Zvikamu Zviduku kare zvikamu zviduku. Nhoroondo chidzoke zvikamu zviduku zveropa

Mumwe matavi masvomhu yakaomesesa vanoonekwa kuti vaizopfurwa nhasi. History of zvikamu zvinopfuura chimwe chemakore. Kugona zviparadzanise rose migove kwakaitika munharaunda muIjipiti yekare uye Bhabhironi. Kwemakore, isu akatonyanya yakaoma kushandiswa, amakavaitira zvikamu zviduku, akashandura chimiro yakarekodwa yavo. Mumwe mamiriro enyika yekare aiva pachavo zvachiri muna "ukama" nebazi ichi wemasvomhu.

Chii chikamu?

Pazvakava zvakakodzera kugovera rose migove pasina zvakavabatsirei, ipapo pachava hacho. History zvikamu zviduku vakanga zvakabatana chaizvo kuti utilitarian mabasa. shoko rokuti "mupumburu" pacharo rine midzi Arabic uye rinobva pashoko rinoreva kuti "kuputsa, kuti zviparadzanise." Kubvira kare, mupfungwa iyi, muduku zvachinja. Tsanangudzo ano riri sezvinotevera: chakapatsanurwa - chikamu Verengai zvikamu kana dzakabatana. Saizvozvowo, mienzaniso ine zvikamu zvinomiririra sequential vakauraya kwemasvomhu remapazi vane zvikamu nhamba.

Nhasi, kune nzira mbiri yakarekodwa. Common uye grade zvikamu zviduku akazviratidza panguva dzakasiyana: aimbova vanonyanyova yekare.

Vakabva kare kare

Kokutanga takatanga kushanda chakapatsanurwa muIjipiti uye muBhabhironi. Mathematicians kusvika kunyika mbiri kunokosha kusiyana. Zvisinei, kutanga uye imomo makanga vakaisa saizvozvo. Yokutanga chakapatsanurwa yaiva hafu kana 1/2. Zvino kwakauya muzvina, wechitatu, uye zvichingodaro. Maererano matongo Zvakafukunurwa, nhoroondo zvikamu ane makore anenge 5000. Kokutanga mugove nhamba inowanikwa chepappryi uye kuBhabhironi evhu.

muIjipiti

Mhando zvikamu nhasi zvinosanganisira anonzi muIjipiti. Ndivo Verengai anoverengeka mashoko muchimiro 1 / n. Numerator - nguva dzose chete uye dhinomineta - dzinongoitika nhamba. Kune chikamu chiduku kwakadaro, zvisinei chakaoma sei zvokufungidzira muIjipiti yekare. Kana pakuverenga mugove zvose vakaedza kunyora muchimiro mari yakadaro (semuenzaniso, 1/2 + 1/4 + 1/8). mazita nomumwe akanga chete zvikamu zviduku 2/3 uye 3/4, uye vamwe vakanga vakakamurwa kuva mazwi. Kwakanga chaiwo matafura umo nhamba nhamba hunomiririrwa Verengai.

Mukuru akazivisa kududzwa yakadaro hurongwa kunowanika Rhind kwemasvomhu Papyrus, kudanana kubva pakutanga mumireniyamu yechipiri BC. Anosanganisira tafura zvikamu uye matambudziko kwemasvomhu pamwe zvinogadzirisa uye nemhinduro, anounzwa inopfupikisa zvikamu zviduku zveropa. VaEgipita vaiziva sei kuwedzera, zviparadzanise uye muwande uwandu mugove. Nezvikamu Mumupata murwizi zvakanyorwa vachishandisa hieroglyphs.

Mharidzo nhamba senhamba chitsama mashoko muchimiro 1 / N, hunhu muIjipiti yekare, inoshandiswa mathematicians, kwete chete munyika iyi. Kusvika Middle Ages, muIjipiti chakapatsanurwa akashandiswa Greece uye dzimwe nyika.

Pokumuka masvomhu muBhabhironi

Zvikasadaro, tarisai samhu yeBhabhironi umambo. Nhoroondo panowanikwa zvikamu zvine chokuita zvaidiwa nhamba hurongwa zvakananga, nhaka vekare mamiriro nhaka kubva nowakautangira wayo, Sumerian-weAkkadian budiriro. Settlement Equipment muBhabhironi yamunenge uye pakukura pane muIjipiti. Masvomhu munyika akagadzirisa zvikuru siyana mabasa.

VaBhabhironi kuzotonga nebudiriro nhasi zvinogona akachengetedzwa ivhu mahwendefa ecuneiform akazadzwa. Nokuda peculiarities kwemashoko vauya pasi kwatiri vazhinji. Maererano mamwe masayendisiti, mathematicians muBhabhironi pamberi Achibvuma pfungwa yaPythagoras akavhura inonyatsozivikanwa theorem no, izvo pasina mubvunzo inoratidza kukura nesayenzi yekare mamiriro.

Zvikamu Zviduku kare zvikamu zviduku muBhabhironi

nhamba maitiro akanga sexagesimal muBhabhironi. chikamu chimwe nechimwe chitsva rakasiyana yapfuura 60. gadziriro iyi rakachengetedzwa munyika yanhasi, nokuti nguva uye pamakona. Zviduku Zveropa vaiva sexagesimal. Kunyora vachishandisa chaiwo mifananidzo. Sezvo muIjipiti, mienzaniso ine zvikamu zviduku zvine zvimwe zviratidzo nokuda 1/2, 1/3 uye 2/3.

Babylonian maitiro haana kubviswa pamwe nehurumende. Nezvikamu zvakanyorwa 60-hexadecimal hurongwa, anoshandiswa vanoongorora nyeredzi vekare uye Arab uye mathematicians.

Greece yekare

History of zvikamu vafumiswa ne zvishoma pane muGirisi yekare. Vagari Greece vaidavira kuti masvomhu vanofanira unoshanda chete integers. Saka, mashoko okuti pamwe nezvikamu mumapeji echiGiriki akadhindwa vekare anenge kumbobvira akasangana. Zvisinei, vamwe mupiro kubazi iri masvomhu akaita Pythagoreans. Vanonzwisisa zvikamu zviduku sezvo ratios kana kukura, uyewo indivisible chairema pfungwa. Achibvuma pfungwa yaPythagoras pamwe vadzidzi ane vakawanda dzidziso zvikamu zviduku vakadzidza kubata zvose zvina svomhu akavhiyiwa uye kuenzanisa zvikamu zviduku nokuenda navo rwakafanana dhinomineta.

Holy Roman Empire

Negadziriro zvikamu Roman aishamwaridzana kwakati uremu, rinonzi "the". It yakakamurwa migove 12. 1/12 Ace anonzi magiramu. Kuratidza zvikamu zviduku, paiva nemazita 18. Heano mamwe acho:

• Semis - hafu Ace;

• sextant - yechitanhatu mugove Ace;

• semiuntsiya - hafu magiramu kana 1/24 Ace.

Zvakaipira ino ndiko kutadza kumiririra nhamba sezvo chikamu chete dhinomineta 10 kana 100. masvomhu Roman kukurira chinetso achishandisa muzana.

Kunyora zvakafanana zvikamu zviduku

In kare, kuti chikamu chiduku ratova avanoziva kwatiri, isu akanyora izvi: nhamba imwe pamusoro perimwe. Zvisinei, paiva nomumwe musiyano zvikuru. The numerator riri pasi dhinomineta. Kokutanga kubvira kunyora zvikamu zviduku vakatanga India yekare. Nzira dzemazuva ano vedu vakatanga kushandisa navaArabhu. Asi hapana marudzi aya havana kushandisa chinjikira mutsetse kusiyanisa numerator uye dhinomineta. Iye pakutanga rinowanikwa mabasa Leonardo Pizanskogo, nani kuzivikanwa Fibonacci, muna 1202.

China

Kana nhoroondo kwaita zvikamu akatanga muIjipiti grade wokutanga akaonekwa China. The hweKudenga Empire zvaishandiswa kubva pamusoro III remakore BC. History decimals vakatanga Chinese yemasvomhu Liu Hui, uyo akafunga kushandisa dzokubudisa zvemasikweya midzi.

Muzana III remakore BC decimals mu China zvave dzemaitirwe youremu uye vhoriyamu. Zvishoma nezvishoma, vakatanga kupinda zvakadzama kupinda masvomhu. Zvisinei, muna Europe, grade zvikamu zviduku zvaishandiswa zvikuru paya.

Al-Kashi kubva Samarkand

Zvisinei China vamutangira decimals akazarurwa zvomuchadenga al-Kashi rekare guta Samarkand. Akararama uye aishanda XV remakore. Pfungwa dzake musayendisiti akatsanangura mu bhuku rake "Kiyi svomhu," rakabudiswa muna 1427. Al-Kashi zvinganaka kushandisa idzva muchimiro kunyora zvikamu zviduku. Uye wose, uye fractional chikamu zvino zvakanyorwa rimwe mutsetse. Kuparadzana kubva Samarkand muongorori wenyeredzi haana kushandisa koma. Akanyora integer uye fractional chikamu mavara akasiyana, vachishandisa nhema uye tsvuku neingi. Dzimwe kuparadzana Al-Kashi akashandisawo wehunyambiri kubhawa.

Decimals mu Europe

A mhando itsva zvikamu vakatanga kuonekwa nemabasa mathematicians European kubvira XIII remakore. Zvinofanira kucherechedzwa kuti basa al-Kashi, uyewo michina yacho Chinese havana kujaira. Grade nezvikamu akazviratidza murugwaro Jordanus of Nemore. Vari ipapo kushandiswa XVI remakore Fransua Viet. nyanzvi French akanyora "The kwemasvomhu seakafuridzirwa", yaiva trigonometric pamatafura. Ivo Việt decimals. Kusiyanisa integer uye fractional chikamu musayendisiti akashandisa wehunyambiri mutsetse, uye yakasiyana Schriftgröße.

Zvisinei, izvi zvakanga chete chaiyo zviitiko kushandiswa nesayenzi. Nokuti mabasa epamba decimals mu Europe vakatanga kuiswa pashure. Izvi zvakaitika nemhaka Dutch musayendisiti Simon Stevin pakupera yacho XVI remakore. Akabudisa kwemasvomhu basa "Wechigumi" muna 1585. Mairi musayendisiti akatsanangura dzidziso kushandisa grade svomhu, mune mari ino uye kuona muzviyereso.

Point, pfungwa, koma

Stevin haana kushandisa koma. Iye akaparadzanisa zvikamu zviduku maviri uchishandisa razero vachiapoteredza vari denderedzwa. First koma vaparadzane zvikamu maviri grade chakapatsanurwa chete muna 1592. Zvisinei, kuEngland, zvakatanga kushandiswa pachinzvimbo pfungwa. MuUnited States achiri decimals kunyora kuti nzira.

Mumwe initiators wokushandiswa zvose nyora kuti zviparadzanise integer uye fractional chikamu chaiva wokuScotland yemasvomhu Dzhon Neper. Akataura mutongo wake 1616-1617 gg. Nongedzera uye akanakidzwa musayendisiti wokuGermany Iogann Kepler.

Zviduku Zveropa muna Rus

Paivhu Russian yemasvomhu wokutanga, vakasimuka weboka yose migove, Novgorod akava mumongi Kirik. Muna 1136, akanyora basa, umo makaisa nzira "radix makore." Kirik vaishanda muronga uye karenda. In basa rake Akapinza, kusanganisira weboka maawa migove miviri: wechishanu, makumi maviri namashanu, uye saka pamusoro mugove.

Kupatsanura yose muzvikamu kushandiswa pakuverenga kukura mutero XV-XVII emakore. Used kushanda Uyezve, kubvisa, kupesana uye chokuwanziridza pamwe fractional nhengo.

Shoko "bara" akazviratidza Russia muna VIII remakore. Rinobva pashoko rechiito "kupwanya, akatsemura zvidimbu." To zita zvikamu zviduku namadzibaba edu akashandisa mashoko anokosha. Somuenzaniso, 1/2 akanga asarudzwa somunhu-hafu kana poltina 1/4 - Chet, 1/8 - polchet, 1/16 - polpolchet uye zvichingodaro.

A kwakakwana dzidziso zvikamu zviduku, kwete kusiyana nhasi, yakataurwa rokutanga bhuku iri svomhu, akanyorwa muna 1701 Leontiem Filippovichem Magnitskim. "Svomhu" yaisanganisira zvakawanda zvikamu. About munyori rinoudza zvikamu zviduku zvakadzama "On nhamba worutsanga kana migove" chikamu. Magnitsky anotungamirira akavhiyiwa kuti "kuputsa" nhamba, mazita avo akasiyana.

Nhasi ichiri pakati pamatavi yakaomesesa masvomhu anonzi zvikamu zviduku. Nhoroondo zvikamu zviduku aivawo zvisiri nyore. vanhu vakasiyana dzimwe nguva pasina, dzimwe nguva nenzira nokukwereta zvakaitika vamutangira, akawana zvakakodzera kutanga, kukudziridza uye kushandisa nhamba migove. Nguva dzose achidzidzisa zvikamu zviduku zveropa hwakabuda dzinoshanda zvaanorumbidza uye nemhaka kudzvanya matambudziko. Zvakanga zvakakodzera kuti vagovane chingwa, mutarisise nyika vakaenzana, overenga mitero, kuyera nguva uye zvichingodaro. Zvakakurukurwa kushanda zvikamu uye akarongeka akavhiyiwa navo zvaitsamira nhamba wemuTesitamende pehurumende mukuru nenhanho kugadzira masvomhu. Zvisinei, nokuputsa anopfuura chiuru chimwe apfuura, nemasvomhu chikamu wakayeriswa kuti migove nenhamba, kuumbwa, akakudziridza uye zvinobudirira kushandiswa nhasi zvakasiyana-siyana zvinodiwa zvose zvinobatsira uye yokungotaura.