File Henry I of Germany and Charles III of France.PNG thumb A 921 meeting between Charles and Henry I of Germany resulted in a treaty. In 923 Henry supported Robert against Charles and promptly attempted to annex Lotharingia. Charles III 17 September 879 7 October 929 , called the Simple or the Straightforward ... by Charles the Simple in 915 red On 7 October 919 Charles re married to Eadgifu of England Eadgifu , the daughter of Edward the Elder , King of England . By this time Charles excessive favouritism towards ... III vi Charles III c a Ph p vls Karel III van West Franci yo Charles the Simple ... . As a child, Charles was prevented from succeeding to the throne at the time of the death in 884 ... cousin, Charles the Fat , to rule them. He was also prevented from succeeding the unpopular Charles ... Guy III of Spoleto . Charles was put under the protection of Ranulf II of Aquitaine Ranulf ... title himself until making peace with Odo. Finally, in 893 Charles was crowned by a faction opposed ... , ed. Timothy Reuter Cambridge Cambridge University Press, 2005 , 313 15. ref In 911 Charles defeated ... vassal and converted him to Christianity. Charles then gave him land around Rouen , the heart of what ... Charles their new king, breaking from Germans who had elected Conrad I of Germany Conrad of Franconia king. ref name Parisse Charles tried to win their support by marrying a Lotharingian woman ... the Fowler in 919. ref name Parisse Opposition to Charles in Lotharingia was not universal, however ... s brother, was elected by the rebels and crowned in opposition to Charles, who had to flee to Lotharingia. On 2 July 922, Charles lost his most faithful supporter, Herve, Archbishop of Rheims, who ... June near Soissons by Robert, who died in the battle. ref name Parisse Charles was captured and imprisoned ... to succeed him. In 925 the Lotharingians accepted Rudolph as their king. Charles died in prison ... . In the initial aftermath of Charles s defeat, Eadgifu and Louis fled to England. References Reflist ... more details
For the version of Wikipedia that uses simple English Wikipedia Simple English Wikipedia wiktionary simpleSimple may refer to Technology SIMPLE , an instant messaging protocol SiMPLE , a programming development system SIMPLE algorithm , a widely used numerical procedure SIMPLE dark matter Superheated Instrument for Massive ParticLe Experiments , an experimental search for evidence of dark matter Simple, a steam engine that expands steam only once, as opposed to Compound engine a compound engine that expands it more than once Other uses Simple abstract algebra , an algebraic structure which sometimes cannot be divided Simple company , an online banking company Simple Shoes, a shoe brand which is part of Deckers Outdoor Corporation Simple philosophy , a thing that has no proper parts Simple, a medicinal Herbalism herb or a medicine made from one Simple album Simple album , an album by Andy Yorke Simple a 2005 song by Katy Perry, released on the soundtrack to The Sisterhood of the Traveling Pants film The Sisterhood of the Traveling Pants Simpl , a commune in France Fort Simple , an American Civil War fort in Topeka Kansas Simple Kapadia 1958 2009 , Indian Bollywood actress and costume designer Simple Kaur , Indian weightlifter SIMPLE Group , a conglomeration of separately run companies specializing in tax planning See also List of people known as the Simple Special Prefixindex Simple Pages beginning with Simple Special Prefixindex Simply Pages beginning with Simply Peter Simple disambiguation Simplicity disambiguation Simples disambiguation disambiguation de SIMPLE eo Simpla fr Simple ko pt Simple ru Simple ... more details
SiMPLE a recursive acronym for SiMPLE Modular Programming Language & Environment is a programming development ... for beginners. The programming language that they created was called SiMPLE. SiMPLE is vaguely .... However, SiMPLE is not and was never intended to be merely a clone of Applesoft BASIC. It was merely ... was an interpreted language, and so it ran somewhat slowly even for a 1MHZ processor . SiMPLE ... faster, but those programs can even run on computers that don t have SiMPLE installed. Another difference between the two languages is in the use of line numbers. Applesoft required them SiMPLE doesn t even use them. Instead of typing program statements onto the black Apple screen, SiMPLE uses a text ... in SiMPLE. But they function in much the same way . However, aside from a few differences in their outward appearances, writing programs in SiMPLE has a similar feel to what one experienced when writing programs in Applesoft. For example, when using SiMPLE in command line mode, a program is run by simply typing the word RUN on a black screen just as was done on the Apple The Three Faces of SiMPLESimple is a generic term for three slightly different versions of the language Micro SiMPLE, Pro SiMPLE, and Ultra SiMPLE. a Micro SiMPLE is an introductory programming language designed to use only 4 keywords Call, Set, If, and Goto. An example of a Micro SiMPLE program listing and a snapshot of the output display it generates is shown in the figure below b Pro SiMPLE is the DOS based version of SiMPLE ... with a resolution of only 640 x 480 pixels. Its sound capabilities are limited to simple beeps through the computer s built in speaker. c Ultra SiMPLE is the Windows based version of SiMPLE. It utilizes exactly the same 23 keywords as Pro SiMPLE. Its graphics capabilities allow millions of colors ... type of media file including movies . Prior to 2011 June, SiMPLE was available only for 32 bit computers ... is now the standard version. In this newer version of SiMPLE, the terms Pro SiMPLE and Ultra SiMPLE ... more details
about the instant messaging protocol the computational fluid dynamics algorithm SIMPLE algorithm the retirement plan SIMPLE IRA IPstack SIMPLE , the S ession Initiation Protocol for I nstant M essaging and P resence L everaging E xtensions , is an instant messaging IM and presence protocol suite based on Session Initiation Protocol SIP managed by the IETF. ref http www.ietf.org html.charters simple charter.html SIMPLE Working Group ref Like Extensible Messaging and Presence Protocol XMPP , and in contrast to the vast majority of IM and presence protocols used by software deployed today, SIMPLE is an open standard. Purpose SIMPLE applies SIP to the problems of registering for presence information and receiving notifications when such events occur, for example when a user logs in or comes back from lunch sending short messages, analogous to SMS or two way paging managing a session of real time messages between two or more participants. Implementations of the SIMPLE based protocols can be found in Comparison of VoIP software SIP Softphones and also in SIP Hardphones. Technical description Presence The SIMPLE presence specifications can be broken up into The core protocol machinery . This provides the actual SIP extensions for subscriptions, notifications and publications. RFC 3265 defines the SUBSCRIBE and NOTIFY methods. SUBSCRIBE allows to subscribe to an event on a server, the server responds with NOTIFY whenever the event come up. RFC 3856 defines how to make use of SUBSCRIBE NOTIFY for presence. Two models are defined an end to end model in which each User Agent handles presence subscriptions itself and a centralized model. The latter introduces the concept of a presence server all subscriptions are handled by this server. The message PUBLISH RFC 3903 allows User Agents ... IM clients de SIP for Instant Messaging and Presence Leveraging Extensions es SIMPLE fr SIP for Instant Messaging and Presence Leveraging Extensions nl SIMPLE ru SIMPLE zh SIMPLE ... more details
Infobox Single See Wikipedia WikiProject Songs Name As Simple as That Cover Artist Mike Reid American football Mike Reid Album Turning for Home B side Released 1991 Format Recorded Genre Country music Country Length 3 28 Label Columbia Records Columbia Writer Mike Reid br Allen Shamblin Producer Steve Buckingham record producer Steve Buckingham Last single Till You Were Gone br 1991 This single As Simple as That br 1991 Next single I ll Stop Loving You br 1991 Misc As Simple as That is the title of a song co written and recorded by American country music artist Mike Reid American football Mike Reid . Released in 1991, it was the third single from his album Turning for Home . The song reached number 14 on the Billboard magazine Billboard Hot Country Songs Hot Country Singles & Tracks chart in October 1991. ref cite web title Mike Reid Hot Country Songs Chart History url http www.billboard.com artist mike reid chart history 97741 work Billboard magazine Billboard accessdate February 3, 2012 ref Chart performance class wikitable sortable align left Chart 1991 align center Peak br position align left U.S. Billboard Hot Country Singles & Tracks align center 14 align left Canadian RPM Country Tracks align center 11 References reflist Category 1991 singles Category Mike Reid songs Category Songs written by Mike Reid Category Songs written by Allen Shamblin Category Columbia Records singles Category Songs produced by Steve Buckingham record producer ... more details
Wiktionary simple English Simple English usually refers to a simplified form of the English language , such as Basic English , a constructed language, created by Charles Kay Ogden, which only contains a small number of words Simplified English , a controlled language originally developed for aerospace industry maintenance manuals Special English , a simplified form of English used by broadcasting service Voice of America See also Simple English Wikipedia Plain English disambig be x old pam Simple English ms Bahasa Inggeris Mudah simpleSimple English uk zh ... more details
Two other uses the band the band s self titled album Simple Plan album A Simple Plan disambiguation Infobox musical artist name Simple Plan image Spstjean.jpg caption Simple Plan in 2009. From left to right ... Comeau br Jeff Stinco Former members website URL simpleplan.com Simple Plan is a French Canadian pop ... Any... 2004 , Simple Plan album Simple Plan 2008 and Get Your Heart On 2011 as well as two widely marketed ..., 20 June 2009. Simple Plan began in 1993 with the formation of a band named Reset band Reset by friends Pierre Bouvier , Chuck Comeau Charles Andr Chuck Comeau , Philippe Jolicoeur , and Adrian ... band Face to Face , but only managed to gain modest popularity. ref name Simple Plan Biography cite web url http www.starpulse.com Music Simple Plan Biography title Simple Plan Biography publisher ..., and combined to create Simple Plan. ref name Reset Biography In late 1999, Comeau and Bouvier reacquainted at a Sugar Ray concert ref name Simple Plan Biography and Bouvier left Reset soon after ... to join Simple Plan. ref name Reset Biography ref name Simple Plan Biography This allowed Bouvier ... that the band was their simple plan to avoid obtaining a job at McDonald s , or similar fast food restaurant chains. However, most likely, the name is derived from the 1998 A Simple Plan film film and novel A Simple Plan novel A Simple Plan . ref name Rock Louder Interview with Simple Plan cite web url http www.rocklouder.co.uk news article Interview Simple Plan.html title Rock Louder Interview with Simple Plan publisher Rocklouder.co.uk date accessdate 2011 02 21 ref No Pads, No Helmets...Just Balls 2002 2004 In 2002, Simple Plan released their first studio album, No Pads, No Helmets...Just Balls which led to the subsequent singles I m Just a Kid , I d Do Anything Simple Plan song I d Do Anything , Addicted Simple Plan song Addicted , and Perfect Simple Plan song Perfect . Simple Plan is noted as saying that they were aiming at a pure pop punk record. ref name Archived Simple Plan Bio ... more details
A Simple Story may refer to A Simple Story novel A Simple Story novel by Elizabeth Inchbald A Simple Story , a novella by Shmuel Yosef Agnon , translated from the 1935 Hebrew original, Sippur Pashut A Simple Story 1958 film A Simple Story 1958 film , a 1958 film A Simple Story 1970 film A Simple Story 1970 film , a 1970 Tunisian film A Simple Story 1978 film A Simple Story 1978 film , a 1978 film disambig Long comment to avoid being listed on short pages ... more details
Peter Simple may mean Peter Simple, pseudonym of and newspaper column by the British journalist Michael Wharton Peter Simple novel Peter Simple novel , 1834 seafaring novel by Marryat Peter Simple racehorse disambig ... more details
Simple Simon may refer to Simple Simon nursery rhyme , a nursery rhyme Simple Simon musical Simple Simon musical , a Broadway musical Simple Simon solitaire , a solitaire patience card game Simple Simon film Simple Simon film , a 2010 Swedish film Simple Simon , an animated short film in 1935. Simple Simon , a book written by Ryne Douglas Pearson on which the 1998 action thriller Mercury Rising is based disambig ... more details
Simple Man may refer to Simple Man Klaus Nomi album Simple Man Klaus Nomi album , 1982 Simple Man Charlie Daniels album Simple Man Charlie Daniels album , 1989 Simple Man Charlie Daniels song Simple Man Charlie Daniels song Simple Man Lynyrd Skynyrd song Simple Man Lynyrd Skynyrd song , a 1973 song on Pronounced L h n rd Skin n rd Simple Man a song on Bad Company s 1976 album Run with the Pack Simple Man a song by Hardcore Superstar from their Hardcore Superstar album self titled album Simple Man CSI Miami Simple Man CSI Miami , a 2003 episode of CSI Miami See also I Am a Simple Man , a song by Ricky Van Shelton disambiguation ... more details
expert subject multiple Linguistics France date August 2010 refimprove date August 2010 The pass simple IPA fr pase s pl , simple past or preterite , also called the pass d fini IPA fr pase defini IPA , definite past , is the literary equivalent of the pass compos in the French language , used only in formal writing including history and literature , journalism, and formal speech. As with other preterites, it is used when the action has a definite beginning and end and has already been completed. In writing it is most often used for narration. While literary and refined language still hangs on to the pass simple , the spoken language has simply renounced pass simple for the passe compos , which means that in French, there is no longer a nuance between Je suis arriv . I have arrived ... that I am not still here. The difference regarding written language is subtle. The pass simple ... to the present and may even still be happening. Constructing the pass simple Many students of French ... the pass simple , even though it is only taught to learners of French in advanced classes. The pass simple is formed by dropping the last two letters off the infinitive form of the verb and adding ... simple tense in the following way class wikitable aimer to like j aim ai nous aim mes tu ... recognized because the pass simple often resembles the past participle. For example, il courut ... and Modern Usage In modern spoken French, the pass simple has practically disappeared. Localised ... ate it. br From Histoire du chien de Brisquet by Charles Nodier Even though it has been abandoned by the spoken language, the pass simple is still very common in the written language as a narrative tense, even in children s books and popular literature. In modern spoken French, the pass simple ... DEFAULTSORT Passe Simple Category Grammatical tenses Category French grammar de Pass simple fr Pass simple nl Pass simple ... more details
Unreferenced stub auto yes date December 2009 The Simple Past Le pass simple is a novel written by Driss Chra bi . DEFAULTSORT Simple Past, The Category 1954 novels Category French novels 1950s novel stub cy Le pass simple ... more details
Simple Life may refer to Simple living , different voluntary practices to simplify one s lifestyle Simple Life Records , American record label Simple Life album Simple Life album , 2002 album by Mason Jennings Simple Life Carolyn Dawn Johnson song Simple Life Carolyn Dawn Johnson song , 2003 song by Carolyn Dawn Johnson Simple Life Elton John song Simple Life Elton John song , 1992 song by Elton John A Simple Life , 2011 Hong Kong film The Simple Life , American reality television series The Simple Life Josh Woodward album The Simple Life Josh Woodward album , 2008 album by Josh Woodward The Simple Life Magnet album The Simple Life Magnet album , 2007 album by Magnet See also Mabel and Fatty s Simple Life , 1915 American film Disambiguation ... more details
in mathematics the term simple root can refer to one of two unrelated notions A simple root polynomial simple root of a polynomial is a root of a polynomial root of multiplicity mathematics multiplicity one A simple root root system simple root in a root system is a member of a subset determined by a choice of positive roots disambig ... more details
Simple Things can refer to Simple Things Zero 7 album Simple Things Zero 7 album , from Zero 7 2001 Simple Things Amy Grant album Simple Things Amy Grant album , from Amy Grant 2003 Simple Things , a song by the British trio Dirty Vegas Simple Things , a song written and produced by Armin van Buuren and Justine Suissa Simple Things Jim Brickman song Simple Things , a song by Jim Brickman with Rebecca Lynn Howard The Simple Things , an animated Mickey Mouse short disambig it Simple Things ... more details
About a movie Vanessa Amorosi song The Simple Things Something Emotional Unreferenced date December 2009 Infobox Hollywood cartoon cartoon name The Simple Things series Mickey Mouse image image size alt caption director Charles August Nichols Charles Nichols producer Walt Disney uncredited voice actor Jimmy MacDonald sound effects artist Jimmy Macdonald as Mickey Mouse Mickey and Pinto Colvig as Pluto Disney Pluto Unknown as Pelican uncredited musician Paul Smith composer Paul Smith animator Marvin Woodward , Fred Moore animator Fred Moore and Norm Ferguson animator Norman Ferguson layout artist Lance Nolley background artist Ed Starr studio Walt Disney Productions distributor Walt Disney Motion Pictures Group Buena Vista Distribution release date April 18, 1953 color process Technicolor runtime 7 minutes and 2 seconds country Film US language English The Simple Things is a 1953 animation animated short subject , part of the Mickey Mouse series, produced by Walt Disney Productions . Released by RKO Pictures RKO Radio Pictures on April 18, 1953, the short is notable as the final regular entry in the Mickey Mouse theatrical cartoon series. Following this short, three special one shot Mickey shorts were produced Mickey s Christmas Carol 1983 , The Prince and the Pauper 1990 film The Prince and the Pauper 1990 , and Runaway Brain 1995 . Plot At the start of the cartoon, Mickey mouse Mickey is seen whistling to the tune of The Simple Things , Pluto Disney Pluto sniffing behind him, spots a mussel as he tries to cover up miniature geysers along the way. The mussel then squirts water at him. Pluto barks at the mussel and the mussel barks back. The mussel gets trapped on Pluto s tail after they fight. He pulls the mussel up and attempts to shove it off his tail but instead he pulls ... in his mouth singing the song The Simple Things . External links imdb title 0046318 References reflist DEFAULTSORT Simple Things, The Category 1953 films Category Mickey Mouse short films Category ... more details
A Simple Plan may refer to A Simple Plan novel A Simple Plan novel , a 1993 novel by American novelist Scott Smith A Simple Plan film A Simple Plan film a 1998 film based on the novel of the same name SIMPLE IRA plan, a type of retirement plan in the United States Simple Plan , a pop punk band formed in 1999 in Montreal, Canada Simple Plan album , a self titled album released by the band of the same name disambig ja ... more details
Infobox album See Wikipedia WikiProject Albums Name Simple Math Type studio Artist Manchester Orchestra ... Everything to Nothing br 2009 This album Simple Math br 2011 Next album Misc Singles Name Simple Math Type studio single 1 Simple Math single 1 date February 28, 2011 ref name AltPress Single cite web url http www.altpress.com news entry download manchester orchestras new single simple math title Download Manchester Orchestra s new single Simple Math publisher Alternative Press author Karan, Tim date 28 February 2011 accessdate 4 May 2011 ref Simple Math is the third studio album from Atlanta based ... web url http favoritegentlemen.com 2011 01 26 manchester orchestra simple math release date title Manchester Orchestra Simple Math Release Date publisher Favorite Gentleman author date accessdate 26 January 2011 ref ref name Amazon cite web url http www.amazon.co.uk dp B004T8IPNS title Simple Math ... 4 May 2011 ref Andy Hull , the band s lyricist and vocalist, has said that Simple Math is a concept ... Announces New Album, Simple Math publisher Paste magazine Paste author Spicer, Nathan date 26 January ... http www.altpress.com news entry manchester orchestra stream upcoming album simple math title Manchester Orchestra to stream upcoming album, Simple Math publisher Alternative Press author Karan, Tim date 2 May 2011 accessdate 4 May 2011 ref Led by the title track and lead single single Simple Math , the album ... name BB cite web url http www.billboard.com album manchester orchestra simple math 1488697 album manchester orchestra simple math 1488697 title Simple Math Manchester Orchestra publisher Billboard ... all music Manchester Orchestra ref name Credits cite album notes title Simple Math bandname Manchester ... length4 4 21 title5 Pale Black Eye length5 4 17 title6 Virgin length6 4 28 title7 Simple Math length7 ... 7 14 Reception Commercial performance Simple Math was a moderate commercial success for the band ... http www.billboard.com album manchester orchestra simple math 1488697 album manchester orchestra mean ... more details
About the concept in physics the Internet forum software Simple Machines Forum File Table of Mechanicks, Cyclopaedia, Volume 2.png thumb 250px Table of simple mechanisms, from Chambers Cyclopedia , 1728 ... 528, Plate 11 . ref Simple machines provide a vocabulary for understanding more complex machines. A simple ...&pg PA88&dq Asimov simple machine&cd 1 v onepage&q&f false page 88 postscript . ref Usually the term refers to the six classical simple machines which were defined by Renaissance scientists ref cite ... mechanical device Wedge Screw simple machine Screw These simple machines fall into two classes i the inclined ... equilibrium of torque s and movement around a pivot. A simple machine is an elementary device ... with other devices and movements to form a machine mechanical machine . Thus simple machines are considered ... view of machine mechanical machine s as decomposable into simple machines first arose in the Renaissance ... U.S. Navy Bureau of Naval Personnel year 1971 url http www.webpal.org SAFE aaarecovery 5 simple technology ... . ref Between the simple machines and complex assemblies, several intermediate classes can be defined ... Springer url http books.google.com books?id G9sZf7D24a8C&pg PA136&vq simple machines&source gbs ... of a compound machine is simply the product of the mechanical advantages of the simple machines of which it is composed. Various authors have compiled lists of simple machines and machine elements, sometimes lumping them together under a single term such as simple machines , ref name Mechanicks ... or machine elements the use of the term simple machines in this broader word sense sense is a departure from the neoclassical sense of the six essential simple machines, which is why many authors prefer ... and synthetic connection from simple to compound to complex is at work. A page from a 1728 ... elements calling them simple machines . Models of these devices can be found at Cornell University ... rx collection.php publisher Cornell University postscript . ref History The idea of a simple ... more details
Simple Song may refer to any of the following Simple Song , a song by American alternative country artist Lyle Lovett off his 1987 album Pontiac album Pontiac Simple Song , a song by American punk rock band Avail off their third album 4am Friday Simple Song, a song by American musician actress Miley Cyrus off her 2008 album Breakout Miley Cyrus album Breakout Simple Song The Shins song Simple Song , a single by American indie rock band The Shins off their 2012 album Port of Morrow album Port of Morrow disambig ... more details
advert date January 2011 no footnotes date December 2011 Infobox Brand name Simple Skincare logo File Simple Skincare Logo.gif type sensitive skin type Sensitive Skin currentowner Unilever origin United ... simple.co.uk Simple Skincare is a United Kingdom British brand of soap and skincare products ... and Finance Director Peter Hatherly, for 140m resulted in the formation of Accantia , owner of the Simple brand. Accantia rapidly grew the Simple brand, expanding into all the major toiletries & skincare ... for 2008 was 72m, up 9 over 2007 at 66m. In April 2009 Accantia, changed its name to Simple Health & Beauty Group Limited. In December 2009, Simple Health & Beauty Group Limited was bought by the US ... by Unilever September 27, 2010 for US3.7 billion, and Simple was formally taken over around six months later after the soap brands were licenced to another company due to competition concerns. Simple .... Simple now has products for almost every health and beauty need facial skincare, from teens to anti ... and the range of Simple Derma products for very dry problem skin prone to eczema and dermatitis. Product History 1960 Simple soap is introduced. This first ever perfume and colour free soap was recommended by doctors for sensitive skin. 1978 Simple introduces the UK s first cleanse, tone and moisturise skincare regime. 1982 First Simple TV ad is aired, and features the tagline It s the Simple things .... 1999 Launch of Simple Cleansing Facial Wipes now the UK s No1 Facial skincare product. 2001 Simple introduces the Skin Defence for Men, Simple Oil Control and Simple Regeneration lines. 2005 Simple Sun for babies and kids is launched. 2009 Repair Anti Wrinkle range is launched while the Simple ... The Simple Advisory Board of experts is created to provide holistic advice on skin health to consumers ... Hunter. Simple also creates the http www.simple.co.uk teen juniorboard.aspx Simple Junior Board of Skincare ... Darnley, Lauren Barden, Megan Maunder, Rebecca McGrattan and Suzannah Leigh. 2010 Simple s 50th ... more details
of varying types. In geometry a simple polygon IPAc en icon p l n is defined as a flat shape ... path. If the sides intersect then the polygon is not simple. The qualifier simple is frequently ... will be considered parts of a single edge. Simple polygons are also called Jordan polygons , because ..., the region inside it and the region outside it. A simple polygon in the plane is topologically ... simple polygon File Weakly simple polygon.svg 150px left If a closed polygonal chain embedded in the plane ... is called a weakly simple polygon . ref http books.google.com books?id byesH9oM2mIC&pg PA177&dq 22weakly simple polygon 22 v onepage&q 22weakly 20simple 20polygon 22&f false ref Informally, a weakly simple polygon is a polygon in which some sides can touch but cannot cross over . In the image on the left, ABCDEFGHJKLM is a weakly simple polygon with the color blue marking its interior. In a more general definition of weakly simple polygons, they are the limits of sequences of simple polygons ... be empty. For example, referring to the image above, the polygonal chain ABCBA is a weakly simple polygon it may be viewed as the limit of squeezing of the polygon ABCFGHA. Non simple weakly simple ... with the exterior and is traversed twice in the resulting weakly simple polygonal representation. Computational ... in the form of a simple polygon in each of these problems, the distinction between the interior and exterior .... ref Point in polygon testing involves determining, for a simple polygon P and a query point q , whether q lies interior to P . Simple formulae are known for computing polygon area that is, the area of the interior of the polygon. Polygon triangulation dividing a simple polygon into triangles. Although convex polygons are easy to triangulate, triangulating a general simple polygon is more difficult ... Chazelle showed in 1991 that any simple polygon with n vertices can be triangulated in Big O notation ... polygonal chain forms a simple polygon. Polygon union finding the simple polygon or polygons containing ... more details
In mathematics , specifically in ring theory , an algebra ring theory algebra is simple if it contains no non trivial two sided ideal ring theory ideal s and the set ab a , b are elements of the algebra &ne 0 . The second condition in the definition precludes the following situation consider the algebra math begin bmatrix 0 & alpha 0 & 0 end bmatrix , , alpha in mathbb C math with the usual matrix operations. This is a one dimensional algebra in which the product of any two elements is zero. This condition ensures that the algebra has a minimal nonzero left ideal, which simplifies certain arguments. An immediate example of simple algebras are division algebras, where every element has a multiplicative inverse, for instance, the real algebra of quaternions . Also, one can show that the algebra of n × n matrices with entries in a division ring is simple. In fact, this characterizes all finite dimensional simple algebras up to isomorphism, i.e. any finite dimensional simple algebra is isomorphic to a matrix algebra over some division ring . This result was given in 1907 by Joseph Wedderburn ... Mathematical Society . Wedderburn s thesis classified simple and semisimple algebra s. Simple algebras are building blocks of semi simple algebras any finite dimensional semi simple algebra is a Cartesian product, in the sense of algebras, of simple algebras. Wedderburn s result was later generalized to semisimple ring s in the Artin Wedderburn theorem . Examples A central simple algebra sometimes called Brauer algebra is a simple finite dimensional algebra over a field mathematics field F whose center of an algebra center is F . Simple universal algebras In universal algebra , an abstract algebra A is called simple if and only if it has no nontrivial congruence relation s, or equivalently ... ring theory a ring is simple in the sense that it has no nontrivial ideals if and only if it is simple in the sense of universal algebra. See also simple group simple ring central simple algebra References ... more details
In geometry , a simple path is a simple curve , namely, a continuous function continuous injective function from an interval mathematics interval in the set of real number s math R math to math R n math or more generally to a metric space or a topological space . In graph theory a simple path is a path in a graph which does not have repeating vertices. See path graph theory . disambig ... more details
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