Yintoni uPi?

Inombolo pi mhlawumbi lelona nani lidumileyo elingenangqiqo ehlabathini. Inkoliso yabantwana ifunda ngayo esikolweni, yaye idume ngokwaneleyo ukuba ibe nosuku lwayo. Kwiifomula zemathematika, ubhalwa njengo-π, ongunobumba wesiGrike u-'pi.' Ngaphandle kolu nxibelelwano kwiGrisi yaMandulo, abantu babesazi ingcamango yepi kwimpucuko yangaphambili. UPi uye wafumana indawo kwinkcubeko edumileyo kunye neentliziyo zabaninzi, kodwa yintoni iPi ngokwenene kwaye yafunyanwa njani?

Yintoni uPi?

I-Pi ngumlinganiselo wesangqa sesangqa ukuya kwidayamitha yaso. Oku kuyinyaniso kwisangqa ngasinye, kungakhathaliseki ubungakanani. I-Pi yimathematika engaguqukiyo kunye nenani elingenangqiqo, oku kuthetha ukuba ayinakuchazwa njengeqhezu elilula. Oku kuthetha ukuba inani yidesimali engenasiphelo kwaye iingcali zezibalo zibonise ukuba inani alinazo iipatheni eziphinda-phindayo. Xa usebenza ngenani iindawo zokuqala ezintlanu zedesimali zisetyenziswa ngokubanzi, ezithi 3.14159. Abanye abantu baphinde bayenze mfutshane ibe yi-3.14.

tamzin outhwaite amaqhinga amatsha

Ukusetyenziswa kwePi

Ekuqaleni, inani le-pi lalisetyenziswa kakhulu kwijometri. Isetyenziswa ekubaleni ukumisela i-circumference kunye nommandla wesangqa kunye nomthamo kunye nommandla womphezulu wengqukuva. Ikwasetyenziswa ngokubanzi kwitrigonometry. Kwifiziksi, i-pi ihlala isetyenziswa kwiifomyula njengoko izinto ezininzi kwihlabathi elibonakalayo zingqukuva, kubandakanya iiplanethi. Ithiyori yamanani kunye neenkcukacha-manani zisebenzisa i-pi kwaye i-pi yokubala isoloko isetyenziswa kuvavanyo lwekhompyutha.

Pi ngamaxesha aMandulo

Ubungqina bubonisa ukuba amaYiputa namaBhabhiloni amandulo ayemalunga nepi. Ezinye ii-Egyptologists ziye zacebisa ukuba i-pi yayisetyenziselwa izibalo ekwakheni iPiramidi enkulu yaseGiza, kodwa ubungqina be-pi abubonakali kude kube kamva. Amacwecwe aseBhabhiloni asusela kowe-1900-1680 B.C. bhala inani eliqikelelweyo le-3.125. EYiphutha, iRhind Papyrus yamalunga no-1650 B.C. ibonisa izibalo zemathematika zaseYiputa zendawo yesangqa, usebenzisa inani elingu-3.1605 kwi-pi.

Uqikelelo lwePi

U-Archimedes (287-212 B.C.) wazoba iipolygons ngaphakathi kwesangqa kwaye wasebenzisa iTheorem yePythagorean ukubala indawo yeepolygons. Oku kwamvumela ukuba aqikelele indawo yesangqa. Usebenzise oku ukuqikelela ixabiso le-pi malunga ne-3 1/7. Lo msebenzi yiyo loo nto i-pi ngamanye amaxesha ibizwa ngokuba yiArchimedes Constant. Ingcali yezibalo yaseTshayina uZu Chongzhi (429-501) wasebenzisa inkqubo efanayo waza wabala ukuba i-pi ilingana nama-355/113 kunye neengcali zezibalo zaseIndiya zelo xesha linye nazo zazinoqikelelo lwe-pi.

Amanani okuQala achanekileyo kaPi

Ingcali yemathematika yaseIndiya uMādhava wayengumseki weSikole se-Kerala se-Astronomy neMathematika ekupheleni kweNkulungwane ye-14. Wayengomnye wabokuqala ukusebenza ngengcamango yokungenasiphelo. Uluhlu lwakhe olungenasiphelo lusebenza ngokudibanisa kunye nokuthabatha amaqhezu amanani a-odd afana no-1/3 kunye no-1/5 kwaye wavumela uMādhava ukuba abale i-pi ngokuchanekileyo kwiindawo zokuqala ezili-13. Ingcali yezibalo yaseYurophu uGottfried Leibniz yafikelela kwizigqibo ezifanayo kwiinkulungwane ezimbini kamva, kwaye olu ngcelele ngoku lwaziwa njengothotho lweMadhava-Leibniz.

Pi kwiXesha langoku

Ngexesha le-1700s iingcali zezibalo zasebenza ekwandiseni ukuchaneka kwe-pi, kwaye ngeli xesha babonisa ukuba linani elingenangqiqo. Kwakungelo xesha apho isimboli π yaqala ukusetyenziswa. Ngaphambi koku, inani lalibhekiselwa kulo ligama lesiGrike elithetha iperiphery. Ngo-1706, isazi sezibalo sase-Welsh uWilliam Jones wenza mfutshane oku ku-π nje, ongunobumba wokuqala wegama. Oku kwaduma kwaza ekugqibeleni kwamkelwa kuyo yonke imisebenzi yemathematika.

Pi kwiXesha leKhompyutha

Nangona inani elishunquliweyo lisetyenziswa kuninzi lwezicelo, abantu basazama ukufumana idecimals ezininzi zika pi. Ngaphambi kokuvela kweekhompyuter, i-pi yayibalwe kwiindawo ezingama-707. Ngo-1961, i-IBM 7090 yathatha iiyure ezisi-8 kunye nemizuzu engama-43 ukubala ipi ukuya kwi-100,000 yeendawo zedesimali. Imida iye yaqhubeka ityhalwa kwaye kwi-2002 i-pi yabalwa kwiindawo ze-24 trillion zedesimali. Kwathatha iqela leYunivesithi yaseTokyo iminyaka emi-5 ukubhala inkqubo eyenza ukubala.

yintoni indoda ye-Renaissance

Ukubala ngesandla Pi

Ukubala i-pi ngesandla, qala ngokulinganisa i-circumference yento ejikelezayo. Ukusonga umtya ojikeleze into kunika ezona ziphumo zichanekileyo. Okulandelayo, linganisa ngapha kwesangqa, uhamba embindini. Oku kububanzi besangqa. Yahlula ubude bomtya omde ngobude bobubanzi ukuze ufumane i-pi. Ukuchaneka kwe-pi kuya kuxhomekeka ekuchanekeni kwemilinganiselo.

Ubugcisa bokukhumbula uPi

Abantu abaninzi bayakonwabela ucelomngeni lokucengceleza ipi. I-Piphilology bubugcisa bokusebenzisa i-mnemonics ukunceda ukukhumbula. Imibongo kapi, okanye iipiem, zakhiwe ngendlela yokuba inani loonobumba kwigama ngalinye lihambelane namanani ka-pi. Owona mbongo udumileyo unamanani ali-15 kwaye uyafundeka: Hayi indlela endifuna ngayo isiselo, utywala ngokuqinisekileyo, emva kwezahluko ezinzima ezibandakanya i-quantum mechanics! Incwadi Hayi uVuka nguMichael Keith wasebenzisa obu buchule kwi-10,000 yokuqala yedijithi ye-pi.

Usuku lwePi

I-Pi Day yaqala ukubhiyozelwa kwi-San Francisco Exploratorium kwi-1988. Ibhiyozelwa ngo-Matshi 14 njengoko umhla ulingana namadijithi amathathu okuqala e-pi xa ibhalwe njenge-3/14. Lo ngumhla wokuzalwa wengcali yefiziksi edumileyo uAlbert Einstein. Ngo-2009, iNdlu yaBameli baseMelika yapasisa isigqibo sokwenza iPi Day ibe ngumsitho wesizwe ojolise ekwandiseni umdla kwizibalo nakwisayensi. Namhlanje, abaninzi babhiyozela inani elingenangqiqo, ngokuphindaphindiweyo ngeqhekeza lepayi.