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2012–13 Los Angeles Lakers season	lakers acquired allstars steve nash dwight howard giving starting lineup five allstars consisting kobe bryant pau gasol metta world peace nash howard expected contend franchises th nba championship.instead lakers struggled qualify playoffs changing head coaches implementing multiple offenses.however weak defense multiple injuries teams biggest problems.exited playoffs first round first time since .additionally first season since without longtime point guard derek fisher helped team win last five championships.the season began head coach mike brown changing lakers offensive strategy princeton offense.
2012–13 Los Angeles Lakers season	– preseason record – start regular season brown fired.assistant bernie bickerstaff named interim coach mike dantoni took fulltime head coach.still lakers began season – worst start since – season.jeopardy missing playoffs trailing houston rockets allstar break ⁄ games eighth final playoff berth western conference.lakers started – break gaining sole possession top spot first time since december moving two games .
2012–13 Los Angeles Lakers season	first time season.swept crosstown rivals los angeles clippers lakers fell half game behind utah jazz final playoff spot.lakers overtook utah standings kobe bryants season ended suffering torn achilles tendon th game season.lakers qualified playoffs last day season defeating houston finish – seeded seventh west.facing san antonio spurs first round injuryriddled lakers swept four games eventual western conference champion.this last season lakers made playoffs – season franchise th championship.
2012–13 Los Angeles Lakers season	key dates june nba draft took place prudential center newark new jersey.july lakers acquired twotime mvp steve nash first roundpicks secondround picks .august lakers acquired threetime dpoy dwight howard fc earl clark pg chris duhon fourteam multiplayer trade also involving c andrew bynum f josh mcroberts gf christian eyenga.october dwight howard made laker debut preseason loss sacramento kings.october lakers opened – nba season losing dallas mavericks .december lakers retired number jersey jamaal wilkes halftime game portland trail blazers.lakers game score .april lakers retired number jersey shaquille oneal halftime game dallas mavericks.lakers game score .draft picks roster offseason eliminated playoffs second round prior two seasons lakers traded threetime defensive player year dwight howard twotime valuable player mvp steve nash.fourth time league history team acquired two players least six allstar selections.
2012–13 Los Angeles Lakers season	players widely considered future hall famers.joined already strong lakers nucleus kobe bryant pau gasol metta world peace.center howard made team younger athletic acquisition appeared start new dynasty lakers.nash lakers first elite point guard decades.trio bryant howard nash expected rival defending league champion miami heats combination lebron james dwyane wade chris bosh.
2012–13 Los Angeles Lakers season	additionally lakers resigned key role player jordan hill signed free agent veteran antawn jamison shooting specialist jodie meeks.coach mike brown began installing princeton offense decision made even july acquisition nash.thought using offense previous season lockout impacted schedule making hectic implement.new assistant coach eddie jordan hired install lakers third offense three years triangle offense coach phil jacksons tenure browns offense previous season.despite addition howard nash bryant insisted remained leader lakers.nash agreed bryants team added team needed provide support.bryant looked forward nash running teams offense.
2012–13 Los Angeles Lakers season	bryant envisioned retired howard would assume role team leader.howard anticipated bryant tough him.ill take heat hes going give know end day thats going make better player better person going make team better howard said.nash said everyone could see relationship bryant howard going tough start.season summary struggles princeton offense howard back surgery earlier april lakers acquired possibility might december january.
2012–13 Los Angeles Lakers season	play basketball training camp october.lakers went winless – preseason howard playing two games still recovering.brown estimated could take january lakers fully master new offense.lakers starting lineup start regular season leagues tallest oldest nash years old bryant gasol world peace howard .five allstars combined allstar appearances team leagues highest payroll million.
2012–13 Los Angeles Lakers season	new york times called one talented lineups nba history.espn wrote lakers expected win title recordbreaking fashion.bryant cautioned athletic team world could limited rebounding transition game.howard ready start season still recovering back surgery.laker debut howard points rebounds free throws fouled lakers lost –.bryant said patience needed team adjusted princeton offense.
2012–13 Los Angeles Lakers season	endorsed new scheme comparing triangle offenses ballsharing principles well difficult learning curve.lakers fell los angeles clippers – home game started season – first time since years ago fourth time franchise history.bryant scored points loss two steals passed magic johnson lakers career leader steals.nash play suffering nondisplaced fracture left leg previous game expected miss least week.lakers beat detroit pistons – first win avoided first – start since .
2012–13 Los Angeles Lakers season	however – start brown fired head coach.team still adjusting new offense committing high number turnovers defense specialty browns also vulnerable.addition nashs howards ailments bryant playing injured foot unable practice.lakers however urgency win compelled wait given aging stars howards pending free agency coming summer owner jerry buss deteriorating health.browns dismissal five games thirdfastest coaching change nba history.
2012–13 Los Angeles Lakers season	dantoni takes media former lakers coach phil jackson became leading candidate replace brown.meantime assistant coach bernie bickerstaff interim head coach.first two games coached crowd staples center chanted want phil games.lakers talked jackson first requested two days consider opening.believed lakers would wait response lakers thought understood would continue search.
2012–13 Los Angeles Lakers season	next day team talked mike dantoni signed multiyear contract unanimous decision front office.felt dantonis fastpaced style play made great fit team suitable jacksons structured triangle offense.buss preference always lakers wideopen offense.dantoni reunited nash league mvp twice four seasons dantoni phoenix suns.bryant also familiar dantoni bryant child knew dantoni star italy bryants father also playing there.
2012–13 Los Angeles Lakers season	bryant grew close dantoni time united states national team.dantonis coaching debut lakers delayed recovered knee replacement surgery.surgery weeks october originally expected taking year coaching would months recover.bickerstaff continued lakers interim coach finished – record winning last two dantoni started leading team practices.older brother dan dantoni named new assistant coach also assisted.first press conference dantoni predicted lakers – ranked th scoring .
2012–13 Los Angeles Lakers season	points per game instead scoring – points game.wanted revive showtime.reiterated general manager mitch kupchaks belief lakers built win nba championship season.dantoni glad back nash noting unsuccessful stint new york knicks without him.november coached first game—nine days hired—in – win brooklyn nets.
2012–13 Los Angeles Lakers season	lakers matched worst start road – since – season snapped streak – win dallas mavericks also first point effort first four games dantoni.with nash still dantoni started – laker minimal improvement browns – start.team struggling get big men gasol howard involved new offense.bryant also adjusting running screenrolls fewer post ups time career.additionally backup point guard steve blake since abdominal injury november would return late january.november lakers made threepoint field goals—tying team record regulation game—in – win denver nuggets.
2012–13 Los Angeles Lakers season	free agent acquisition antawn jamison scored points first time laker scored points reserve since shaquille oneal .jamison also made five threepointers jodie meeks scored careerhigh seven threepointers.howard even added second threepointer career addition points rebounds.lost – orlando magic following home game howards first matchup former team.points rebounds intentionally fouled shot –for free throws.after bothered tendinitis knees since training camp gasol missed next game.
2012–13 Los Angeles Lakers season	struggling seven games dantoni averaging .points .rebounds shooting .percent benched fourth quarter multiple games.lakers lost – knicks dantonis first game back new york since left previous season.
2012–13 Los Angeles Lakers season	lakers allowed another big quarter trailed – first quarter.bryant scored los angeles fell – scored points – without gasol – overall dantoni.gasol returned eightgame absence contributing points nine rebounds five assists – win lowly charlotte bobcats.lakers overcame point deficit third win row second time season streak achieved.nash started golden state warriors missing games points nine assists – overtime road victory.
2012–13 Los Angeles Lakers season	team – absence three first four games return.early struggles lakers lost new years day – record matched worst start games since – season.according bryant team lacked energy old ... prior second meeting crosstown rivals january clippers – fighting best record league lakers nine games behind clippers looking secure playoff spot western conference.fourth time prior meetings since moved los angeles clippers better record lakers entering matchup teams played games.bryant called clippers top contenders championship lakers lost clippers.
2012–13 Los Angeles Lakers season	kupchak told lakers seasonticket holders team needed gasol involved lakers needed play better defense.believe team whose rosters average age .old win championship.lakers followed home loss denver lakers fans revived want phil chants two months earlier.fourth loss five games dropping – th place west three games behind portland trail blazers eighth final playoff spot.
2012–13 Los Angeles Lakers season	nash estimated lakers would need minimum wins qualify playoffs would require team go – .following games playing .ball first games.denver game howard right shoulder heavily wrapped ice.played injury suffered previous game clippers tied career high rebounds denver.
2012–13 Los Angeles Lakers season	gasol suffered concussion game receiving blow face denvers javale mcgee fourth quarter backup big man jordan hill also injured right hip game.howard gasol declared indefinitely.hill brought hustle lacking team required surgery expected keep summer.the team divergent viewpoints would improve.howard thought team chemistry needed improve.bryant believed okay locker room chippy.
2012–13 Los Angeles Lakers season	dantoni said chemistrybuilding overrated team played maximum effort.response new york daily news report howard restrained going bryant posted photo twitter howard jokingly squaring dantoni looks shocked expression.january nash became fifth player nba history reach career assists however los angeles lost game – houston rockets fourth consecutive loss tying longest streak season.due lakers injuries rookie center robert sacre also made first career start rockets finishing points four blocked shots three rebounds losing streak grew losses san antonio spurs oklahoma city thunder dropping lakers – worst start since – season.world peace also suffered right leg injury thunder would hamper two months.compared – team finished – lakers offense improved points per possessions .
2012–13 Los Angeles Lakers season	vs. .defense underperformed.team lacking continuity projected starting lineup beginning season played minutes together primarily due injuries.howard returned following game lakers first game stopping losing streak six win lowly cleveland cavaliers –.move improve teams defense dantoni began bryant guard opponents best perimeter player bryant primary defender cavaliers kyrie irving held points.
2012–13 Los Angeles Lakers season	bryant acknowledged focused defender challenging defensive assignment opposed played ball weaker players.defense disrupted opponents freed nash unfavorable matchups.addition leg injury world peace also suffered injury right arm made difficult bend.things got bad dantoni moved perimeter defense guard power forwards instead.gasol returned missing five games coming bench first game back returning starting lineup.– road loss chicago bulls lakers ninth loss games overall – road record los angeles fell th place west – record midpoint season.
2012–13 Los Angeles Lakers season	calling permanent move dantoni benched gasol game started earl clark form faster smaller lineup coach preferred.team already ranked no.pace.dantoni lakers dropped scoring average .points game surrendering .. offensively reached point threshold eight times games going –.
2012–13 Los Angeles Lakers season	however dantoni stressed teams focus needed defense offense.another new offense lakers struggled run dantonis fastpaced offense.howards back surgery still affecting conditioning struggled nash run pick roll play dantoni expected would staple team.team also lacked shooters speed offense required.playing memphis grizzlies lakers held team meeting clear air los angeles times reported guys went little bit.
2012–13 Los Angeles Lakers season	players told dantoni needed slow pace.coach likened lakers allstar team everybody gets ball goes one one play defense.added havent learned theres pecking order stars need know roles.howard averaging .points .
2012–13 Los Angeles Lakers season	rebounds .blocks said needed bring dominate ways scoring.many times howard upset getting ball enough felt bryant shooting much.howard predicted next game would start new season dantoni made similar declaration week earlier two games losing three row.in first game second half lakers lost – memphis.los angeles four games behind eighthplace portland three games ahead lastplace phoenix new orleans.
2012–13 Los Angeles Lakers season	five western teams ever made playoffs start – worse last denver – went – finish –.defensive rating points per possessions ranked th league.lakers next three home games dropped dantonis offense played without system.play basketball.system move ball play hard defense space floor whos open shoots.
2012–13 Los Angeles Lakers season	difficult thing said dantoni.coach moved nash ball made spotup shooter bryant became primary facilitator offense.defense also energized.bryant least assists three wins threegame total assists career.missed tripledouble game nine rebounds twice eight other.
2012–13 Los Angeles Lakers season	prior role change bryant leading league scoring though much first games.howard bryant credited meeting memphis bringing team together.the lakers – road went important sevengame day road trip.lost first game trip suns january blowing point lead fourth quarter.los angeles finished january winless seven games road first time franchise history finished calendar month – worse.howard left phoenix game early reaggravating shoulder.
2012–13 Los Angeles Lakers season	playing without howard gasol returned starting lineup lakers next two games first road wins despite blowing doubledigit leads four games since phoenix.february – brooklyn—their sixth win seven games third straight without howard—but lost gasol estimated sixtoeight weeks tore plantar fascia right foot towards end game.bryant urged howard return play pain saying center worries much tentative return doesnt want let anyone down.howard mentioned bryant shaquille oneal needed three years win title together bryant replied dont three years.weve got year.
2012–13 Los Angeles Lakers season	howard responded bryant doctor im doctor.thats opinion.howard returned next game missing three games lakers lost – boston celtics.finished road trip – loss defending nba champion miami heat.lakers tied half trailed heat five entering final period committed eight turnovers final minutes.next game home bryant eight turnovers scored four points—his lowest since twopoint game second season —but nine assists win weak phoenix team.
2012–13 Los Angeles Lakers season	last game allstar break outscored clippers – start game lost – clinching season series clippers first time years since –.lakers entered break – winning last games.represented allstar game bryant howard starters.jerry buss death post allstar success break howard committed better second half.avid candy lover howard adopted healthier diet get better shape anchor lakers defense run dantonis preferred pick rolls.
2012–13 Los Angeles Lakers season	february day allstar game buss died hospitalized months cancer.honor owner team wore commemorative patches initials jb jerseys remainder season.lakers entered postallstar schedule – .record ⁄ games behind eighthplace houston.dantoni predicted lakers needed least wins qualify playoffs requiring finish – .. lakers remaining games half teams winning records compared rockets.
2012–13 Los Angeles Lakers season	three previous full nba seasons final playoff seed west averaged wins.the lakers – first week back including win rival celtics.bryant named western conference player week averaging .points .rebounds .assists.
2012–13 Los Angeles Lakers season	scored points shooting least consecutive games first time career also became oldest player accomplish feat.bryant said attack mode since allstar break reacting defense determine score playmaker.howard looking fresher since break yet still said even close physically wanted be.dantoni attributed conditioning difficulty running pick roll.february lakers lost – denver failing reach .
2012–13 Los Angeles Lakers season	first time since new years day.last nba points allowed fast breaks outscored nuggets – fast breaks.lakers threepoint shooting turnovers contributed seasons fast break woes.mediocre threepoint shooting resulted increase long rebounds among worst league turnovers last points allowed per game turnovers.lakers – february ending month – record entering .
2012–13 Los Angeles Lakers season	bryant named western conference player month averaging .points .assists .rebounds game.on march lakers – quality opponent atlanta hawks reached .first time since december .
2012–13 Los Angeles Lakers season	blew point lead second half bryant scored lakers final six points including gamewinner nine seconds left game.four lead changes final minute.lakers improved – fourth best record nba since team meeting memphis.also gained ⁄ games final playoff seed span.however dropped .
2012–13 Los Angeles Lakers season	– loss oklahoma city.lakers fell – road – top five teams western conference.next two games point comebacks new orleans toronto respectively.bryant scored least points least assists games becoming first laker accomplish feat since jerry west .march los angeles beat chicago – moved ⁄ game ahead utah jazz final playoff spot west.
2012–13 Los Angeles Lakers season	first time owned sole possession top spot since december first time two games .season.– week averaged points .assists .rebounds bryant named western conference player week.
2012–13 Los Angeles Lakers season	lakers – since allstar break howard straight games rebounds averaging .points .rebounds .blocks.howards first return orlando march scored seasonhigh points rebounds – lakers win.
2012–13 Los Angeles Lakers season	second time los angeles four straight season.booed throughout game howard made free throws setting lakers records free throws made attempted tying nba record attempts.made free throws fouled intentionally magic.injuries lakers lost next game atlanta – bryant severely sprained left ankle.declared indefinitely landing hawks dahntay jones foot.
2012–13 Los Angeles Lakers season	bryant suggested jones intentionally put foot jones denied.bryant said worst sprain since landed jalen roses foot game nba finals rose later admitted purpose.lakers failed th time win games played backtoback nights fell – road – teams .. bryant gutted minutes play next game indiana pacers lakers – bryant scoreless th time year nba career.however sat next two games due ankle sprain.lakers went – failing win backtoback games losing second night phoenix.
2012–13 Los Angeles Lakers season	suns tied new orleans wests worst record lakers scored season low – loss.bryant returned washington wizards along gasol played first time six weeks lakers lost – home leading .march lakers lost warriors virtually eliminating chance lakers advancing th th playoffs seeds past golden state houston seemed feasible weeks earlier.lakers also lost world peace game tore lateral meniscus left knee.underwent surgery originally estimated sideline six weeks.lakers threegame losing streak partially attributed dantoni reintegrating gasol starting lineup clark making team taller slower.
2012–13 Los Angeles Lakers season	winning next game minnesota lakers failed win consecutive nights th time losing – milwaukee bucks.nash sat end game due hip hamstring issues.bothered bone spur left foot bryant also left game.lakers fell behind utah standings.bryant nash played next game – win sacramento kings nash left game less two minutes strained hamstring.nash remained lakers next two games pull ahead utah half game.
2012–13 Los Angeles Lakers season	bryant tripledouble points rebounds assists dallas followed points nine assists win memphis.playing game elbow offense gasol added points nine rebounds three assists.using right way bryant said.april lakers lost – clippers clinched first pacific division title franchise history.lakers previous division titles.
2012–13 Los Angeles Lakers season	loss also completed season sweep clippers –.franchise swept lakers since – buffalo braves.defeat coupled jazz win dropped lakers – half game behind utah – would win event tie winning season series –.jazz would finish ahead lakers remaining four games schedule.fight playoffs april utah lost oklahoma city los angeles defeated new orleans – regain halfgame lead eighth place.
2012–13 Los Angeles Lakers season	bryant scored points fourth quarter gasol points rebounds four assists three blocks.world peace played minutes game returning days surgery though initial estimates six weeks.absence dantoni using reduced sevenman rotation bryant playing close minutes game.next night lakers played portland lost previous since .portland appeared vulnerable without three starters starting four rookies led – fourth quarter.
2012–13 Los Angeles Lakers season	lakers came back win – bryant scored points playing minutes.lakers first sweep backtoback games attempts season.gasol also points seven rebounds nine assists howard contributed points rebounds.bryant gasol howard combined points highest season.lakers moved full game ahead jazz three games remaining home playoffbound golden state san antonio houston.on april lakers beat warriors – bryant left torn achilles tendon ended season expected sideline six nine months.
2012–13 Los Angeles Lakers season	bryant injured knees collisions warriors festus ezeli third quarter played every minute leaving left game.finished points gasol points rebounds assists sixth career tripledouble.howard points making free throws.bryants injury came playing seven consecutive quarters least minutes seven consecutive games.averaging minutes .
2012–13 Los Angeles Lakers season	six years portland rookie damian lillard averaging minutes.kupchak spoken bryant extensive playing time days earlier bryant insisted minutes needed continue given lakers playoff push.frustrated injury bryant expressed range emotions ranting facebook middle night.in first game without bryant lakers – spurs.howard points rebounds blake added points.lakers went – week bryant player week honors third time despite missing san antonio game.
2012–13 Los Angeles Lakers season	led league scoring week .ranked second western conference steals .per game averaged .rebounds .assists.
2012–13 Los Angeles Lakers season	last day season lakers still risked missing playoffs qualified loss jazz.lakers defeated rockets – overtime moved past seventh seed west.gasol another triple double points rebounds assists.blake added points howard points rebounds.nash missed eighth straight game.dantoni named western conference coach month lakers went – april.
2012–13 Los Angeles Lakers season	finished season – dropping – january day team meeting memphis.defense also improved th span finishing season th .points per possessions.lakers expected starting five bryant nash howard gasol world peace started together seven times season without registering win.lakers didnt help things making coaching change putting dantoni situation glad take.
2012–13 Los Angeles Lakers season	think little bit tougher thought would kupchak said.firstround playoff exit lakers faced san antonio first round playoffs.game howard points rebounds gasol added points rebounds lakers take full advantage inside game lost –.nash returned missing nine games scored points.meeks sprained ankle game missed game .
2012–13 Los Angeles Lakers season	lakers shot better spurs los angeles lost –.jordan hill returned played first time since injury january.however blake left game injuring right hamstring declared indefinitely.nash also reinjured hamstring continued play gamewith nash blake game lakers instead started secondyear guards darius morris andrew goudelock.first playoff start goudelock scored careerhigh points lakers lost – staples worst home playoff loss franchise history.
2012–13 Los Angeles Lakers season	gasol added third tripledouble six games.due lakers injuries world peace played spite running discomfort fluid drained cyst behind surgically repaired left knee.ruled game along nash blake meeks.swept spurs losing game –.howard ejected game nine minutes left third quarter receiving second technical foul.
2012–13 Los Angeles Lakers season	shortly quiet home crowd roared bryant hobbled bench making first appearance court since tearing achilles.gasol received standing ovation left game remaining.lakers exited opening round playoffs first time since suffered first openinground sweep since .standings notesc – clinched home court advantage conference playoffsy – clinched division titlex – clinched playoff spoto – eliminated playoff contention game log preseason regular season playoffs player statistics regular season playoffs awards records milestones awards weekmonth allstar kobe bryant voted allstar starter th consecutive time.dwight howard made seventh consecutive allstar appearance nba allstar game held houston.allnba bryant named allnba first team th time career th overall selection.
2012–13 Los Angeles Lakers season	howard named third team.records march game former team orlando magic dwight howard tied nba record free throw attempts.made attempts.previously set league mark free throw attempts game playing orlando magic vs. golden state warriors january .dwight howard led league defensive rebounds sixth consecutive season sixth season overall career league records.led nba defensive rebounds every season starting – season.
2012–13 Los Angeles Lakers season	milestones november pau gasol scored th career point game houston rockets.december kobe bryant scored th career point win new orleans hornets.december metta world peace became th player record points rebounds steals pointers made win new orleans.january steve nash became fifth player nba history reach career assists.january dwight howard recorded th career assist loss toronto raptors.march bryant passed wilt chamberlains career point total win sacramento kings become fourthhighest scorer nba history.april howard became youngest player nba history reach career rebounds win houston rockets.transactions overview additions subtractions trades future draft picks credits secondround draft pick memphismemphis secondround pick l.a. lakers top protected draft.memphis secondround pick top picks memphis obligations l.a. lakers shall extinguished.l.a. lakers – memphis february debits first round draft pick phoenixthe l.a. lakers send least favorable st round pick top protected clevelands st round pick sacramentos st round pick top protected miamis st round pick phoenix.l.a. lakers st round pick within top selections phoenix automatically receive l.a. lakers st round pick.
2012–13 Los Angeles Lakers season	l.a. lakersphoenix first round draft pick clevelandcleveland right swap least favorable st round pick miamis st round pick top protected sacramentos st round pick top protected l.a. lakers first round pick top protected.l.a. lakers first round pick l.a. lakers obligation cleveland shall extinguished.clevelandl.a.lakers second round draft pick dallasdallas right swap nd round pick l.a. lakers nd round pick.dallasl.a.
2012–13 Los Angeles Lakers season	lakers second round draft pick minnesotathe l.a. lakers nd round pick minnesota via phoenix.l.a. lakersphoenix minnesotanew orleansphoenix first round draft pick phoenixthe l.a. lakers st round pick phoenix.l.a. lakersphoenix second round draft pick orlandothe l.a. lakers nd round draft pick orlando top protected.l.a. lakers nd round pick within top selections l.a. lakers obligation orlando shall extinguished.denver – l.a. lakers – orlando – philadelphia first round draft pick orlandothe l.a. lakers st round draft pick orlando top protected.
History of mathematics	l.a. lakers st round pick within top selections l.a. lakers convey second round picks orlando.l.a. lakers – orlando notes references external links – los angeles lakers roster stats basketballreference.commodern age worldwide spread knowledge written examples new mathematical developments come light locales.bc mesopotamian states sumer akkad assyria followed closely ancient egypt levantine state ebla began using arithmetic algebra geometry purposes taxation commerce trade also patterns nature field astronomy record time formulate calendars.the earliest mathematical texts available mesopotamia egypt – plimpton babylonian c. – bc rhind mathematical papyrus egyptian c. bc moscow mathematical papyrus egyptian c. bc.texts mention socalled pythagorean triples inference pythagorean theorem seems ancient widespread mathematical development basic arithmetic geometry.the study mathematics demonstrative discipline began th century bc pythagoreans coined term mathematics ancient greek μάθημα mathema meaning subject instruction.greek mathematics greatly refined methods especially introduction deductive reasoning mathematical rigor proofs expanded subject matter mathematics.although made virtually contributions theoretical mathematics ancient romans used applied mathematics surveying structural engineering mechanical engineering bookkeeping creation lunar solar calendars even arts crafts.
History of mathematics	chinese mathematics made early contributions including place value system first use negative numbers.hindu–arabic numeral system rules use operations use throughout world today evolved course first millennium ad india transmitted western world via islamic mathematics work muḥammad ibn mūsā alkhwārizmī.islamic mathematics turn developed expanded mathematics known civilizations.contemporaneous independent traditions mathematics developed maya civilization mexico central america concept zero given standard symbol maya numerals.many greek arabic texts mathematics translated latin th century onward leading development mathematics medieval europe.ancient times middle ages periods mathematical discovery often followed centuries stagnation.
History of mathematics	beginning renaissance italy th century new mathematical developments interacting new scientific discoveries made increasing pace continues present day.includes groundbreaking work isaac newton gottfried wilhelm leibniz development infinitesimal calculus course th century.end th century international congress mathematicians founded continues spearhead advances field.prehistoric origins mathematical thought lie concepts number patterns nature magnitude form.modern studies animal cognition shown concepts unique humans.
History of mathematics	concepts would part everyday life huntergatherer societies.idea number concept evolving gradually time supported existence languages preserve distinction one two many numbers larger two.the ishango bone found near headwaters nile river northeastern congo may years old consists series marks carved three columns running length bone.common interpretations ishango bone shows either tally earliest known demonstration sequences prime numbers sixmonth lunar calendar.peter rudman argues development concept prime numbers could come concept division dates bc prime numbers probably understood bc.also writes attempt made explain tally something exhibit multiples two prime numbers numbers almost multiples .
History of mathematics	ishango bone according scholar alexander marshack may influenced later development mathematics egypt like entries ishango bone egyptian arithmetic also made use multiplication however disputed.predynastic egyptians th millennium bc pictorially represented geometric designs.claimed megalithic monuments england scotland dating rd millennium bc incorporate geometric ideas circles ellipses pythagorean triples design.disputed however currently oldest undisputed mathematical documents babylonian dynastic egyptian sources.babylonian babylonian mathematics refers mathematics peoples mesopotamia modern iraq days early sumerians hellenistic period almost dawn christianity.majority babylonian mathematical work comes two widely separated periods first hundred years second millennium bc old babylonian period last centuries first millennium bc seleucid period.
History of mathematics	named babylonian mathematics due central role babylon place study.later arab empire mesopotamia especially baghdad became important center study islamic mathematics.in contrast sparsity sources egyptian mathematics knowledge babylonian mathematics derived clay tablets unearthed since s. written cuneiform script tablets inscribed whilst clay moist baked hard oven heat sun.appear graded homework.the earliest evidence written mathematics dates back ancient sumerians built earliest civilization mesopotamia.developed complex system metrology bc.around bc onward sumerians wrote multiplication tables clay tablets dealt geometrical exercises division problems.
History of mathematics	earliest traces babylonian numerals also date back period.babylonian mathematics written using sexagesimal base numeral system.derives modernday usage seconds minute minutes hour × degrees circle well use seconds minutes arc denote fractions degree.likely sexagesimal system chosen evenly divided .also unlike egyptians greeks romans babylonians placevalue system digits written left column represented larger values much decimal system.power babylonian notational system lay could used represent fractions easily whole numbers thus multiplying two numbers contained fractions different multiplying integers similar modern notation.
History of mathematics	notational system babylonians best civilization renaissance power allowed achieve remarkable computational accuracy example babylonian tablet ybc gives approximation √ accurate five decimal places.babylonians lacked however equivalent decimal point place value symbol often inferred context.seleucid period babylonians developed zero symbol placeholder empty positions however used intermediate positions.zero sign appear terminal positions thus babylonians came close develop true place value system.other topics covered babylonian mathematics include fractions algebra quadratic cubic equations calculation regular numbers reciprocal pairs.tablets also include multiplication tables methods solving linear quadratic equations cubic equations remarkable achievement time.
History of mathematics	tablets old babylonian period also contain earliest known statement pythagorean theorem.however egyptian mathematics babylonian mathematics shows awareness difference exact approximate solutions solvability problem importantly explicit statement need proofs logical principles.egyptian egyptian mathematics refers mathematics written egyptian language.hellenistic period greek replaced egyptian written language egyptian scholars.mathematical study egypt later continued arab empire part islamic mathematics arabic became written language egyptian scholars.the extensive egyptian mathematical text rhind papyrus sometimes also called ahmes papyrus author dated c. bc likely copy older document middle kingdom – bc.
History of mathematics	instruction manual students arithmetic geometry.addition giving area formulas methods multiplication division working unit fractions also contains evidence mathematical knowledge including composite prime numbers arithmetic geometric harmonic means simplistic understandings sieve eratosthenes perfect number theory namely number .also shows solve first order linear equations well arithmetic geometric series.another significant egyptian mathematical text moscow papyrus also middle kingdom period dated c. bc.consists today called word problems story problems apparently intended entertainment.one problem considered particular importance gives method finding volume frustum truncated pyramid.finally berlin papyrus c. bc shows ancient egyptians could solve secondorder algebraic equation.
History of mathematics	greek greek mathematics refers mathematics written greek language time thales miletus bc closure academy athens ad.greek mathematicians lived cities spread entire eastern mediterranean italy north africa united culture language.greek mathematics period following alexander great sometimes called hellenistic mathematics.greek mathematics much sophisticated mathematics developed earlier cultures.surviving records pregreek mathematics show use inductive reasoning repeated observations used establish rules thumb.greek mathematicians contrast used deductive reasoning.
History of mathematics	greeks used logic derive conclusions definitions axioms used mathematical rigor prove them.greek mathematics thought begun thales miletus c. –c.bc pythagoras samos c. –c.bc.although extent influence disputed probably inspired egyptian babylonian mathematics.according legend pythagoras traveled egypt learn mathematics geometry astronomy egyptian priests.thales used geometry solve problems calculating height pyramids distance ships shore.
History of mathematics	credited first use deductive reasoning applied geometry deriving four corollaries thales theorem.result hailed first true mathematician first known individual mathematical discovery attributed.pythagoras established pythagorean school whose doctrine mathematics ruled universe whose motto number.pythagoreans coined term mathematics study mathematics sake begins.pythagoreans credited first proof pythagorean theorem though statement theorem long history proof existence irrational numbers.
History of mathematics	although preceded babylonians chinese neopythagorean mathematician nicomachus – ad provided one earliest grecoroman multiplication tables whereas oldest extant greek multiplication table found wax tablet dated st century ad found british museum.association neopythagoreans western invention multiplication table evident later medieval name mensa pythagorica.plato bc – bc important history mathematics inspiring guiding others.platonic academy athens became mathematical center world th century bc school leading mathematicians day eudoxus cnidus came.plato also discussed foundations mathematics clarified definitions e.g.line breadthless length reorganized assumptions.
History of mathematics	analytic method ascribed plato formula obtaining pythagorean triples bears name.eudoxus –c.bc developed method exhaustion precursor modern integration theory ratios avoided problem incommensurable magnitudes.former allowed calculations areas volumes curvilinear figures latter enabled subsequent geometers make significant advances geometry.though made specific technical mathematical discoveries aristotle –c.bc contributed significantly development mathematics laying foundations logic.in rd century bc premier center mathematical education research musaeum alexandria.
History of mathematics	euclid c. bc taught wrote elements widely considered successful influential textbook time.elements introduced mathematical rigor axiomatic method earliest example format still used mathematics today definition axiom theorem proof.although contents elements already known euclid arranged single coherent logical framework.elements known educated people west middle th century contents still taught geometry classes today.addition familiar theorems euclidean geometry elements meant introductory textbook mathematical subjects time number theory algebra solid geometry including proofs square root two irrational infinitely many prime numbers.
History of mathematics	euclid also wrote extensively subjects conic sections optics spherical geometry mechanics half writings survive.archimedes c. – bc syracuse widely considered greatest mathematician antiquity used method exhaustion calculate area arc parabola summation infinite series manner dissimilar modern calculus.also showed one could use method exhaustion calculate value π much precision desired obtained accurate value π known π .also studied spiral bearing name obtained formulas volumes surfaces revolution paraboloid ellipsoid hyperboloid ingenious method exponentiation expressing large numbers.also known contributions physics several advanced mechanical devices archimedes placed far greater value products thought general mathematical principles.regarded greatest achievement finding surface area volume sphere obtained proving surface area volume cylinder circumscribing sphere.apollonius perga c. – bc made significant advances study conic sections showing one obtain three varieties conic section varying angle plane cuts doublenapped cone.
History of mathematics	also coined terminology use today conic sections namely parabola place beside comparison ellipse deficiency hyperbola throw beyond.work conics one best known preserved mathematical works antiquity derives many theorems concerning conic sections would prove invaluable later mathematicians astronomers studying planetary motion isaac newton.neither apollonius greek mathematicians made leap coordinate geometry apollonius treatment curves ways similar modern treatment work seems anticipate development analytical geometry descartes years later.around time eratosthenes cyrene c. – bc devised sieve eratosthenes finding prime numbers.rd century bc generally regarded golden age greek mathematics advances pure mathematics henceforth relative decline.nevertheless centuries followed significant advances made applied mathematics notably trigonometry largely address needs astronomers.
History of mathematics	hipparchus nicaea c. – bc considered founder trigonometry compiling first known trigonometric table also due systematic use degree circle.heron alexandria c. – ad credited herons formula finding area scalene triangle first recognize possibility negative numbers possessing square roots.menelaus alexandria c. ad pioneered spherical trigonometry menelaus theorem.complete influential trigonometric work antiquity almagest ptolemy c. ad – landmark astronomical treatise whose trigonometric tables would used astronomers next thousand years.ptolemy also credited ptolemys theorem deriving trigonometric quantities accurate value π outside china medieval period ..following period stagnation ptolemy period ad sometimes referred silver age greek mathematics.
History of mathematics	period diophantus made significant advances algebra particularly indeterminate analysis also known diophantine analysis.study diophantine equations diophantine approximations significant area research day.main work arithmetica collection algebraic problems dealing exact solutions determinate indeterminate equations.arithmetica significant influence later mathematicians pierre de fermat arrived famous last theorem trying generalize problem read arithmetica dividing square two squares.diophantus also made significant advances notation arithmetica first instance algebraic symbolism syncopation.among last great greek mathematicians pappus alexandria th century ad.
History of mathematics	known hexagon theorem centroid theorem well pappus configuration pappus graph.collection major source knowledge greek mathematics survived.pappus considered last major innovator greek mathematics subsequent work consisting mostly commentaries earlier work.the first woman mathematician recorded history hypatia alexandria ad –.succeeded father theon alexandria librarian great library wrote many works applied mathematics.political dispute christian community alexandria stripped publicly executed.
History of mathematics	death sometimes taken end era alexandrian greek mathematics although work continue athens another century figures proclus simplicius eutocius.although proclus simplicius philosophers mathematicians commentaries earlier works valuable sources greek mathematics.closure neoplatonic academy athens emperor justinian ad traditionally held marking end era greek mathematics although greek tradition continued unbroken byzantine empire mathematicians anthemius tralles isidore miletus architects hagia sophia.nevertheless byzantine mathematics consisted mostly commentaries little way innovation centers mathematical innovation found elsewhere time.roman although ethnic greek mathematicians continued rule late roman republic subsequent roman empire noteworthy native latin mathematicians comparison.
History of mathematics	ancient romans cicero – bc influential roman statesman studied mathematics greece believed roman surveyors calculators far interested applied mathematics theoretical mathematics geometry prized greeks.unclear romans first derived numerical system directly greek precedent etruscan numerals used etruscan civilization centered tuscany central italy.using calculation romans adept instigating detecting financial fraud well managing taxes treasury.siculus flaccus one roman gromatici i.e.land surveyor wrote categories fields aided roman surveyors measuring surface areas allotted lands territories.aside managing trade taxes romans also regularly applied mathematics solve problems engineering including erection architecture bridges roadbuilding preparation military campaigns.
History of mathematics	arts crafts roman mosaics inspired previous greek designs created illusionist geometric patterns rich detailed scenes required precise measurements tessera tile opus tessellatum pieces average measuring eight millimeters square finer opus vermiculatum pieces average surface four millimeters square.the creation roman calendar also necessitated basic mathematics.first calendar allegedly dates back th century bc roman kingdom included days plus leap year every year.contrast lunar calendar republican era contained days roughly tenandonefourth days shorter solar year discrepancy solved adding extra month calendar rd february.calendar supplanted julian calendar solar calendar organized julius caesar – bc devised sosigenes alexandria include leap day every four years day cycle.calendar contained error minutes seconds later corrected gregorian calendar organized pope gregory xiii r. – virtually solar calendar used modern times international standard calendar.at roughly time han chinese romans invented wheeled odometer device measuring distances traveled roman model first described roman civil engineer architect vitruvius c. bc – c. bc.
History of mathematics	device used least reign emperor commodus r. – ad design seems lost experiments made th century western europe.perhaps relying similar gearwork technology found antikythera mechanism odometer vitruvius featured chariot wheels measuring feet .diameter turning fourhundred times one roman mile roughly ft m. revolution pinandaxle device engaged tooth cogwheel turned second gear responsible dropping pebbles box pebble representing one mile traversed.chinese analysis early chinese mathematics demonstrated unique development compared parts world leading scholars assume entirely independent development.oldest extant mathematical text china zhoubi suanjing variously dated bc bc though date bc warring states period appears reasonable.
History of mathematics	however tsinghua bamboo slips containing earliest known decimal multiplication table although ancient babylonians ones base dated around bc perhaps oldest surviving mathematical text china.of particular note use chinese mathematics decimal positional notation system socalled rod numerals distinct ciphers used numbers additional ciphers powers ten.thus number would written using symbol followed symbol symbol followed symbol followed symbol .advanced number system world time apparently use several centuries common era well development indian numeral system.rod numerals allowed representation numbers large desired allowed calculations carried suan pan chinese abacus.date invention suan pan certain earliest written mention dates ad xu yues supplementary notes art figures.the oldest existent work geometry china comes philosophical mohist canon c. bc compiled followers mozi – bc.
History of mathematics	mo jing described various aspects many fields associated physical science provided small number geometrical theorems well.also defined concepts circumference diameter radius volume.in bc emperor qin shi huang commanded books qin empire officially sanctioned ones burned.decree universally obeyed consequence order little known ancient chinese mathematics date.book burning bc han dynasty bc– ad produced works mathematics presumably expanded works lost.important nine chapters mathematical art full title appeared ad existed part titles beforehand.
History of mathematics	consists word problems involving agriculture business employment geometry figure height spans dimension ratios chinese pagoda towers engineering surveying includes material right triangles.created mathematical proof pythagorean theorem mathematical formula gaussian elimination.treatise also provides values π chinese mathematicians originally approximated liu xin d. ad provided figure .subsequently zhang heng – approximated pi .well .
History of mathematics	taking square root .liu hui commented nine chapters rd century ad gave value π accurate decimal places i.e... though matter computational stamina theoretical insight th century ad zu chongzhi computed value π seven decimal places i.e..remained accurate value π almost next years.
History of mathematics	also established method would later called cavalieris principle find volume sphere.the highwater mark chinese mathematics occurred th century latter half song dynasty – development chinese algebra.important text period precious mirror four elements zhu shijie – dealing solution simultaneous higher order algebraic equations using method similar horners method.precious mirror also contains diagram pascals triangle coefficients binomial expansions eighth power though appear chinese works early .chinese also made use complex combinatorial diagram known magic square magic circles described ancient times perfected yang hui ad –.even european mathematics began flourish renaissance european chinese mathematics separate traditions significant chinese mathematical output decline th century onwards.jesuit missionaries matteo ricci carried mathematical ideas back forth two cultures th th centuries though point far mathematical ideas entering china leaving.japanese mathematics korean mathematics vietnamese mathematics traditionally viewed stemming chinese mathematics belonging confucianbased east asian cultural sphere.
History of mathematics	korean japanese mathematics heavily influenced algebraic works produced chinas song dynasty whereas vietnamese mathematics heavily indebted popular works chinas ming dynasty –.instance although vietnamese mathematical treatises written either chinese native vietnamese chữ nôm script followed chinese format presenting collection problems algorithms solving followed numerical answers.mathematics vietnam korea mostly associated professional court bureaucracy mathematicians astronomers whereas japan prevalent realm private schools.indian earliest civilization indian subcontinent indus valley civilization mature phase bc flourished indus river basin.cities laid geometric regularity known mathematical documents survive civilization.the oldest extant mathematical records india sulba sutras dated variously th century bc nd century ad appendices religious texts give simple rules constructing altars various shapes squares rectangles parallelograms others.
History of mathematics	egypt preoccupation temple functions points origin mathematics religious ritual.sulba sutras give methods constructing circle approximately area given square imply several different approximations value π. addition compute square root several decimal places list pythagorean triples give statement pythagorean theorem.results present babylonian mathematics indicating mesopotamian influence.known extent sulba sutras influenced later indian mathematicians.china lack continuity indian mathematics significant advances separated long periods inactivity.pāṇini c. th century bc formulated rules sanskrit grammar.
History of mathematics	notation similar modern mathematical notation used metarules transformations recursion.pingala roughly rd–st centuries bc treatise prosody uses device corresponding binary numeral system.discussion combinatorics meters corresponds elementary version binomial theorem.pingalas work also contains basic ideas fibonacci numbers called mātrāmeru.the next significant mathematical documents india sulba sutras siddhantas astronomical treatises th th centuries ad gupta period showing strong hellenistic influence.significant contain first instance trigonometric relations based halfchord case modern trigonometry rather full chord case ptolemaic trigonometry.
History of mathematics	series translation errors words sine cosine derive sanskrit jiya kojiya.around ad aryabhata wrote aryabhatiya slim volume written verse intended supplement rules calculation used astronomy mathematical mensuration though feeling logic deductive methodology.though half entries wrong aryabhatiya decimal placevalue system first appears.several centuries later muslim mathematician abu rayhan biruni described aryabhatiya mix common pebbles costly crystals.in th century brahmagupta identified brahmagupta theorem brahmaguptas identity brahmaguptas formula first time brahmasphutasiddhanta lucidly explained use zero placeholder decimal digit explained hindu–arabic numeral system.translation indian text mathematics c. islamic mathematicians introduced numeral system adapted arabic numerals.islamic scholars carried knowledge number system europe th century displaced older number systems throughout world.

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