and hagiographic account of the combat careers of highly decorated German tank commanders. Smelser and Davies describe Kurowski's version of the war on the Eastern Front as "well-nigh chivalrous", with German troops "showing concerns for the Russian wounded, despite the many atrocities" of the Soviets against the Germans. In one of Kurowski's accounts, Wittmann takes out eighteen tanks in a single engagement, for which Sepp Dietrich, the commanding officer, presents him with an Iron Cross and inquires whether Wittmann has a request. Without hesitation, Wittmann asks for assistance for a wounded Russian soldier he has spotted. Many similar acts of "humanity" are present in the book, amounting to a distorted image of the German fighting men.


title: Frank Sutton

text: Frank Spencer Sutton (October 23, 1923 – June 28, 1974) was an American actor best remembered for his role as Gunnery SergeantVince Carter on the CBS television series "Gomer Pyle, U.S.M.C.".


title: Frank Sutton

text: Born in Clarksville, Tennessee, Sutton developed an interest in acting, playing his first role at age nine and also starring in the drama club at East Nashville High School, where he graduated in 1941. He later said, "The first time I walked out on a stage, I had a warm feeling. I knew then I wanted to be an actor."


title: Frank Sutton

text: After high school, Sutton returned to Clarksville to become a radio announcer. During World War II he volunteered for service in the Marine Corps, but he was medically rejected due to his color blindness. He then enlisted in the U.S. Army and served in the South Pacific, taking part in 14 assault landings. Sutton was a sergeant who served from 1943 to 1946 in the 293rd Joint Assault Signal Company. He was awarded the Bronze Star and Purple Heart.


title: Frank Sutton

text: Honorably discharged after the war as a sergeant, he began acting on stage. He attended the Columbia University School of General Studies, graduating "cum laude" with a bachelor's degree in drama in 1952.


title: Frank Sutton

text: Throughout the 1950s and early 1960s, Sutton played small roles in television shows such as "Decoy", "Route 66", "Naked City", "The Greatest Show on Earth", "The Fugitive", "The Goldbergs", "87th Precinct", "Gunsmoke", "", "Empire", "The Twilight Zone", and "The Untouchables". He had a continuing role as Cadet Eric Rattison, the great rival of the Polaris Unit manned by the series' heroes, in "Tom Corbett, Space Cadet" from 1950 to 1955. In 1955, he received his big break in the Academy Award-winning movie "Marty", in which he played the title character's friend, Ralph. He also had a role in "The Satan Bug", a 1965 spy thriller. He returned to the stage in "The Andersonville Trial" in the early 1960s.


title: Frank Sutton

text: Having primarily acted in dramas, Sutton's breakthrough role was on "Gomer Pyle, U.S.M.C.", a 1964 episode of "The Andy Griffith Show", in which he played the cynical and easily exasperated Gunnery Sergeant Vince Carter opposite Jim Nabors' character Gomer Pyle. This episode was the pilot for a spin-off TV comedy, "Gomer Pyle, USMC", where Sutton continued the role for five seasons, until the show ended its run in 1969. He also appeared in public service announcements in the role of Gunnery Sergeant Carter. After "Gomer Pyle" ceased production, Sutton appeared regularly on Nabors' variety show "The Jim Nabors Hour" with "Gomer Pyle" co-star Ronnie Schell. Sutton played the brother-in-law of Nabors' character in comedy sketches. Sutton performed in dinner theater, playing, among other roles, the father in "Norman, Is That You?" and made guest appearances on other television programs.


title: Frank Sutton

text: In 1946, Sutton married soap-opera writer Toby M. Igler, with whom he had two children, Joe Sutton and Amanda.


title: Frank Sutton

text: On June 28, 1974, while preparing for a performance in the comedy play "Luv" at the Beverly Barn Dinner Playhouse in Shreveport, Louisiana, Sutton died of a heart attack. He is buried in the Greenwood Cemetery in his hometown of Clarksville, Tennessee.


title: Comic Sans

text: Comic Sans MS is a sans-serif typeface designed by Vincent Connare and released in 1994 by Microsoft Corporation. It is a non-connecting script inspired by comic book lettering, intended for use in cartoon speech bubbles, as well as in other casual environments, like informal documents and children's materials.


title: Comic Sans

text: The typeface has been supplied with Microsoft Windows since the introduction of Windows 95, initially as a supplemental font in the Microsoft Plus! Pack and later in Microsoft Comic Chat. Describing it, Microsoft has explained that "this casual but legible face has proved very popular with a wide variety of people."


title: Comic Sans

text: The typeface's widespread use, often in situations it was not intended for, has been the subject of much derision and criticism.


title: Comic Sans

text: Microsoft designer Vincent Connare began working on Comic Sans in 1994 after having already created other fonts for various applications. When he saw a beta version of Microsoft Bob that used Times New Roman in the word balloons of its cartoon characters, he believed the typeface gave the software an overly formal appearance. He believed this was inappropriate for the aesthetics of the program, which was created to introduce younger users to computers. In order to make Microsoft Bob look more suitable for its intended purposes, he decided to create a new typeface with only a mouse and cursor, based on the lettering style of comic books he had in his office, specifically "The Dark Knight Returns" (lettered by John Costanza) and "Watchmen" (lettered by Dave Gibbons).


title: Comic Sans

text: He completed Comic Sans too late for inclusion in Microsoft Bob, and the typeface would go unreleased until the programmers of Microsoft 3D Movie Maker, which also used cartoon guides and speech bubbles, adopted it. The speech bubbles were eventually phased out and replaced by actual sound, but Comic Sans stayed for the program's pop-up windows and help sections. The typeface later shipped with the Windows 95 Plus! Pack. It was later included as a system font for the OEM versions of Windows 95. Finally, it became one of the default fonts for Microsoft Publisher and Microsoft Internet Explorer. Comic Sans is also used in Microsoft Comic Chat, which was released in 1996 with Internet Explorer 3.0.


title: Comic Sans

text: Comic Sans Pro is an updated version of Comic Sans created by Terrance Weinzierl from Monotype Imaging. While retaining the original designs of the core characters, it expands the typeface by adding new italic variants, in addition to swashes, small capitals, extra ornaments and symbols including speech bubbles, onomatopoeia and dingbats, as well as text figures and other stylistic alternatives. Originally appearing as part of Ascender 2010 Font Pack as Comic Sans 2010, it was first released on April Fools' Day, causing some to initially assume it was a joke.


title: Comic Sans

text: Comic Sans has become infamous for its use in serious circumstances, like warning signs and formal documents, in which it might appear too informal, unprofessional, or inappropriate.


title: Comic Sans

text: During the summer of 2010, NBA superstar LeBron James left the Cleveland Cavaliers in free agency, in a highly publicized media affair that culminated in a TV special called "The Decision". The majority owner of the team (at the time), Dan Gilbert, reacted by posting a letter to Cavalier fans. The letter was criticized for its use of Comic Sans.


title: Comic Sans

text: In October 2012, a Dutch World War II memorial called "Verzoening" ("Reconciliation") was revealed on which the names of Jewish, Allied and German military deaths alike were written alongside each other in Comic Sans. The names were eventually scraped off after complaints from Jewish organizations, but the rewritten message was once again in Comic Sans. According to the city government, this was done because the letters fit the shape of the stone and were easily visible from a distance. It was, however, criticized for making the memorial appear "ugly" and "cheap".


title: Comic Sans

text: In September 2014, "The Sydney Morning Herald" printed a front page with Comic Sans, causing an uproar, despite its use being within speech bubbles in keeping with the origin of the typeface.


title: Comic Sans

text: In August 2015, a number of Greek Prime Minister Alexis Tsipras's Syriza party members split and formed a new party, headed by Panagiotis Lafazanis. The official document of resignation was allegedly written in Comic Sans.


title: Comic Sans

text: In July 2018, a statue of former Chilean President Pedro Aguirre Cerda was inaugurated in Santiago. The plaques on the monument were written in Comic Sans, drawing negative attention on social media.


title: Comic Sans

text: In October 2019, when the United States House Intelligence Committee requested that two of Rudy Giuliani's associates, Lev Parnas and Igor Fruma, present documentation regarding their involvement in the Ukraine scandal, former Trump attorney John Dowd penned a letter of explanation printed in Comic Sans.


title: Comic Sans

text: That same month, as part of the United Kingdom's Brexit debate, the Conservative Party tweeted an image stating "MPs must come together and get Brexit done" using Comic Sans. The tweet was heavily ridiculed, but some commentators saw it as a deliberate attempt to use the typeface's notoriety in order to bring their message to a wider audience.


title: Comic Sans

text: A research article published by "Cognition" in 2010 showed disfluency could lead to improved retention and classroom performance. The article stated that disfluency can be produced merely by adopting fonts that are slightly more difficult to read. In the case studies cited in the article, Comic Sans was used to introduce disfluency. A 2010 Princeton University study involving presenting students with text in a font slightly harder to read found that they consistently retained more information from material displayed in fonts perceived as ugly or disfluent (Monotype Corsiva, Haettenschweiler, and Comic Sans Italic) than in a simpler, more traditional typeface such as Helvetica.


title: Comic Sans

text: More often, however, Comic Sans is described as especially legible, and is frequently used in school settings or as an aid for people with dyslexia. Some people have reported that typing in Comic Sans has helped to clear writer's block, claiming that its casual appearance and high legibility create less mental tension. Compared to other typefaces, Comic Sans has fewer rotated and mirror-image glyphs (ex. the letters "b", "d", "p", and "q"), has particularly wide letter spacing, and is sans serif.


title: Comic Sans

text: Several reinterpretations of Comic Sans have been created as a result of its popularity. In April 2014, font designer Craig Rozynski released a modernized version of Comic Sans called Comic Neue. In 2015, graphic designer Ben Harman created Comic Papyrus (later renamed "Comic Parchment" for legal reasons), which combines the features of Comic Sans with the similarly panned typeface Papyrus. In 2019, Tabular Type Foundry released Comic Code, a monospaced version of the typeface.


title: Comic Sans

text: Because of its ubiquity and misuse, Comic Sans has been opposed by a majority of graphic designers. The "Boston Phoenix" reported on disgruntlement over the widespread use of the typeface, especially its incongruous use for writing on serious subjects, with the complaints urged on by a campaign started by two Indianapolis graphic designers, Dave and Holly Combs, via their website "Ban Comic Sans". The movement was conceived in 1999 by the two designers after an employer insisted that one of them use Comic Sans in a children's museum exhibit. The website's main argument is that a typeface should match the tone of its text and that the humorous appearance of Comic Sans often contrasted with a serious message, such as a "do not enter" sign. The movement ran until 2019, when it was renamed "Use Comic Sans," which was because Dave Combs believed the hatred had "gotten out of hand" and "it's gotten to be so bad that it's almost cool again."


title: Comic Sans

text: Dave Gibbons, whose work was one of the inspirations for Comic Sans, said that it was "a shame they couldn't have used just the original font, because [Comic Sans] is a real mess. I think it's a particularly ugly letter form."


title: Comic Sans

text: Film producer and "The New York Times" essayist Errol Morris wrote in an August 2012 posting, "The conscious awareness of Comic Sans promotes—at least among some people—contempt and summary dismissal." With the help of a professor, he conducted an online experiment and found that Comic Sans, in comparison with five other typefaces (Baskerville, Helvetica, Georgia, Trebuchet MS, and Computer Modern), makes readers slightly less likely to believe that a statement they are reading is true.


title: Comic Sans

text: In the Netherlands, radio DJs Coen Swijnenberg and Sander Lantinga decided to celebrate the typeface by having a Comic Sans day on the first Friday of July. Comic Sans Day has been held since 2009. Some Dutch companies have their website in Comic Sans on this day.


title: Comic Sans

text: According to a 2020 Twitter poll held by TES, 44% of teachers sampled used Comic Sans in their teaching resources. Comic Sans is widely used in schools due to its high legibility. Other reasons include:


title: Comic Sans

text: Vincent Connare is reportedly not offended by the negative backlash over Comic Sans. At the Fourth Annual Boring Conference, he claimed to find the contempt for his work to be "mildly amusing." He has stated that he is proud of his creation, offering different rationales. One of these was that "Comic Sans does what it was commissioned to do, it is loved by kids, mums, dads and many family members. So it did its job very well. It matched the brief!" He has also referred to it as "the best joke I've ever told." In 2014, commenting on Comic Sans' critics and fans alike, Connare said, "If you love it, you don't know much about typography, [but] if you hate it, you really don't know much about typography either, and you should get another hobby."


title: Comic Sans

text: Lauren Hudgins of "The Establishment" argued that people who use Comic Sans should be treated with respect, not mockery, because "People without dyslexia need empathy for those who need concessions to manage the disability."


title: Comic Sans

text: In the 2005 session of the youth model parliament in Ontario, Canada, the New Democratic Party included the clause, "Ban the font known as Comic Sans" in an omnibus ban bill.


title: Comic Sans

text: In July 2012, when the discovery of the Higgs boson was announced at CERN, Fabiola Gianotti, the spokesperson of the ATLAS experiment, attracted comment by using Comic Sans in her presentation of the results. As a 2014 April Fools' Day joke, CERN claimed that it would be switching all its publications to Comic Sans.


title: Comic Sans

text: The Internet meme Doge, which became popular in late 2013, consists of different colored sets of words in broken English written in Comic Sans around the head of a Shiba Inu dog.


title: Comic Sans

text: In April 2014, OpenBSD announced the LibreSSL project in Comic Sans, claiming to be the first to "weaponize" it as a means for soliciting donations.


title: Comic Sans

text: In the 2015 video game "Undertale" and its followup "Deltarune", the character Sans is a comic (i.e. comedian) named after the typeface. His dialogue is displayed in lowercase Comic Sans. He is paired with his brother named Papyrus, in reference to the typeface of the same name.


title: Comic Sans

text: On May 22, 2012, The Comic Sans Song was released by YouTube content creator and musician Gunnarolla, in collaboration with musician Andrew Huang. The song makes reference to Comic Sans and features commentary around the impact the font has had on pop-culture.


title: Comic Sans

text: In October 2022, Comic Sans became the representative of Dyslexia Scotland and their ad campaign, "There's Nothing Comic About Dyslexia". The campaign's purpose is to inform people on the typeface's benefits among dyslexic people, and to encourage the creation of typefaces that are more formal, but also dyslexic-friendly.


title: Oral Roberts University

text: Oral Roberts University (ORU) is a private evangelical university in Tulsa, Oklahoma. Founded in 1963, the university is named after its founder, evangelist Oral Roberts.


title: Oral Roberts University

text: Sitting on a campus, ORU offers over 70 undergraduate degree programs along with 20 graduate programs across six colleges. ORU is classified among "Baccalaureate Colleges: Diverse Fields". Most popular majors include ministry and leadership, nursing, engineering, psychology, and business administration. The university enrolls approximately 4,000 students.


title: Oral Roberts University

text: Students may take part in mission trips as part of 60 clubs that are available through the university. In 2018, over 500 students completed trips across five continents. Students are required to attend weekly chapel services.


title: Oral Roberts University

text: Ground was officially broken for Oral Roberts University in 1962 in the southern part of Tulsa, Oklahoma. The university received its charter the following year from the State of Oklahoma and Oral Roberts University officially opened in 1965 with an enrollment of 300 students and seven major completed buildings. The university was founded by Oral Roberts "as a result of the evangelist Oral Roberts' obeying God’s mandate to build a university on God’s authority and the Holy Spirit. God’s commission to Oral Roberts was to 'Raise up your students to hear My voice, to go where My light is dim, where My voice is heard small, and My healing power is not known, even to the uttermost bounds of the earth. Their work will exceed yours, and in this I am well pleased'." Roberts placed special importance on the Prayer Tower, even though the concept of a building specifically dedicated to prayer at the center of the campus caused considerable tension, as some academic leaders were afraid the school would be unable to receive accreditation with such a building. But the tower, designed by architect Frank Wallace, was completed in 1967 at a cost of $2 million, a further source of contention. After its completion, Roberts called for a three-day period of prayer and fasting. At the university's dedication ceremony in 1967, the evangelist Billy Graham was the keynote speaker.


title: Oral Roberts University

text: The first partial graduation took place in 1968 and the first full graduation in 1969. In 1971, Oral Roberts University was accredited by the North Central Association.


title: Oral Roberts University

text: ORU was accredited in 1971 by the Higher Learning Commission of the North Central Association of Colleges and Schools. It is also accredited by the Association of Theological Schools in the United States and Canada.


title: Oral Roberts University

text: During the first decade of the school's existence many of the campus's iconic structures were completed, such as the Howard Auditorium, the Graduate Center, the Mabee Center, and Christ's Chapel.


title: Oral Roberts University

text: The O. W. Coburn School of Law opened in 1979. In 1986 the university "shut down its ailing law school and sent its library to Pat Robertson's Bible-based college in Virginia", which subsequently founded the Regent University School of Law.


title: Oral Roberts University

text: The university built the City of Faith Medical and Research Center hospital in 1981 and started the Oral Roberts University School of Medicine in 1978. Severe financial difficulties with both of these institutions led to their closure in 1989. Oral Roberts's son Richard was named president in 1993.


title: Oral Roberts University

text: In January 1996, Golden Eagle Broadcasting, a small digital satellite Christian and family programming television network owned and operated by Oral Roberts University, was founded.


title: Oral Roberts University

text: On February 5, 1997, several ORU students reportedly disrupted services at a mosque near the University of Tulsa. The students mistakenly thought it was the 27th night of Ramadan when it was actually the 28th day of Ramadan. A university spokesman indicated that the students would not be disciplined and that university officials were discussing with the students their accounts of the events, which differed from what those attending services at the mosque reported. On February 7, 1997, the Islamic Society of Tulsa received a formal apology from Reverend Bill Shuler, who led religious services on campus.


title: Oral Roberts University

text: Due to alleged discrimination against LGBT students at ORU, Soulforce placed the university on its 2006 Equality Ride route, with a rally taking place on March 20, 2006. University administration refused the activists entrance to the campus, which resulted in several activists being arrested after they entered despite the university administration's decision. Soulforce members objected to the university's honor code pledge's ban on homosexual activity. All students are required to sign and abide by the honor code which places the same restriction on all sexual activity outside "traditional marriage of one man and one woman."


title: Oral Roberts University

text: While homosexual activity is against the school's honor code, many LGBTQ students have still attended the school. Over time, ORU alumni have made groups such as ORU-OUT and gay-straight alliances to allow LGBTQ students and alumni to have social support groups. Since ORU-OUT's founding, some of the university's LGBTQ+ alumni have publicly marched in Tulsa's pride parade.


title: Oral Roberts University

text: In 2010, ORU teamed up with the National Hispanic Christian Leadership Conference to open a bilingual Hispanic Center on campus.The goals of this partnership include targeting a 25% Hispanic population within the student body and to reduce the approximately 50% high school dropout rate among Hispanic students.


title: Oral Roberts University

text: ORU was granted an exception to Title IX in 2017 which allows it to legally discriminate against LGBT students for religious reasons. It is ranked among the "Absolute Worst Campuses for LGBTQ Youth" by Campus Pride.


title: Oral Roberts University

text: ORU and G12 Vision announced in 2019 they had reached an agreement over a partnership. It was hoped that the agreement would make ORU's theological education more accessible worldwide.


title: Oral Roberts University

text: ORU moved to virtual classes for the remainder of the 2020 spring semester after the outbreak of the COVID-19 pandemic in the United States. In fall 2020, students were required to get tested for COVID-19 before moving into the dorms. All students and staff were required to wear masks on campus at all times. The university also rearranged class schedules in order for the semester to end early.


title: Oral Roberts University

text: In 2021, the university expanded its campus through the addition of 3 new buildings: a welcome center (which broke ground in April), Media Arts Center, and library. The expansion was part of ORU's $75 million campaign, which allocated $60 million to these new structures with the remainder going towards student scholarships. ORU also announced in April 2021 the development of the Mike Carter Athletic Center, which is expected to be over 40,000 square feet, and renovation of the Mabee Center.


title: Oral Roberts University

text: In October 2007, three former professors filed a wrongful termination lawsuit against ORU in Tulsa County. The professors also alleged university president Richard Roberts misused university assets and illegally ordered the university to participate in Republican candidate Randi Miller's political campaign for Tulsa mayor.


title: Oral Roberts University

text: Lindsay Roberts, the wife of Richard Roberts, was accused of spending university funds on clothes, awarding nonacademic scholarships to the children of family friends and sending text messages on university-issued cell phones to "underage males." The lawsuit also alleged a longtime maintenance employee was fired for the purpose of giving the job to an underage male friend of Lindsay Roberts.


title: Oral Roberts University

text: The plaintiffs filed an amended lawsuit adding the university's Board of Regents (Oral and Richard Roberts, along with George Pearsons, Kenneth Copeland, Creflo Dollar, Michael A. Hammer, John Hagee, Marilyn Hickey, Jerry Savelle and Charles Watson) to the suit and alleged that Roberts fired the university's financial comptroller and "voluminous materials and documents were shredded and destroyed, constituting spoliation of evidence." The filing also alleged Lindsay Roberts had spent nights in the ORU guest house with a 16-year-old male who also was allowed to live in the Roberts family residence on campus.


title: Oral Roberts University

text: On October 17, 2007, Richard Roberts announced a "temporary leave of absence" as president of the university, citing the "toll" the lawsuit and attendant allegations had taken on him and his family. Billy Joe Daugherty became Executive Regent of the Board of Regents and Interim President. Chairman of the Board George Pearsons noted the temporary resignation was not an admission of guilt.


title: Oral Roberts University

text: In November 2007, the tenured faculty of Oral Roberts University approved by a simple majority a non-binding vote of no confidence in Richard Roberts. Roberts tendered his letter of resignation to the board of regents on November 23. Pearsons said the university planned to separate its finances and leadership from the Oral Roberts Evangelistic Association, to the apparent relief of many students and faculty members. On January 10, 2008, ORU settled with plaintiff John Swails, who was reinstated to his previous teaching position. The school also announced a formal search committee for a new president, to be headed by board of regents member and Tulsa resident Glenda Payas.


title: Oral Roberts University

text: Tulsa evangelist Billy Joe Daugherty was named interim President and executive regent. The same month, the school was reportedly "struggling financially" with over $50 million in debt.


title: Oral Roberts University

text: ORU's operating budget for 2007-08 was over $82 million. On January 14, 2008, ORU's board of regents voted unanimously to accept $62 million from the Mart Green family, the owners of Oklahoma City-based Hobby Lobby, Mardel educational, and various Christian supply stores, an offer which included changes to the university's governing board. In October of that year, an ORU spokesman said the university was still $52.5 million in debt. The school accepted an additional $8 million from the Greens in November. Of the $82 million given to Oral Roberts University, approximately half went toward eliminating its debt. The remaining half was allocated to "campus renovations, technology upgrades, academic enhancement, financial aid for new and returning students, marketing and operations", according to the university website. In February 2008, the Renewing the Vision campaign was initiated in an effort to erase this debt. To free the university from its burgeoning debt, the board of trustees announced plans for a $25 million matching campaign, in which the board agreed to match dollar-for-dollar all donations. In addition to eliminating debt, funds from the Renewing the Vision campaign contributed to the 2008 summer campus renovations, as well as scholarships provided by the university. During the summer of 2008, $10 million went to campus upgrades and deferred maintenance. Many dormitories were extensively renovated and most other buildings received restoration and upgrades. In January 2009, the university's presidential search committee recommended Mark Rutland, President of Southeastern University of the Assemblies of God in Florida, to succeed Richard Roberts, which the trustees approved. On January 14, Rutland confirmed that he had been offered the position and intended to accept it. The university began to implement the employment reduction plans, laying off 53 employees and cutting about 40 unfilled positions. On January 29, 2009, the Green family committed $10.4 million to additional campus renovations and upgrades to take place during summer 2009. Following Mart Green's contribution, the university's debt was reduced to $25 million.


title: Oral Roberts University

text: On April 15, 2009, Chairman of the Armand Hammer Foundation and university trustee Michael Armand Hammer made a $1 million donation to the school's Whole Person Scholarship. As of June 3, 2009, donations and pledges had reduced the university's debt to $720,000. On September 23, 2009, it was announced at the end of the university's chapel service that the school was debt-free. The announcement was made two days before Rutland's September 25, 2009 inauguration ceremony, held at the Mabee Center.


title: Oral Roberts University

text: In December 2010, ORU announced that the Green family would make another $10 million gift in 2011, to be used for renovations and technology improvements. The gift raised the Greens' total donations to $110 million.


title: Oral Roberts University

text: On August 25, 2015, ORU Administration learned of Sabrina Bradford's recent marriage to a woman and two days later she was informed she was not welcome back on campus. In March 2006 eight peaceful protesters were arrested while rallying across the street from ORU's main entrance. Ronnie Roberts, the son of Oral Roberts, came out as gay to the Rev. Troy Perry, founder of the Metropolitan Community Church, in the early 1980s. Six months later, Ronnie Roberts committed suicide. As of December 7, 2021, an online petition to "Tell Oral Roberts University: Change your anti-LGBTQ honor code" had gained over 10,000 signatures. March 2021 - The Religious Exemption Accountability Project, or REAP, filed a class action lawsuit Hunter v. the U.S. Department of Education on March 26, 2021, against this campus and other named campuses citing the abuses that thousands of LGBTQ+ students endured at these colleges and universities over the years. LGBTQ+ students document their own direct discrimination, harassment and negative harms in the filing.  Those abuses include “conversion therapy, expulsion, denial of housing and health care, sexual and physical abuse and harassment.” The abuses also include the “less visible, but no less damaging, consequences of institutionalized shame, fear, anxiety, and loneliness.” On November 1, 2017, Billy Wilson preaches chapel service titled, "Holy Sex" and says, “If a man has sexual relations with a man as one does with a woman, both of them have done what is detestable, they are put to death." Within three months of graduation, Andrew Hartzler joined a class-action lawsuit against the U.S. Department of Education, seeking to strike down a religious exemption provision in U.S. civil rights law that allows ORU and other schools to receive federal funds despite such discriminatory policies. The lawsuit contends it is a violation of the Establishment Clause of the First Amendment and of the students’ equal protection rights.


title: Oral Roberts University

text: On January 31, 2013, ORU announced that William "Billy" Wilson, executive director of the International Center for Spiritual Renewal and vice-chair of the ORU board of trustees, had been selected to succeed Rutland as president, effective July 1, 2013. A day earlier, the ORU student newspaper had briefly posted an erroneous report on its website, mistakenly identifying someone else as the new president. Rutland criticized the report at a student assembly and the newspaper's longtime faculty adviser left the school the next day.


title: Oral Roberts University

text: In 2018, the university announced that it would retain Wilson as president for 10 years or at least until 2028. Under Wilson's presidency, ORU completed a $50 million developmental campaign, which helped construct its Global Learning Center and ONEOK Sports Complex. Student enrollment rose from approximately 3,000 in 2008 to over 4,100 in 2019.


title: Oral Roberts University

text: In 2020, the university began its $75 million Impact 2030 campaign, a program focusing on making ORU a “maximum global impact” by 2030. A component of achieving this global impact will be ORU's goal of educating students from 195 nations. Fundraising this campaign is due to span over three years and be divided as such: $60 million for buildings, $10 million for international scholarships in order to enroll at least one student from every country around the world, and $5 million for reconverting the university's current library into the Center for Global Leadership. The David Green family has promised to match every campaign gift up to $45 million with a 3-to-1 match.


title: Oral Roberts University

text: The campus began construction in 1963 with a futuristic look and architecture, which historian Margaret Grubiak noted as being inspired by the 1933 Chicago World's Fair. Architects Stanfield, Imel & Walton of Tulsa designed the 1963 master plan, but most of the buildings were designed by Tulsa architect Frank Wallace. In 1981, the City of Faith Medical and Research Center opened. The buildings were south of the ORU campus, and were originally built as a 60-story clinic, a 30-story hospital, and a 20-story research center. The original tenants left in 1989 because of financial problems and a lack of demand for medical services. As of 2007, some floors (in the 20-story building) have never been leased. The facility is now mostly leased out as commercial office space under the name CityPlex Towers. A 60 ft (18.2 m), 30 ton bronze sculpture "Healing Hands", by sculptor Leonard McMurray (cast in Ciudad Juárez, Mexico in 1980) and originally in front of the towers, was moved to the ORU campus entrance in the summer of 1991. By 2007, the campus was described as "a perfect representation of the popular modernistic architecture of the time... the set of "The Jetsons"" but also "shabby" and "dated, like Disney's Tomorrowland." Interviewed in 2010, Wallace characterized his ORU buildings as "sculptures", noting that an inspiration for his artistic sensibility was "whittling since I was a kid". It has also been suggested that the buildings may have been inspired by Tulsa's art deco architectural heritage, along with Bruce Goff's individualistic style and creative use of new materials.


title: Oral Roberts University

text: Maintenance of the many unique but aging buildings, structures, and architectural details on campus was cited as a growing problem for the university. In 2008, $10 million was set aside from Green family donations for long-deferred maintenance on many campus buildings, along with the Prayer Tower. The Green family donated another $10 million for work during the summer of 2009.


title: Oral Roberts University

text: ORU opened its Global Learning Center and the ONEOK Sports Complex, a track stadium with tennis courts in 2017. The campus added its first student housing since 1976, the Niko Njotorahardjo Residence Hall, in 2019. It also started a $75 million fund for scholarships and campus expansion.


title: Oral Roberts University

text: The front entrance onto campus is a divided, landscaped roadway, originally called The Avenue of Flags and now renamed Billy Joe Daugherty circle, lined with lighted flags representing the more than 60 nations from which ORU students have come.


title: Oral Roberts University

text: The main academic building is the John D. Messick Learning Resource Center / Marajen Chinigo Graduate Center, an immense 900,000 square foot (80,000 m) facility with many pylon-like columns, gold-tinted windows and a lozenge-shaped footprint that university publicity says was styled after King Solomon's Temple. The Howard Auditorium is a gold, Buckminster Fuller-style geodesic dome used for movies, theatre productions, classes and seminars. Biweekly university chapel services are held in Christ's Chapel, a 3,500-seat building constructed in drape-like fashion as an echo of Oral Roberts's early tent revivals. The Googie style Prayer Tower at the center of campus was intended to resemble "an abstract cross and Crown of Thorns" and also houses a visitor center. The Mabee Center is an 11,000-seat arena on the southwestern edge of campus and is used for basketball games, concerts, church services and satellite television productions. Timko-Barton Hall houses musical and theatrical performance halls as well as classrooms devoted to the university's programs in the performing arts. The building's performance halls are often the scene of concerts and recitals by performing arts students.


title: Oral Roberts University

text: The Kenneth H. Cooper Aerobics Center houses basketball courts, an elevated running track, a free-weights and exercise room, a swimming pool and classrooms for students who are enrolled in health fitness courses (a requirement for all students). J.L. Johnson Stadium is a 2,200 seat baseball stadium located on the north of the campus.


title: Oral Roberts University

text: The Armand Hammer Alumni-Student Center was designed by KSQ Architects, PC, and constructed and completed in 2013. It is the first building to be built on the ORU campus in decades. It totes the largest TV in Oklahoma, a "living room" for students, a gaming center equipped with Wiis and Xboxes, pool tables, ping pong, and more. The building is a modern design fitting for the campus. Students also enjoy addition restaurants and a coffee shop. The Armand Hammer Student-Alumni Center also houses student government offices as well as board rooms for special meetings. No classes meet in this building; it is strictly for the use and enjoyment of the student body.


title: Oral Roberts University

text: The Hamill Student Center is between Ellis Melvin Roberts and Claudius Priscilla Roberts Halls and houses restaurants on its lower level. Zoppelt Auditorium is on the ground level and is often used as a lecture hall for classes, forums and special events. Campus Security and the "Fireside Room" are also on ground level with the university cafeteria (called "Saga" by students) on the upper level.


title: Oral Roberts University

text: There are eight residence halls on campus. The university has strict guidelines concerning student access to the upper floors of residence halls by members of the opposite sex, which is limited to designated occasions called "Open Dorms."


title: Oral Roberts University

text: The university has weekly chapel services in Christ's Chapel, which are recorded and broadcast live through the university's television station and also via satellite.


title: Oral Roberts University

text: A typical chapel service features contemporary worship, a missions offering, special music, and a sermon, typically from President William Wilson, as well as special guests, including some of the world's biggest and most well-known pastors, evangelists, and spiritual leaders. Attendance at Chapel is mandatory and attendance is taken by student leadership.


title: Oral Roberts University

text: ORU is accredited by the Higher Learning Commission. Some programs have additional specialized accreditation as shown in this list of the academic colleges and accreditors:


title: Oral Roberts University

text: In addition to its undergraduate programs, the university also has a graduate seminary and graduate programs in business, education, and computer science.


title: Oral Roberts University

text: ORU has signed an early assurance program with the Oklahoma State University Center for Health Sciences in 2011, allowing high achieving students to receive conditional admission to OSU's osteopathic medical school program. ORU is also one of the few undergraduate colleges in the southwest to have a human cadaver dissection class. While ORU is considered a Christian university, the College of Science and Engineering does not ignore evolutionary theories to teach creationism.


title: Oral Roberts University

text: From its founding, ORU has placed emphasis on Charismatic doctrines of Christianity; its initial presidential leadership, including Oral Roberts and his son Richard Roberts, also espoused the doctrine of seed faith. This belief was closely connected to fundraising efforts by both Oral and Richard.


title: Oral Roberts University

text: While the majority of ORU staff were happy with including other doctrines of faith, some such as Charles Farah have disagreed publicly, indirectly leading to the publishing of a PhD thesis from a student a number of years later about his opinions on seed faith.


title: Oral Roberts University

text: The university's residential policy requires all unmarried undergraduate students younger than 25 to live on campus, although exceptions are made for those students who live with their parents in the Tulsa area. Men and women are housed in separate dormitory facilities on campus with student access to housing of the opposite sex largely restricted. In addition to having a chaplain on every "wing" of each dormitory, there are also residential advisers for each floor, who enforce curfew, take attendance at Chapel services, and serve as "go-to persons" for students on their floors. Every Monday night is a mandatory Hall Meeting at which announcements are made by dorm leadership.


title: Oral Roberts University

text: All students are required to sign a pledge stating they will live according to the university's honor code. Prohibited activities include lying, cursing, smoking, drinking, and a range of sexual acts, including homosexual behavior and sex outside marriage. In early 2003, the student dress code was relaxed for the first time in 40 years and described as business casual. For most of the school's history, men were required to wear collared shirts and ties and women were required to wear skirts (an exception for winter months was added in 2000). In 2006, campus-wide dress code rules were eased further, allowing students to wear jeans to class and dress more casually in non-academic settings. Since 2009, men are allowed to have neatly trimmed facial hair. Restrictions on men's hair length were relaxed in 2013.


title: Oral Roberts University

text: Oral Roberts University is a member of The Summit League after leaving its former conference home, Southland Conference, in July 2014. Its athletic programs include basketball, cross country, golf, soccer and tennis along with track and field for men and women. There is also a baseball program for men and volleyball for women.


title: Oral Roberts University

text: ORU's early sports team nicknames were the Titans for men and the Lady Titans for women, adopted in 1965 by a vote of the student body. On April 30, 1993, all teams for both men and women became known as the Golden Eagles. ORU's mascot is Eli the golden eagle, who hatched out of his papier-mâché egg on November 17, 1993, before the start of an exhibition basketball game as the official symbol of a new era in ORU athletics. The mascot's name is an acronym for education, life skills and integrity.


title: Oral Roberts University

text: Notable players include: Max Abmas (men's basketball), Jose Trevino and Alex “Chi Chi” Gonzalez (baseball), Kevi Luper (women's basketball), Jeffery Gibson (track and field), Jack Whitt (track and field), and Austin Hannah (golf).


title: Oral Roberts University

text: The women's basketball team has appeared in four NCAA tournaments in the past eight seasons. In 2018, former NBA player Lee Mayberry was appointed as assistant coach for the women's basketball team.


title: Oral Roberts University

text: Paul Mills has been the head coach of the Golden Eagles men's basketball team since 2017. On March 19, 2021, the ORU men's basketball team defeated the #2 seed Ohio State in the 2021 NCAA tournament as a #15 seed in the first round. This was the first time a #15 seed won an NCAA tournament game since Middle Tennessee defeated Michigan State in the first round of the 2016 NCAA tournament. ORU then defeated #7 seed Florida in the Round of 32 to advance to the Sweet Sixteen. It is only the second #15 seed to ever reach the Sweet Sixteen, after Florida Gulf Coast in 2013. Player Max Abmas was named the Summit League Men's Basketball Player of the Year in March 2021.


title: Oral Roberts University

text: The ORU baseball team has played in 21 NCAA regional tournaments. ORU advanced to the College World Series in 1978. In 2006, ORU advanced to the NCAA Super Regional against Clemson. ORU baseball once won 12 consecutive conference championships and played in 12 consecutive NCAA regional tournaments (1998 to 2009).


title: Riemann sum

text: In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann. One very common application is approximating the area of functions or lines on a graph, but also the length of curves and other approximations.


title: Riemann sum

text: The sum is calculated by partitioning the region into shapes (rectangles, trapezoids, parabolas, or cubics) that together form a region that is similar to the region being measured, then calculating the area for each of these shapes, and finally adding all of these small areas together. This approach can be used to find a numerical approximation for a definite integral even if the fundamental theorem of calculus does not make it easy to find a closed-form solution.


title: Riemann sum

text: Because the region by the small shapes is usually not exactly the same shape as the region being measured, the Riemann sum will differ from the area being measured. This error can be reduced by dividing up the region more finely, using smaller and smaller shapes. As the shapes get smaller and smaller, the sum approaches the Riemann integral.


title: Riemann sum

text: Let formula_1 be a function defined on a closed interval formula_2 of the real numbers, formula_3, and formula_4 a partition of formula_2, that is


title: Riemann sum

text: One might produce different Riemann sums depending on which formula_14's are chosen. In the end this will not matter, if the function is Riemann integrable, when the difference or width of the summands formula_15 approaches zero.


title: Riemann sum

text: All these Riemann summation methods are among the most basic ways to accomplish numerical integration. Loosely speaking, a function is Riemann integrable if all Riemann sums converge as the partition "gets finer and finer".


title: Riemann sum

text: While not derived as a Riemann sum, taking the average of the left and right Riemann sums is the trapezoidal rule and gives a trapezoidal sum. It is one of the simplest of a very general way of approximating integrals using weighted averages. This is followed in complexity by Simpson's rule and Newton–Cotes formulas.


title: Riemann sum

text: Any Riemann sum on a given partition (that is, for any choice of formula_14 between formula_25 and formula_26) is contained between the lower and upper Darboux sums. This forms the basis of the Darboux integral, which is ultimately equivalent to the Riemann integral.


title: Riemann sum

text: The five Riemann summation methods are usually best approached with subintervals of equal size. The interval is therefore divided into formula_27 subintervals, each of length


title: Riemann sum

text: For the left rule, the function is approximated by its values at the left endpoints of the subintervals. This gives multiple rectangles with base Δ"x" and height "f"("a" + "i"Δ"x"). Doing this for "i" = 0, 1, …, "n" − 1, and summing the resulting areas gives


title: Riemann sum

text: The left Riemann sum amounts to an overestimation if "f" is monotonically decreasing on this interval, and an underestimation if it is monotonically increasing.


title: Riemann sum

text: For the right rule, the function is approximated by its values at the right endpoints of the subintervals. This gives multiple rectangles with base Δ"x" and height "f"("a" + "i"Δ"x"). Doing this for "i" = 1, …, "n", and summing the resulting areas gives


title: Riemann sum

text: The right Riemann sum amounts to an underestimation if "f" is monotonically decreasing, and an overestimation if it is monotonically increasing.


title: Riemann sum

text: For the midpoint rule, the function is approximated by its values at the midpoints of the subintervals. This gives "f"("a" + Δ"x"/2) for the first subinterval, "f"("a" + 3Δ"x"/2) for the next one, and so on until "f"("b" − Δ"x"/2). Summing the resulting areas gives


title: Riemann sum

text: where formula_40 is the maximum value of the absolute value of formula_41 over the interval. This error is half of that of the trapezoidal sum; as such the middle Riemann sum is the most accurate approach to the Riemann sum.


title: Riemann sum

text: For the trapezoidal rule, the function is approximated by the average of its values at the left and right endpoints of the subintervals. Using the area formula formula_42 for a trapezium with parallel sides "b" and "b", and height "h", and summing the resulting areas gives


title: Riemann sum

text: The approximation obtained with the trapezoidal sum for a function is the same as the average of the left hand and right hand sums of that function.


title: Riemann sum

text: For a one-dimensional Riemann sum over domain formula_2, as the maximum size of a subinterval shrinks to zero (that is the limit of the norm of the subintervals goes to zero), some functions will have all Riemann sums converge to the same value. This limiting value, if it exists, is defined as the definite Riemann integral of the function over the domain,


title: Riemann sum

text: For a finite-sized domain, if the maximum size of a subinterval shrinks to zero, this implies the number of subinterval goes to infinity. For finite partitions, Riemann sums are always approximations to the limiting value and this approximation gets better as the partition gets finer. The following animations help demonstrate how increasing the number of subintervals (while lowering the maximum subinterval size) better approximates the "area" under the curve:


title: Riemann sum

text: Since the red function here is assumed to be a smooth function, all three Riemann sums will converge to the same value as the number of subintervals goes to infinity.


title: Riemann sum

text: Taking an example, the area under the curve over [0, 2] can be procedurally computed using Riemann's method.


title: Riemann sum

text: The interval [0, 2] is firstly divided into "n" subintervals, each of which is given a width of formula_49; these are the widths of the Riemann rectangles (hereafter "boxes"). Because the right Riemann sum is to be used, the sequence of "x" coordinates for the boxes will be formula_50. Therefore, the sequence of the heights of the boxes will be formula_51. It is an important fact that formula_52, and formula_53.


title: Riemann sum

text: If the limit is viewed as "n" → ∞, it can be concluded that the approximation approaches the actual value of the area under the curve as the number of boxes increases. Hence:


title: Riemann sum

text: Because the function is continuous and monotonically increasing over the interval, a right Riemann sum overestimates the integral by the largest amount (while a left Riemann sum would underestimate the integral by the largest amount). This fact, which is intuitively clear from the diagrams, shows how the nature of the function determines how accurate the integral is estimated. While simple, right and left Riemann sums are often less accurate than more advanced techniques of estimating an integral such as the Trapezoidal rule or Simpson's rule.


title: Riemann sum

text: The example function has an easy-to-find anti-derivative so estimating the integral by Riemann sums is mostly an academic exercise; however it must be remembered that not all functions have anti-derivatives so estimating their integrals by summation is practically important.


title: Riemann sum

text: The basic idea behind a Riemann sum is to "break-up" the domain via a partition into pieces, multiply the "size" of each piece by some value the function takes on that piece, and sum all these products. This can be generalized to allow Riemann sums for functions over domains of more than one dimension.


title: Riemann sum

text: While intuitively, the process of partitioning the domain is easy to grasp, the technical details of how the domain may be partitioned get much more complicated than the one dimensional case and involves aspects of the geometrical shape of the domain.


title: Riemann sum

text: In two dimensions, the domain formula_58 may be divided into a number of two-dimensional cells formula_59 such that formula_60. Each cell then can be interpreted as having an "area" denoted by formula_61. The two-dimensional Riemann sum is


title: Riemann sum

text: In three dimensions, the domain formula_64 is partitioned into a number of three-dimensional cells formula_65 such that formula_66. Each cell then can be interpreted as having an "volume" denoted by formula_67. The three-dimensional Riemann sum is


title: Riemann sum

text: where formula_71, that is, it is a point in the "n"-dimensional cell formula_65 with "n"-dimensional volume formula_67.


title: Riemann sum

text: where formula_75 stands for any arbitrary point contained in the set formula_65 and formula_77 is a measure on the underlying set. Roughly speaking, a measure is a function that gives a "size" of a set, in this case the size of the set formula_65; in one dimension this can often be interpreted as a length, in two dimensions as an area, in three dimensions as a volume, and so on.


title: James Wilson (House)

text: James Evan Wilson, M.D., is a fictional character on the Fox medical drama "House". He is played by Robert Sean Leonard. The character first appears in the show's pilot episode when he introduces a medical case to Dr. Gregory House. Wilson is Dr. House's only true friend, and frequently provides him with consultations and aid. Wilson is the head of the Department of Oncology at Princeton-Plainsboro Teaching Hospital.


title: James Wilson (House)

text: During the show's run, the characters of House and Wilson have been compared to Sherlock Holmes and Dr Watson. Wilson's portrayer, Robert Sean Leonard, has stated that his character and Dr. House were originally supposed to play these roles; but Dr. House's diagnostic team has taken over Dr. Wilson's part. Leonard also read the script of the pilot episode of CBS' "Numb3rs" and was planning to audition. He auditioned for Wilson instead because he felt he would more enjoy playing the character that House went to for help and because he liked the "Odd Couple" dynamic of the relationship.


title: James Wilson (House)

text: The character was positively received. Alan Sepinwall of "The Star-Ledger" described Wilson as "the only irreplaceable supporting character" of the show.


title: James Wilson (House)

text: Wilson is one of three brothers. He has an undergraduate degree from McGill University, and graduate degrees from Columbia University and the University of Pennsylvania. He played tennis for his college team. His father was Christian and his mother was Jewish; Wilson was raised in his mother's faith but he celebrates Christmas in addition to Hanukkah and sometimes refers to Christian history, philosophy, and practices, as well as secular self-actualization advice.


title: James Wilson (House)

text: During a medical convention in New Orleans, shortly after graduating medical school, Wilson accidentally broke an antique mirror and started a bar fight when another customer repeatedly played "Leave A Tender Moment Alone" by Billy Joel; Wilson was going through a divorce with his first wife at the time. House met him in jail and, motivated by a desire for companionship and by sheer boredom, bailed him out and hired an attorney to clear his name, thus starting their professional and personal relationship. In the Season 1 episode "Histories", it is revealed that one of his brothers is homeless and that Wilson is unaware if he is still alive as he has not seen him in nine years. Wilson has a history of failed marriages: he is married to his third wife during Season 1 and, with the discovery of his wife's infidelity, separates from her during Season 2. After the failure of his third marriage, Wilson lives in various temporary accommodations (including a stint at House's own apartment) until he meets Amber Volakis, who is a female substitute for House. He is described as "nearly 40" in "Don't Ever Change", in Season 4, and by the end of Season 8, House describes him during a semi-mock DDx as a "46-year-old oncologist". Wilson and House's relationship has been sorely tested on many occasions.


title: James Wilson (House)

text: He is diagnosed with stage II thymoma in the Season 8 episode "Body and Soul" and given six months to live. In the series finale, at House's funeral, Wilson gives an honest description of House as opposed to everyone's kind words and gets a text message telling him to "Shut up, you idiot."


title: James Wilson (House)

text: To his shock, Wilson discovers House alive and well, having faked his death in order to spend Wilson's final months with him (House was facing a return to prison), and House asks Wilson how he wants to spend his last five months. Sometime later, Wilson and House are seen in the countryside on motorcycles, Wilson having presumably quit his job to spend his last five months as he wants. He asks House about what they will do when the cancer gets bad, but House simply tells him that "cancer is boring" and they ride off together.


title: James Wilson (House)

text: House describes Wilson as "a buddy of mine people say 'Thank you' to, when he tells them they are dying." House also describes Wilson as an "emotional vampire". On a date with Dr. Lisa Cuddy (Lisa Edelstein), Wilson evades a question as to whether or not he wants children.


title: James Wilson (House)

text: However, Wilson defends House when House's career is in jeopardy, after billionaire entrepreneur and then chairman of Princeton-Plainsboro's Board Edward Vogler (Chi McBride) proposes a motion for House's dismissal. Wilson is the only one to vote against the motion. In response, Vogler proposes and succeeds in obtaining Wilson's dismissal, but Wilson is soon reinstated thanks to Cuddy after she convinces the board that Vogler is the real threat to the hospital and his money is not worth his business-obsessed mindset. In a third-season episode, it is revealed that Wilson suffers from clinical depression and takes medication. Wilson is also seen to write with his left hand, a trait he shares with Cuddy and Foreman, but when he performs detailed medical work, such as injections or incisions, or gesticulates while speaking, appears to be right-handed in general, suggesting he may be ambidextrous.