Indlela ukufumana indawo kwisangqa

Wew wesangqa na inxalenye moya, nto leyo anqongophele ngenxa kwisangqa. Ilizwi ukuba isebe yemathematika, iinkcazelo esishiyekileyo mbali bamandulo bamaGrike uHerodotus, lithatyathwe amagama lesiGrike "geo" - mhlaba "metro" - ngomlinganiselo. Kumaxesha amandulo, emva konogumbe ngamnye kuMlambo umNayile, abantu kwafuneka ukuba ukuphinda-mark iindawo zomhlaba otyebileyo kunxweme yayo. Le achazwe apha na igophe evaliweyo kuyafana, yaye zonke iingongoma kwaso bubuxoki equidistant ukusuka kwiziko yi kumgama ebizwa ngokuba radius (siyafana isiqingatha ububanzi we - umgca osuka iingongoma ezimbini wesangqa watyhutyha ilizwe embindini wayo). Kukholelwa ukuba lowo oye wafunda iimpawu isangqa, akukho bakwazi ukubona ubude balo okanye akakwazi ukuphendula lo mbuzo, "indlela yokubala indawo kwisangqa?", Akazi geometry. Ekubeni theorems kakhulu umdla, umngeni umdla onxulumene isangqa.

Wedini njenge "geometry ivili." axis ayo asoloko ukusuka kumgangatho apho ukuziqengqa, kwi kumgama elifanayo - le yenye iimpawu eziphambili. Enye impahla ebalulekileyo kwisangqa kuxhomekeke kwinto yokuba le ndawo nezisekelwe yiyo - isangqa - nezithelekiswa kummandla ubuninzi ezinye iimilo, esicaciswe ngemigca ezaphukileyo, ubude apho lilingana achazwe apha. Indlela ukufumana indawo kwisangqa? Xa uphendula lo mbuzo simele sikhumbule malunga rhoqo zezibalo: geometry mathematics inani ebalulekileyo π (unobumba Greek kufuneka libizwe ngokuba PI), nto leyo ebonisa ukuba la manani achazwe maxa wambi 3,14159 ubukhulu bayo: L = π • d = 2 • π • r (d - ubukhulu, r - radius). Oko kukuthi, isangqa enobubanzi kwimitha 1, ubude iya kulingana 3,14159 m. Khangela ixabiso ngqo kule nombolo ngokudlul ine- imbali umdla olwaba ngaxeshanye kunye kuphuhliso lwemathematika.

Le π Inombolo kwakhona kusetyenziswa ukubala kummandla isangqa. Imbali inani ngokuqhelekileyo izigaba ezithathu: ixesha yamandulo (zejometri), ixesha classical kunye nexesha omtsha ezinxulumene kokufika kweekhompyutha digital. Nokuba umYiputa, baseBhabhiloni, Geometers bamandulo amandulo Indian namGrike wayesazi ukuba lulwahlulo achazwe apha obude kancinci 3. olu lwazi kuye kwanceda izazinzulu ukumisela mmandla ungqonge formula kwisangqa. Ekubeni ixabiso π inani yaziwa, unako ukufumana indawo isangqa, endaweni ifomula: S = π • R2, isikweri r kwalo mgama. Izazinzulu ngamaxesha ahlukeneyo (kodwa Archimedes, emva kwinkulungwane 3 BC, kulo mba waba ngowokuqala) kusetyenziswa iindlela ngeendlela ukugqiba PI inombolo, yaye namhlanje iyaqhubeka ukukhangela iindlela, ibalwe kwi-computer. Le ngqo ngayo oko yenzelwe ngo-2011, sele ifikelele amanqaku alishumi ezigidi.

Iifomula ebonisa ukufumana indlela kummandla isangqa okanye indlela yokufumana indawo achazwe apha, azise nawuphi na abadala. Bezisetyenziselwa eminyaka yi zezibalo iikhalityhuleyitha, ofundele umdla ngokucokisekileyo ngakumbi igqitywe le π inani waqala ukufana umdlalo zemathematika, ngazo namhlanje ubonisa ithuba kunye neenzuzo iinkqubo kunye neekhompyutha. AmaYiputa amandulo kunye Archimedes wayekholelwa ukuba π inani ukusuka-3 ukuya 3.160. zezibalo Arab, oko kwaba ukuba ilingana 3.162. Isazinzulu Chinese Chzhan Hen kwi ngenkulungwane yesi-2, wathi ixabiso ≈ 3,1622, njalo njalo - usetsho luyaqhubeka, kodwa ngoku nazo intsingiselo entsha. Hi xikombiso, le sentengo 3.14 kuvela umhla sesikweni Matshi 14, nto leyo iya kuqwalaselwa ngemini π inani.

indawo isangqa, embindini lokwazi kwaye usebenzisa sentengo ye π inani, kube lula ibalwe. Kodwa ukufumana njani kummandla isangqa ukuba radius ayaziwa? Kwimeko kwecacileyo, ukuba indawo angohlulwa elisebenzileyo ngokwezikweri, oku kulingana kwinani izikwere, kodwa kwimeko kwisangqa, le ndlela yeyona nto efanelekileyo. Ngoko ke, ukuba ukusombulula ingxaki equlethwe umbuzo "ukuze ufumane indlela kummandla kwisangqa?", Ukusebenzisa iindlela nendima. iimpawu ngamanani ezikumila kumacala mabini inani zejometri, ebonisa ubungakanani bayo, fumana usebenzisa palettes okanye planimeter.