Yadda za a sami fannin da'ira

A lissafi na da'irar ne wani ɓangare na jirgin, wanda aka iyakance ta da wani da'irar. The, MaganarMu ga wani reshe na lissafi, da kwatancin bar ta zamanin d Girkanci tarihi Herodotus, aka samu daga Girkanci kalmomi "geo" - ƙasar da kuma "Metro" - gwargwado. A zamanin da, bayan kowace ruwan tsufana na Kogin Nilu, mutane sun sake lamba yankunan m ƙasar a kan ta gaba. A karkara na cikin rufaffiyar kwana ne guda, kuma duk da maki kanta ƙarya equidistant daga cibiyar da nesa da ake kira radius (shi yayi dace da rabin diamita daga cikin - line a haɗa da maki biyu daga cikin da'irar da kuma wucewa ta hanyar da cibiyar). An yi imani da cewa, wanda bai karantar da kaddarorin wani da'irar, ba zai iya sanin ko ta tsawon ko ba zai iya amsa tambaya, "yadda za a lissafta da yankin na da'irar?", Da ba ka san lissafi. Tun da mafi ban sha'awa, kalubale da kuma ban sha'awa theorems da alaka da da'irar.

Karkara dauke "dabaran lissafi." Its axis ne ko da yaushe daga surface a kan wanda shi ne mirgina, a wannan nesa - wannan shi ne daya daga cikin babban Properties. Wani muhimmin dukiya daga cikin da'irar ta'allaka ne da cewa yankin circumscribed da shi - da'irar - idan aka kwatanta da matsakaicin yanki na sauran siffofi, delineated ta karye Lines, na tsawon abin da yake daidai ga karkara. Yadda za a sami fannin da'irar? Lokacin da amsa wannan tambaya ya kamata mu tuna game da wani ilmin lissafi m: a lissafi da kuma ilmin lissafi shi ne m yawan π (Girkanci harafi kamata a furta kamar yadda pi), wanda ya nuna cewa karkara a 3,14159 sau da diamita: L = π • d = 2 • π • r (d - diamita, r - radius). Wannan shi ne, a da'irar da diamita na 1 mita, tsawon zai zama daidai da 3,14159 m. Search daidai darajar wannan transcendental yawan yana da wani ban sha'awa tarihi wanda ya gudu a layi daya da ci gaban ilmin lissafi.

Yawan π ana amfani da yin lissafi da yankin na da'irar. A tarihin da lambar conventionally kasu kashi uku lokaci: zamanin d lokaci (lissafi), da na gargajiya zamanin da wani sabon lokaci hade tare da zuwan dijital kwakwalwa. Ko tsoho Masar, Kaldiyawa, tsohuwar India da kuma Greek geometers san cewa rabo na karkara da kuma diamita kadan mafi tsawon 3. Yana da wannan ilmi ya taimaka masana kimiyya Ya tabbatar da tsoho dabara yanki na da'irar. Tun da darajar da lambar π aka sani, shi ne zai yiwu a sami fannin da'ira, musanya dabara: S = π • r2, da square na ta radius r. Masana kimiyya a daban-daban sau (amma Archimedes, baya a cikin karni 3rd BC, a wannan batun shi ne na farko) amfani da dama hanyoyin domin sanin yawan pi, da kuma a yau ya ci gaba da neman hanyoyin, shi da aka lasafta a kan kwakwalwa. A daidaici da abin da aka tsara a shekarar 2011, ya kai goma tiriliyan alamomi.

Dabarbari nuna yadda za a samu a yankin na da'irar ko yadda za a sami wani karkara, da aka sani ga kowane tsofaffi. Da suka kasance sunã yi amfani for millennia da lissafi da kuma calculators, m kamar yadda sha'awa sosai da sosai ƙayyade yawan π fara kama wani ilmin lissafi wasanni, da wanda a yau ya nuna yiwuwar kuma amfanin shirye-shirye da kuma kwakwalwa. Ancient Masarawa da kuma Archimedes yi imani da cewa yawan π ne daga 3 zuwa 3.160. Arab lissafi, an tabbatar da cewa shi ne daidai to 3.162. Sin masanin kimiyya Chzhan Hen a 2nd karni AD, ya ce darajar ≈ 3,1622, kuma haka a - cikin search ci gaba, amma yanzu sun kai a kan wani sabon ma'anar. Alal misali, m darajar 3.14 daidai da na yau da kullum kwanan wata Maris 14, wanda aka dauke da ranar da lambar π.

yankin na da'ira, cikin radius na sanin da kuma amfani da m darajar da lambar π, za a iya sauƙi lasafta. Amma yadda za a sami fannin da'irar idan radius ne ba a sani ba? A cikin sauki hali, idan yankin za a iya raba murabba'ai, shi daidaita da adadin murabba'ai, amma a yanayin saukan daga cikin da'irar, wannan hanya ne ba su dace. Saboda haka, don magance matsalar dauke a cikin tambaya "yadda za a sami fannin da'ira?", Amfani instrumental hanyoyin. Na lamba halaye na biyu-girma geometrical adadi, nuna ta size, sami yin amfani da palettes ko planimeter.