Zosakaniza: mbiri ya magawo. Mbiri ya maonekedwe a tizigawo ting'onoting'ono

Chimodzi mwa magawo ovuta kwambiri a masamu mpaka lero ndi tizigawo ting'onoting'ono. Mbiri ya tizigawo ting'onoting'ono zoposa zaka chikwi chimodzi. Kukhoza kugawa magawo onsewo kunayambira m'madera a Igupto wakale ndi Babulo. Kwa zaka zambiri, machitidwewa opangidwa ndi tizigawo ting'onoting'ono takhala ovuta, mawonekedwe awo ojambula anasintha. Dziko lililonse lakale linali ndi maonekedwe ake mu "chiyanjano" ndi gawo ili la masamu.

Kodi ndi gawo lanji?

Pomwe panafunika kugawaniza mbali zonse popanda kuyesayesa kwina, ndiye kuti timagawidwe tawoneka. Mbiri ya tizigawo tingathe kugwirizana kwambiri ndi njira yothetsera mavuto. Mawu akuti "fraction" ali ndi mizu ya Chiarabu ndipo amachokera ku mawu akuti "kuphwanya, kugawa". Kuyambira kalekale, mwanjira imeneyi, pang'ono zasintha. Tsatanetsatane wamakono ndi izi: gawo limodzi ndi gawo kapena gawo la unit. Choncho, zitsanzo ndi tizigawo ting'onoting'ono ndi ntchito yopangira masamu pamagulu a ziwerengero.

Lero, pali njira ziwiri zozilembera. Zigawo zapadera ndi zapamwamba zinayambira nthawi zosiyana: zoyambazo ndizokale kwambiri.

Zinachokera zaka zakuya

Kwa nthawi yoyamba, tizigawo ting'onoting'ono tayamba kugwira ntchito m'dera la Egypt ndi Babulo. Kufikira kwa masamu a masamu awiriwa kunali ndi kusiyana kwakukulu. Komabe, chiyambicho chinayikidwa chimodzimodzi mmalo onse awiri. Gawo loyamba linali theka kapena theka. Ndiye anadza kotala, lachitatu, ndi zina zotero. Malinga ndi zomwe akatswiri ofukula zinthu zakale anafukufuku, mbiri yakale ya kupanga tizigawo ting'onoting'ono ndi pafupifupi zaka zikwi zisanu. Kwa nthawi yoyamba, chiwerengero cha chiwerengerocho chikupezeka mu mapepala a ku Igupto komanso pa mapale a ku Babulo.

Igupto wakale

Mitundu ya zigawo zochepa lero zimaphatikizapo otchedwa Aigupto. Ndizowerengeka za mawu angapo a mawonekedwe a 1 / n. Chiwerengero nthawi zonse chimagwirizana, ndipo chipembedzo ndi chiwerengero cha chilengedwe. Pali magawo amenewa, ziribe kanthu zovuta kuganiza, ku Igupto wakale. Powerengera magawo onse omwe amayesedwa kulemba monga mawonekedwe (monga, 1/2 + 1/4 + 1/8). Zigawo zosiyana zikanangokhala ndi tizigawo 2/3 ndi 3/4, zina zonse zidagawanika. Panali magome apadera omwe magawo a chiwerengerocho anayimiridwa ngati ndalama.

Kutchulidwa kokalamba kwamtundu wotereku kumapezeka mu mpukutu wa masamu wa Rind, kuyambira pachiyambi cha zaka chikwi chachiwiri BC. Zimaphatikizapo tebulo la tizigawo ting'onoting'ono ndi mavuto a masamu ndi mayankho ndi mayankho, omwe amaimira mawonekedwe. Aigupto anatha kuwonjezera, kugawa ndi kuchulukitsa magawo a chiwerengero. Zigawo za m'mtsinje wa Nile zinalembedwa mothandizidwa ndi zilembo zamakono.

Kuyimira kwa chigawo cha chiwerengerocho monga mawonekedwe a mawonekedwe a 1 / n, chikhalidwe cha Igupto wakale, chinali kugwiritsidwa ntchito ndi masamu osati dziko lokha. Mpaka zaka zapakati pazaka za m'ma Middle Ages, zida za Aigupto zinkagwiritsidwa ntchito m'dera la Greece ndi mayiko ena.

Kupititsa patsogolo masamu ku Babulo

Masamu mu ufumu wa Babiloni ankawoneka mosiyana. Mbiri ya maonekedwe a tizigawo timagwirizanitsa mwachindunji ndi zenizeni za chiwerengero cha chiwerengero chomwe chinatengedwa kuchokera ku chikhalidwe cha kale, chikhalidwe cha Sumerian-Akkadian. Kuwerengera njira mu Babeloni kunali kosavuta komanso kosavuta kuposa ku Egypt. Masamu m'dziko lino adathetsa ntchito zambiri.

Kuona zomwe Ababulo anachita patsikuli zikhoza kukhala kuchokera ku mapale a mapale, omwe ali ndi zilembo zapadera. Chifukwa cha zenizeni za nkhaniyi, zatifikira ife ambiri. Malinga ndi akatswiri ena, akatswiri a masamu ku Babulo Pythagoras asanatuluke maganizo otchuka, omwe mosakayikira amatsimikizira kuti chitukuko cha sayansi chikuchitika m'dzikolo wakale.

Kuphulika: nkhani ya tizigawo ting'onoting'ono ku Babulo

Chiwerengero cha chiwerengero mu Babeloni chinali chiwerewere. Udindo uliwonse watsopano unasiyanasiyana ndi chaka chapitalo ndi 60. Njira yotereyi yasungidwa mu dziko lamakono kuti iwonetse nthawi ndi kukula kwake kwa ma angles. Zagawidwe zinali zogonana. Malembo apadera adagwiritsidwa ntchito pojambula. Monga ku Egypt, zitsanzo ndi tizigawo timene timakhala ndi zizindikiro zosiyana kwa 1/2, 1/3 ndi 2/3.

Mchitidwe wa Babeloni sunathere pamodzi ndi boma. Zigawo zolembedwa m'zigawo 60 zinagwiritsidwa ntchito ndi akatswiri a zakuthambo zakale ndi Aarabu komanso akatswiri a masamu.

Greece wakale

Mbiri ya zigawo zochepa sizinapindule kwambiri ku Greece yakale. Anthu okhala ku Hellas ankakhulupirira kuti masamu ayenera kugwira ntchito mwa nambala yonse. Choncho, mafotokozedwe omwe ali ndi tizigawo ting'onoting'ono ta machitidwe achigiriki akale sanali atakumane nawo. Komabe, zopereka zina ku gawo lino la masamu zinapangidwa ndi Pythagoreans. Iwo amamvetsetsa tizigawo timene timakhala timene timagwirizana kapena timene timayendera, ndipo chiwerengerocho chinkawonedwanso kuti sichitha kuwonekera. Pythagoras ndi ophunzira ake anamanga mfundo zambiri za tizigawo ting'onoting'ono, adaphunzira momwe angagwiritsire ntchito masamu onse a masamu, komanso kuyerekezera magawo powabweretsa ku gulu limodzi.

Ufumu Woyera wa Roma

Mipangidwe ya Aroma inkagwirizanitsidwa ndi kulemera kwake, kutchedwa "bulu". Iyo inagawidwa mu magawo 12. 1/12 Assa ankatchedwa ounce. Kutanthawuza magawo, panali maudindo 18. Nawa ena mwa iwo:

• Semis - theka la bulu;

• Sextant - gawo lachisanu ndi chimodzi la bulu;

• Semi-ounce - theka la ounce kapena bulu wani / 24.

Kusokonezeka kwa dongosolo ngatilo kunali kosatheka kuimira chiwerengero chokhala ndi kachigawo kakang'ono ka 10 kapena 100. Akatswiri a masamu achiroma anagonjetsa zovuta pogwiritsa ntchito chidwi.

Kulemba magawo wamba

Ku Antiquity, tizigawo tazolembedwa kale mwa njira yozolowereka: nambala imodzi pamwambapa. Komabe, panali kusiyana kwakukulu kwakukulu. Nambalayi inali pansi pa chipembedzo. Kwa nthawi yoyamba, iwo anayamba kulemba tizigawo ting'onoting'ono ku India wakale. Njira yamakono kwa ife idagwiritsidwa ntchito ndi Aarabu. Koma palibe wina wotchulidwa kuti anthu omwe amagwiritsa ntchito mzera wopingasa kuti athe kusiyanitsa nambala ndi chipembedzo. Kwa nthawi yoyamba zikuwonekera m'malemba a Leonardo wa Pisa, odziwika bwino monga Fibonacci, mu 1202.

China

Ngati mbiri ya kuchitika kwa tizigawo ting'onoting'ono tayamba ku Egypt, ndiye decimal inkaonekera koyamba ku China. Mu Ufumu Wachifumu, iwo anayamba kugwiritsidwa ntchito pafupifupi kuyambira m'zaka za zana lachitatu BC. Mbiri ya zigawo za decimal zinayambika ndi chiwerengero cha masamu achi China, Liu Huey, amene adawagwiritsa ntchito polemba mizu yambiri.

M'zaka za zana lachitatu AD, zilembo za ku China zinayamba kugwiritsidwa ntchito powerengera kulemera kwake. Pang'onopang'ono iwo anayamba kulowa mkati mwa masamu. Ku Ulaya, zidutswa zapakati zimayamba kugwiritsidwa ntchito patapita nthawi.

Al-Kashi ochokera ku Samarkand

Mosasamala kanthu za akale a ku China, ziwonongeko zinapezedwa ndi katswiri wa zakuthambo al-Qashi kuchokera ku mzinda wakale wa Samarkand. Anakhala ndi kugwira ntchito m'zaka za m'ma XV. Malingaliro ake anafotokozedwa mu chipangano cha "Chinsinsi cha masamu," chomwe chinafalitsidwa mu 1427. Al-Qashi ankanena kugwiritsa ntchito mawonekedwe atsopano a zolembera. Zonse ziwiri ndi gawo lazing'ono zinali zolembedwa mzere umodzi. Chifukwa cha kupatukana kwawo, Samarket wa zakuthambo sanagwiritse ntchito comma. Analemba chiwerengero chonse ndi gawo lochepa mu mitundu yosiyanasiyana, pogwiritsa ntchito inki yakuda ndi yofiira. Al-Qashi nthawi zina amagwiritsira ntchito mzere wolekanitsa.

Magawuni aatali ku Ulaya

Mitundu yatsopano ya tizigawo ting'onoting'ono tayamba kuonekera m'malemba a akatswiri a masamu a ku Ulaya kuyambira m'zaka za m'ma XIII. Tiyenera kukumbukira kuti ndi ntchito ya al-Qashi, komanso ndi chiyambi cha Chinese, iwo sanali odziwa. Magazi ofunika amaoneka m'mabuku a Jordan Nemoraria. Ndiye iwo anali atagwiritsidwa kale ntchito mu zaka za XVI ndi François Viet. Wasayansi wa ku France analemba "Mathematical Canon", yomwe inali ndi matebulo atatu. Mwa iwo, Vietnam imagwiritsidwa ntchito. Kuti athetse gawo lonse ndi laling'ono, wasayansi anagwiritsa ntchito mzere wofanana, komanso kukula kwake kwa ma teti.

Komabe, izi zinali zapadera zokha za sayansi. Pofuna kuthetsa mavuto a tsiku ndi tsiku, ziwonongeko ku Ulaya zinayamba kugwiritsidwa ntchito patapita nthawi. Izi zinachitika chifukwa cha sayansi ya Chidatchi Simon Stevin kumapeto kwa zaka za zana la 16. Iye anafalitsa ntchito ya masamu "The Tenth" mu 1585. Mmenemo, wasayansi akufotokoza chiphunzitso cha kugwiritsiridwa ntchito kwa magawo a decimal mu masamu, mu ndalama zamakhalidwe ndi pakukhazikitsa miyeso ndi zolemera.

Mfundo, mfundo, makina

Stevin nayenso sanagwiritse ntchito comma. Anagawanitsa mbali ziwiri za chidutswa ndi zero, kuzungulira mu bwalo. Kwa nthawi yoyamba, comma inalekanitsa magawo awiri a decimal gawo mu 1592. Ku England, mfundoyi idagwiritsidwa ntchito m'malo mwake. Ku United States, mpaka pano, zolemba zinalembedwa motere.

Mmodzi mwa oyambitsa kugwiritsa ntchito zizindikiro zonse zolemba zizindikiro kuti azilekanitsa gawo lonse ndi laling'ono anali katswiri wamasamu wa ku Scotland John Nepper. Iye adafotokoza zomwe adachita mu 1616-1617. Wasayansi wina wa ku Germany, Johann Kepler, nayenso anagwiritsa ntchito comma.

Zagawo za ku Russia

Pa dziko la Russia, mtsogoleri woyamba wa masamu amene anayambitsa magawano onsewo, anali mtsogoleri wa Novgorod Kirik. Mu 1136 iye analemba ntchito imene adafotokoza njira "yowerengera zaka". Kirik anakambirana ndi mafunso olemba nthawi ndi kalendala. Mu ntchito yake, adatchula, pakati pazinthu zina, kusiyana kwa ola limodzi kukhala mbali: lachisanu, makumi awiri ndi zisanu ndi zina zotero.

Kugawidwa kwa zigawo zonse kunagwiritsidwa ntchito powerengera kuchuluka kwa msonkho m'zaka za XV-XVII. Ntchito za kuwonjezera, kuchotsa, kugawa ndi kuchulukitsa ndi zidutswa zazing'ono zinagwiritsidwa ntchito.

Mawu omwewo "kachigawo" anawonekera ku Russia m'zaka za m'ma VIII. Icho chinachokera ku verebu "kuti azigawidwa, kugawa magawo". Kwa dzina la tizigawo ting'onoting'ono, makolo athu anagwiritsa ntchito mawu apadera. Mwachitsanzo, 1/2 inasankhidwa ngati theka kapena theka, 1/4 - zinayi, 1/8 - theka-count, 1/16 - theka-njira ndi zina zotero.

Chiphunzitso chokwanira cha tizigawo ting'onoting'ono, chomwe chimasiyana pang'ono ndi zamakono, chinakhazikitsidwa m'buku loyamba pa masvomere, lolembedwa mu 1701 ndi Leonty Filippovich Magnitsky. "Masamu" anali ndi magawo angapo. Za magawowa mwatsatanetsatane wolembayo akunena mu gawo "Za nambala ya mizere yosweka kapena magawo". Magnitsky amatsogolera ntchito ndi manambala "osweka", mayina osiyanasiyana.

Masiku ano, chiwerengero cha magawo ovuta kwambiri a masamu amatchedwa tizigawo ting'onoting'ono. Mbiri ya tizigawo ting'onoting'ono sizinali zophweka. Nthawi zina mitundu yosiyanasiyana imasiyanirana wina ndi mzake, ndipo nthawi zina imabwereka zochitika za otsogolera, zinafika pakufunika koyambirira, kuzindikira ndi kugwiritsa ntchito tizigawo ta nambala. Nthawizonse chiphunzitso cha tizigawo ting'onoting'ono tinachokera kuzinthu zenizeni komanso chifukwa cha mavuto. Zinali zofunikira kugawa mkate, kuwonetsa malo ofanana, msonkho, kuyeza nthawi, ndi zina zotero. Zomwe zikugwiritsidwa ntchito pogwiritsira ntchito tizigawo ting'onoting'ono ndi masamu zomwe timagwiritsa ntchito zimadalira chiwerengero cha chiwerengero ku boma komanso pa chiwerengero cha kakulidwe ka masamu. Njira imodzi, chifukwa chogonjetsa zaka zoposa chikwi chimodzi, kupatulidwa kwa algebra kumagwiritsidwa ntchito ku ziwerengero za manambala kwapangidwa, kupangidwa ndi kugwiritsidwa ntchito bwino masiku ano kuti zikhale zofunikira zosiyanasiyana, zogwira ntchito ndi zongopeka.