Imbali amanani. Imbali uphuhliso amanani yokwenene

impucuko Modern nje akunakwenzeka ukuba nomfanekiso ngaphandle amanani. Sihlangabezana nazo yonke imihla, senza ezininzi kubo, amakhulu amawaka yezenzo ngokusebenzisa ikhompyutha. Thina ngoko kusetyenziswa ukuba kwimbali amanani thina banomdla, yaye kuwo nje zange ndicinge ngayo. Kodwa ngaphandle ulwazi ngaphambili zange ukuziqonda wokudla, kwaye ke ngoko kufuneka basoloko befuna ukuqonda ngemvelaphi.

Ngoko ke yintoni na imbali amanani? Xa wabonakala njengomntu weza indalo yazo? Sazise nto!

uphuhliso

Kwimathematika, akukho licandelo ezibaluleke ngakumbi. Nakuba kunjalo, inani njengengqiqo luthe eyavela kwithuba elingaphezu kwewaka leminyaka akufani njengoko iingqondo izazinzulu ehlabathini lonke baye bavuma kodwa ngendlela akukhathalwa.

Isicelo lokuqala uqeqesho, nto leyo ngamandla ngenkani ukuvela kolu luvo, ziye enxulumene nezolimo, ulwakhiwo, kunye kokuma iinkwenkwezi. Ngenxa yoko, ukufundisisa zezulu ukuhlelwa yonke imilinganiselo zibalulekile kuphuhliso lwezeenqanawa kunye norhwebo lwamazwe ngamazwe, ngaphandle apho nako ukuphuhlisa naliphi na ilizwe.

ifilosofi kancinane

Nkqu amanani ezininzi abangekaphuhli zaye usenzile yaye bazisa engqiqweni eqhelekileyo kangangeenkulungwane ezininzi. Abaninzi kubo kwasekwa ngenxa yokuba i zokwazisela enobuchule amagama okanye oonobumba ngamnye. Yayingeyiyo kaPythagoras wathi amanani aziqondakali kunjalo, into zexeshana, indalo yonke into avele kuwo. Ngokubanzi, ngokutsho concepts mihla inzululwazi, yena kakhulu kunene.

I-Chinese wabahlula inani ngokweendidi ezimbini ezibanzi (zisekhona unanamhla):

• Olutenxileyo, okanye yang. -Bulumko yakudala Chinese yayifuzisela izulu auspiciousness.
• Kwangokunjalo, (Yin). Le ngcamango -sibonisa umhlaba kunye nokungazinzi.

Ukususela kumaxesha amandulo ...

Wena mhlawumbi sele ugqibe ukuba imbali amanani uqala uphawu ukusuka kwixesha yamandulo. Ngelo xesha, abalinganiswa twisiseka zazifumaneka kuphela ukuqonda wawuyinyhweba ababingeleli, owaba ngowokuqala kwimbali zemathematika zethu hlabathi.

Izazi bezinto zakudala ngokuqinileyo ziseke ukuba umntu kuqwalaselwa sele Stone Age. Ekuqaleni, inani lokuqala kubonisa isixa ezizodwa leminwe neenzwane. kubo Sasidla ukubala amanyathelo gesi, iintshaba ... Ekuqaleni, abantu kufuneka nje embalwa amanani ezilula, kodwa ke uphuhliso loluntu zifuna iinkqubo letiya. Oku kuphela kukhokelele kuphuhliso iziqalelo yemathematika, kodwa negalelo kuphuhliso lasisiseko senkcubeko yoluntu ngokubanzi, njengoko kufunwa yi-ntshikilelo umsebenzi ophezulu wokuqonda.

Ngoko ke ibali ukuvela nophuhliso zizinto ezingenakwahlulwa kunye kuphuculo ingqondo, nenkanuko koobawo self-ukuphucuka. Okukhona babekhangele iinkwenkwezi, ingcamango ngakumbi malunga regularities zemathematika (nokuba kwinqanaba abangekaphuhli) kwihlabathi elibangqongileyo, kwizilumko abe.

ingqiqo nokuqonda inani

Kamsinya nje bekukho ngempahla yokuqala, abantu baqala ukufunda ukuthelekisa inani kwezinye izinto kunye amaxabiso efanayo imveliso wacela kuye. Ingqiqo ka "ngaphezulu", "ngaphantsi kune", "zilingana", "njengokuba kakhulu." Ulwazi ngokukhawuleza ubanzima, yaye ngenxa yokuba kungekudala kwabakho imfuneko yokuba inkqubo yokubala.

Kufuneka kukhunjulwe ukuba imbali amanani enyanisweni yaqala ukubonakala wokuqala lomntu elifanelekileyo. Yena ungaziva wayesazi ngokuthelekisa indlela inani labantu, izilwanyana, izinto, kodwa hayi ukuba nofifi nkqu izibalo elula. Kodwa yiloo nto engaqhelekanga waba: nantoni na iphathwayo, kwaye uninzi lwabo yaye ngokulula agobe imfumba.

Amanani ezichaza iimpawu zezi zinto ezifanayo zikhona, kodwa ukubamba okanye uzithelekise Yayingekho. Lo mhlaba kuye kwabangela abantu luloyiko, bathi kubo amanani zobugqi, umgangatho angaphezu kwendalo.

Ezinye ubungqina yeengcinga

Oosonzuluwazi kudala kucingelwa ukuba ekuqaleni ezintathu kuphela abantu baye basebenzisa ingqiqo ka "omnye", "ezimbini" yaye "abaninzi". Le hypothesis into eyenziwe krelekrele kuxhaswa yokuba ngeelwimi ezininzi yamandulo ibe ezintathu Iifom (ngesiGrike, umzekelo): isinye, ezimbini kunye nesininzi. Kungekudala emva koko, abantu bafunda ukuba ukwahlula, umzekelo, buffaloes ezimbini ukusuka kwemithathu. Ekuqaleni, lo amanqaku edityaniswa nayiphi iseti ethile yezinto.

Kude kube kamva nje, Australia zomthonyama kunye Polynesians aba namanani amabini kuphela: "enye" yaye "ezimbini", yaye zonke ezinye amanani abantu ezifunyenwe ngokuhlanganisa kubo. Umzekelo, inani abathathu - ezimbini omnye ezine - nababini, nababini kunye. Oku kufana ngokuphawulekayo inkqubo kabini yokubala, nto leyo ngoku usebenzisa ubuchwepheshe computer! Nangona kunjalo, ubomi ngqwabalala baloo maxesha kwanyanzeleka ukuba bafunde, njalo ibizezamandulo ngokukhawuleza yaba isayensi yezibalo.

EBhabhiloni eMesopotamiya

In iBhabhiloni yamandulo nakwimathematika ziphuhliswe ngakumbi kakuhle, ngenxa yokuba kule meko ukudala izakhiwo ezinkulu, lube nzima kakhulu ukuba akukho izibalo ziye akunakwenzeka ukwakha. Isimanga, kodwa amaBhabhiloni zange ukondla mnandi ekhethekileyo amanani, ukuze kwimbali ingqiqo yenani ngokwengqiqo ebanzi yegama yaqala kanye nabo.

BaseBhabhiloni abehlelwa bexesha lakhe ukuba babhale inani liphezulu lezinto, abantu okanye izilwanyana iseti ubuncinane zabalinganiswa. Bona inkqubo ngokokuma yaziswa okokuqala, nto leyo ebonisa ixabiso eyahlukileyo lenombolo kumanani efanayo, abahlala kwiindawo ezahlukeneyo kwimeko yamanani.

Ukongeza, inkqubo yabo yokubala yayisekelwe indlela sexagesimal womlinganiselo, apho amaBhabhiloni njengoko zizazinzulu bathi, waboleka ukusuka Impucuko. Musa ukucinga, nangona kule ndawo kwimbali ingqiqo stop. Sisabona sebenzisa ingqiqo imizuzu engama-60, 60, 360 degrees ngokwemeko nomlinganiselo ojikeleyo.

ngabomvu kaPythagoras

Ababhali yamandulo eBhabhiloni sele kwaziwa kakuhle iimpawu oonxantathu tye. Ngaphezu koko, wenza ukubalwa nomthamo yephiramidi thumbanails. Namhlanje kwakusazeka ukuba imbali kuphuhliso amanani olwamkelweyo kuphuma kanye ukususela ngelo xesha: eMesopotamiya neBhabhiloni imathematika kuphela ngenkuthalo kusetyenziswa amaqhezu, kodwa nokuba ukunceda ukusombulula ingxaki yabo, kunye angaziwa ezintathu!

Ekusondeleni kwexesha elidlulileyo, imathematika mihla bamangaliswa kukufumanisa ukuba langaphambili bamandulo waphumelela ekuthatheni square nje kuphela, kodwa ke ingcambu ityhubhu. Kwakhona kufutshane inkcazelo kwePi, ukusongwa kalukhuni phantsi ezintathu. Kufuneka kuqatshelwe ukuba amaYiputa koko bakwazi ukubala kakhulu ngokucokisekileyo ngakumbi ixabiso (3.16).

amanani zemvelo

Akukho yamandulo kangako yimbali yoqulunqo inani yendalo. Ngoku kukholelwa ukuba ukusetyenziswa yokuqala kule kota kwiincwadi zakhe umphengululi waseRoma Boethius (480-524 GG.), kodwa ngaphambi kokuba Nicomachus of Gerazy wabhala kwiincwadi zakhe phezu zendalo, la manqaku wendalo amanani.

Noko ke, ngengqiqo mihla elithi "inani zendalo" lisetyenziswa kuphela D'Alembert (1717-1783 gg.). Kodwa ukuba avuse: isifundo ngokwayo, ngeengxelo ukuqala nabo. Ngapha koko, ngokwemvelo linani 1, 2, 3, 4, ...

Nge imbonakalo yazo njengenyathelo elibalulekileyo ukuvela yemathematika kunye algebra ngendlela apho thina siyazi namhlanje. izibalo Modern ngokuzithemba sithethe uthotho engenasiphelo amanani zendalo. Kakade ke, kumaxesha amandulo, abantu abazange ungazi nto ngaloo nto. Isixa ukuba abantu bamane abakwazi ukucinga, luchazwa ngegama elithi "ubumnyama", "NdinguMkhosi", "iseti", njalo njalo. Ukuze kwimbali inani kwawu mandulo kakhulu ...

Cwangcisa theory

Okokuqala, amanani yemvelo mfutshane kakhulu. Kodwa Archimedes odumileyo (III. BC. E.) Ngaba nako ukwandisa kakhulu lo mbono. Yaba lo nzulu edume wabhala umsebenzi "I-Sand Reckoner," nto leyo bexesha lakhe ukubizwa ngokuba "Ukubalwa njengentlabathi. ' Yena kubalwa inani amasuntswana amancinane, nto leyo kwakubekwe kungathatha yonke umthamo sphere enobubanzi 15.000.000.000.000 kweekhilomitha.

Ngaphambi kokuba amaGrike Archimedes ikwazile ukufikelela inombolo 10.000.000 inqwaba. Ukudlelana, Noko ke, bathi inani ngo-10 000. Lo gama livela kwisiGrike "Miros", nto leyo iguqulelwe ngeendlela Russian "ngamabona ezinkulu", "kakhulu kakhulu". Kwakhona Archimedes udlulela; yena waqala ukusebenzisa izibalo zayo elithi "amashumi amawaka aphindwe," nto leyo eyakhokelela kamva ukuba adale eyakho, inkqubo ubalo umbhali wakhe.

Elona xabiso liphezulu ukuba akwazi ukuchaza sisazinzulu, iqulathe 80.000.000.000.000.000 amaqanda. Ukuba uprinte le nombolo kwi tape kwiphepha elide, ngoko ke kunokwenzeka ukuba uhlanganise wonke umhlaba kwi-ikhweyitha amaxesha ngaphezulu kwezigidi ezibini.

Ngoko, kuba zonke integers ezakhayo kukho imisebenzi ezimbini ezinkulu:

• Zingakotshwa luphawulwa mali naziphi na izinto.
• Ngoncedo lwabo bachaze iimpawu zezinto kolu thotho inani.

wokuba

Kodwa kuthekani kwimbali uphuhliso yamanani yokwenene? Ngapha koko, kwimathematika asezikhundleni indawo ebaluleke kakhulu! Okokuqala, vuselela inkumbulo. Igama lokwenene kuba nayiphi ezintle, ezingakhiyo, kunye zero. A lot of kuzo zahlulwe zibe esinengqiqo ngqiqweni.

Ukuba ufunda ngenyameko inqaku, unokuthekelela ukuba imbali kuphuhliso amanani yokwenene iqala ekuqaleni uluntu. Ekubeni ingqikelelo zero okokuqala (ulwazi oluphangaleleyo okanye oluthembekileyo ngaphantsi) kwenziwa kunyaka 876 emva kukaKristu, yaye yaqalisa e-India, ungakwazi uphawu lo mhla njengoko eliphakathi.

Njengoko kuba amaxabiso akhabanayo, okwesihlandlo sokuqala wachaza Diophantus (Greece) kwi AD ngenkulungwane yesithathu, kodwa "semthethweni", baba kuphela India, phantse ngaxeshanye ingqiqo ka "zero".

Kufuneka kukhunjulwe ukuba imbali amanani kwimathematika ufuna ukuba zikhona eYiputa yamandulo ngenxa izibalo zidla kubonakaliswa. Apha kanye ngelo xesha babegqalwa 'akunakwenzeka "yaye" alunakufikeleleka ", nangona maxa wambi kusetyenziswa njengoko amaxabiso aphakathi.

amanani enengqondo

Khumbula ukuba inani kwande maqhezu. Xa emilise kwinani elipheleleyo ezisetyenziswa kulo, kunye nezenzo nenani elingaphezulu njenge inani yendalo. Asiyazi nini yaye phi le ngcamango kuye kwavela okokuqala, kodwa ngenkuthalo basebenzisa Sumerians sele iwaka embalwa iminyaka BC. Umzekelo wabo walandelwa amaGrike amaYiputa.

amanani Complex

Kodwa bona bawathabatha kakhulu kutshanje, ngoko nangoko emva ekuchongeni iindlela ukubala iingcambu i'quadratic cubic. Mna le Italian noNiccolò Fontana Tartaglia (1499-1557 gg.) Malunga ekuqaleni kwenkulungwane yeshumi. Kwaye ngoko ke ndafumanisa ukuba ukucombulula iintlobo ezahlukeneyo iingxaki azisoloko ukuba basebenzise amanani yokwenene kuphela.

Ukuba achaze le meko engaqhelekanga kuphela 1572. kwenza ukuba Rafael Bombelli, iqala ibali kuphuhliso amanani ezintsonkothileyo kuzo. Kodwa iziphumo zakhe ixesha elide kubhekwa "ezisungulwe banolwazi lokunyanga kodwa bengenalo," yaye kuphela ngenkulungwane ye-19, sezibalo omkhulu Carl Friedrich GAUSS wabonisa ukuba ezihlangwini zakhe ezikude okulungileyo ngokupheleleyo.

enye imfundiso

Abanye abaphandi bathi ukuba amaxabiso zokuqala wengqikelelo babekhankanywe kwangethuba 1545. Kwathi amaphepha odumileyo ngexesha labour "ubugcisa Enkulu, okanye Imithetho aljibra", owabhala Gerolamo Cardano. Emva koko bazama ukufumana amanani amabini yesisombululo, leyo xa iphinda phindiweyo ngo-10 Yiphani, yaye phinda kwandisa ixabiso labo ku-40.

Kangangexesha elide ngaphambili zezibalo yaba umbuzo wokuba ingaba kukho ezininzi ivaliwe ngokupheleleyo. Makhe achaze: na imisebenzi amaxabiso ezintsonkothileyo kungabangela complex iziphumo zokwenyani okanye uphando nje kungakhokelela kwafunyanwa into entsha ngokupheleleyo? Noko ke, ukuba isisombululo kule ngxaki na imisebenzi ka-Abraham de Moivre (bona asusela 1707), kwakunye iincwadi uRoger nezibaya, apapashwa 1722.

Nantso imbali lonke inani. Ngokufutshane, Kakade, kodwa nqaku lisaziqwalasela zadibana yophando kule ndawo.