kasanu m'diso

Kumapeto kwa 2020, zochitika zingapo zidachitika ku mayunivesite ndi masukulu, zomwe zidayimitsidwa kuyambira ... Marichi. Chimodzi mwa izo chinali "chikondwerero" cha pi day. Pa nthawiyi, pa December 8, ndinakamba nkhani yakutali ku yunivesite ya Silesia, ndipo nkhaniyi ndi chidule cha nkhaniyo. Phwando lonse linayamba pa 9.42, ndipo nkhani yanga ikukonzekera 10.28. Kodi kulondola kumeneku kumachokera kuti? Ndizosavuta: 3 nthawi pi ndi pafupifupi 9,42, ndipo π mpaka 2 mphamvu ndi pafupifupi 9,88, ndipo ola 9 mpaka 88 mphamvu ndi 10 mpaka 28 ...

Mwambo wolemekeza nambala iyi, kufotokoza chiŵerengero cha circumference wa bwalo ndi awiri ake ndipo nthawi zina amatchedwa Archimedes mosalekeza (komanso mu zikhalidwe zolankhula Chijeremani), amachokera ku USA (onaninso: ). 3.14 Marichi "kalembedwe ka America" ​​pa 22:22, ndiye lingaliro. Zofanana ndi Chipolishi zitha kukhala pa Julayi 7 chifukwa kagawo 14/XNUMX ndi pafupifupi π bwino, zomwe…Archimedes ankazidziwa kale. Inde, Marichi XNUMX ndiye nthawi yabwino kwambiri yazochitikira zam'mbali.

Awa ndi mazana atatu ndi khumi ndi anayi ndi amodzi mwa mauthenga ochepa a masamu omwe akhala nafe kuchokera kusukulu kwa moyo wathu wonse. Aliyense akudziwa zomwe zikutanthauza"kasanu m'diso". Zimakhazikika m'chinenerocho kotero kuti zimakhala zovuta kuzifotokoza mosiyana ndi chisomo chomwecho. Nditafunsa pamalo okonzera magalimoto kuti ndalamazo zingawononge ndalama zingati, makanikayo anaganizirapo zimenezi ndipo anati: “kuŵirikiza kasanu pafupifupi ma zloty mazana asanu ndi atatu.” Ndinaganiza zopezerapo mwayi pa nkhaniyi. "Mukutanthauza kuyerekezera koyipa?". Makanikayo ayenera kuti anaganiza kuti sindinamve bwino, choncho anabwereza kuti, “Sindikudziwa kuti ndi zingati, koma kasanu diso lingakhale 800.”

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Ndi chiyani? Nkhondo Yachiwiri Yadziko Lonse isanayambe kugwiritsa ntchito mawu akuti "ayi" palimodzi, ndipo ndinasiya pamenepo. Sitikuchita pano ndi ndakatulo zazikulu zosafunikira, ngakhale ndimakonda lingaliro lakuti "chombo cha golide chimatulutsa chisangalalo." Funsani ophunzira: Kodi ganizoli likutanthauza chiyani? Koma phindu la lemba limeneli lili kwina. Chiwerengero cha zilembo m'mawu otsatirawa ndi manambala a pi. Tiyeni tiwone:

Π ≈ 3,141592 653589 793238 462643 383279 502884 197169 399375 105820 974944 592307 816406 286208 998628 034825 342117 067982 148086 513282 306647 093844 609550 582231 725359 408128 481117 450284 XNUMX XNUMX XNUMX XNUMX XNUMX XNUMX XNUMX XNUMX XNUMX XNUMX XNUMX XNUMX

Mu 1596, wasayansi wachi Dutch wochokera ku Germany Ludolf van Ceulen anawerengera mtengo wa pi mpaka 35 decimal malo. Kenako zithunzizi zinalembedwa pamanda ake. Adapereka ndakatulo ku nambala pi komanso kwa wopambana wathu wa Nobel, Wyslava Szymborska. Szymborska adachita chidwi ndi kusapezeka kwa nambala iyi komanso kuti mwina 1 mndandanda uliwonse wa manambala, monga nambala yathu ya foni, zitha kuwonekera pamenepo. Ngakhale kuti katundu woyamba ali mu nambala iliyonse yopanda nzeru (yomwe tiyenera kukumbukira kuchokera kusukulu), yachiwiri ndi mfundo yosangalatsa ya masamu yomwe imakhala yovuta kutsimikizira. Mutha kupezanso mapulogalamu omwe amapereka: ndipatseni nambala yanu yafoni ndipo ndikuuzeni komwe ili mu pi.

Pamene pali zozungulira, pali tulo. Ngati tili ndi nyanja yozungulira, ndiye kuti kuyenda mozungulira ndi nthawi 1,57 kuposa kusambira. Ndithudi, izi sizikutanthauza kuti tidzasambira pang’onopang’ono kuŵirikiza kamodzi ndi theka kapena kaŵiri kuposa momwe tingadutse. Ndinagawana mbiri yapadziko lonse ya 100m ndi mbiri yapadziko lonse ya 100m. Chochititsa chidwi, mwa amuna ndi akazi, zotsatira zake zimakhala zofanana ndipo ndi 4,9. Timasambira mochedwa nthawi 5 kuposa momwe timathamangira. Kupalasa ndi kosiyana kotheratu - koma vuto losangalatsa. Ili ndi nkhani yayitali kwambiri.

Pothawa Wankhanzayo, Wokongolayo wokongola komanso wolemekezeka adapita kunyanja. Woyipayo amathamangira m'mphepete mwa nyanja ndikudikirira kuti amutsike. Inde, amathamanga kwambiri kuposa mizere ya Dobry, ndipo ngati athamanga bwino, Dobry amathamanga. Chifukwa chake mwayi wokha wa Zoyipa ndikupeza Zabwino kuchokera kugombe - kuwombera kolondola kuchokera ku mfuti sichosankha, chifukwa. Zabwino zili ndi chidziwitso chofunikira chomwe Zoipa akufuna kudziwa.

Good amatsatira njira zotsatirazi. Amasambira kudutsa nyanja, pang'onopang'ono akuyandikira gombe, koma nthawi zonse amayesetsa kukhala kumbali ina ya Woipayo, yemwe amathamangira kumanzere, kenako kumanja. Izi zikuwonetsedwa pachithunzichi. Lolani Zoyipa zoyambira kukhala Z₁, ndipo Dobre ali pakati pa nyanja. Pamene Zly akupita ku Z₁, Good adzasambira mpaka D.₁pamene Zoipa zili mu Z₂, chabwino D₂. Idzayenda mozungulira, koma motsatira lamuloli: momwe zingathere kuchokera ku Z. Komabe, pamene ikuchoka pakatikati pa nyanja, Zabwino ziyenera kuyenda mozungulira zazikulu ndi zazikulu, ndipo panthawi ina sizingatheke. tsatirani mfundo yakuti “kukhala mbali ina ya Choipa.” Kenako anapalasa ndi mphamvu zake zonse mpaka kumtunda, akumayembekezera kuti Woipayo sadzalambalala nyanjayo. Kodi Zabwino zidzatheka?

Yankho limadalira momwe Good angapalase mofulumira poyerekezera ndi mtengo wa Miyendo Yoyipa. Tiyerekeze kuti Munthu Woipayo amathamanga pa liwiro la liwiro la Munthu Wabwino panyanjapo. Chifukwa chake, bwalo lalikulu kwambiri, pomwe Wabwino amatha kupalasa kuti akane Zoipa, ali ndi utali wocheperako nthawi imodzi kuposa utali wa nyanja. Kotero, mu chithunzi chomwe tili nacho. Pamalo W, Mtundu wathu umayamba kupalasa kulowera kugombe. Izi ziyenera kupita 

 ndi liwiro

Amasowa nthawi.

Woipa akuthamangitsa mapazi ake abwino kwambiri. Ayenera kumaliza theka la bwalo, zomwe zingamutengere masekondi kapena maminiti, malingana ndi magawo omwe asankhidwa. Ngati izi ndizoposa mathero abwino:

Wabwino adzapita. Maakaunti osavuta amawonetsa zomwe ziyenera kukhala. Ngati Munthu Woipa athamanga kwambiri kuposa 4,14 nthawi ya Munthu Wabwino, sizimatha bwino. Ndipo apanso, nambala yathu pi ikulowererapo.

Chozungulira ndi chokongola. Tiyeni tiwone chithunzi cha mbale zitatu zokongoletsera - ndili nazo pambuyo pa makolo anga. Kodi dera la curvilinear triangle pakati pawo ndi chiyani? Iyi ndi ntchito yosavuta; yankho lili pachithunzi chomwechi. Sitikudabwa kuti zikuwoneka mu ndondomeko - pambuyo pake, pamene pali kuzungulira, pali pi.

Ndinagwiritsa ntchito liwu lomwe mwina silinali lodziwika bwino:. Ili ndilo dzina la nambala pi mu chikhalidwe cholankhula Chijeremani, ndipo zonsezi zikomo kwa Dutch (kwenikweni Mjeremani yemwe ankakhala ku Netherlands - dziko linalibe kanthu panthawiyo), Ludolf wa Seoulen... Mu 1596 g. anawerengera manambala 35 a kukulitsa kwake ku decimal. Mbiri iyi idachitika mpaka 1853, pomwe William Rutherford adawerengera mipando 440. Yemwe ali ndi mbiri yowerengera pamanja ndi (mwinamwake kwanthawizonse) William Shanksamene, pambuyo pa zaka zambiri za ntchito, lofalitsidwa (mu 1873) kuwonjezera ku manambala 702. Pokhapokha mu 1946, manambala omaliza a 180 adapezeka kuti ndi olakwika, koma zidakhala choncho. 527 ndi zolondola. Zinali zosangalatsa kupeza cholakwikacho. Atangotulutsa zotsatira za Shanks, adakayikira kuti "chinachake chalakwika" - panali zisanu ndi ziwiri zokayikitsa zomwe zikuchitika. Lingaliro lomwe silinatsimikizidwebe (December 2020) likunena kuti manambala onse ayenera kuwoneka pafupipafupi. Izi zidapangitsa D.T. Ferguson kukonzanso kuwerengera kwa Shanks ndikupeza cholakwika cha "wophunzira"!

Pambuyo pake, ma Calculator ndi makompyuta anathandiza anthu. Yemwe ali pano (December 2020) yemwe ali ndi mbiri ndi Timothy Mullican (50 thililiyoni malo decimal). Zowerengerazo zidatenga ... masiku 303. Tiyeni tisewere: kuchuluka kwa malo omwe nambalayi ingatenge, yosindikizidwa mu bukhu lokhazikika. Mpaka posachedwa, "mbali" yosindikizidwa ya malembawo inali zilembo 1800 (mizere 30 ndi mizere 60). Tiyeni tichepetse chiwerengero cha zilembo ndi m'mphepete mwamasamba, tiwonjezere zilembo 5000 pa tsamba, ndikusindikiza mabuku amasamba 50. Chifukwa chake zilembo XNUMX thililiyoni zitha kutenga mabuku mamiliyoni khumi. Osati zoipa, chabwino?

Funso nlakuti, kodi kulimbana koteroko kuli ndi phindu lanji? Malinga ndi kaonedwe ka chuma kokha, n’chifukwa chiyani wokhometsa msonkho ayenera kulipira “zosangulutsa” zoterozo za akatswiri a masamu? Yankho silovuta. Choyamba, kuchokera ku Seoulen anatulukira zosowekapo zowerengera, ndiye zothandiza pakuwerengera kwa logarithmic. Akadauzidwa kuti: chonde, pangani malo opanda kanthu, akanayankha: chifukwa chiyani? Mofananamo lamulo:. Monga mukudziwira, kutulukira uku sikunangochitika mwangozi, koma kumachokera ku kafukufuku wamtundu wina.

Chachiwiri, tiyeni tiwerenge zomwe amalemba Timothy Mullican. Pano pali kubereka kwa chiyambi cha ntchito yake. Pulofesa Mullican ali pachitetezo cha cybersecurity, ndipo pi ndimasewera ang'onoang'ono kotero kuti adangoyesa makina ake atsopano a cybersecurity.

Ndipo kuti 3,14159 mu uinjiniya ndiyokwanira, ndiye nkhani ina. Tiyeni tiwerenge mophweka. Jupiter ndi 4,774 Tm kutali ndi Dzuwa (terameter = 1012 metres). Kuti muwerenge mozungulira bwalo loterolo wokhala ndi utali wozungulira mpaka kulondola kosamveka kwa milimita imodzi, zingakhale zokwanira kutenga π = 1.

Chithunzi chotsatira chikuwonetsa kotala la njerwa za Lego. Ndidagwiritsa ntchito 1774 pads ndipo inali pafupifupi 3,08 pi. Osati zabwino kwambiri, koma zomwe mungayembekezere? Bwalo silingapangidwe ndi mabwalo.

Ndendende. Nambala pi imadziwika kuti ndi bwalo lalikulu - vuto la masamu lomwe lakhala likuyembekezera yankho lake kwa zaka zoposa 2000 - kuyambira nthawi zachi Greek. Kodi mungagwiritse ntchito kampasi ndi njira yowongoka kuti mupange lalikulu lomwe dera lake ndi lofanana ndi dera lomwe mwapatsidwa?

Mawu akuti "square of a circle" alowa m'chinenero cholankhulidwa ngati chizindikiro cha chinthu chosatheka. Ndikukankhira fungulo kuti ndifunse, kodi uku ndiko kuyesa kudzaza ngalande yaudani yomwe imalekanitsa nzika za dziko lathu lokongola? Koma ndimapewa kale mutuwu, chifukwa mwina ndimangomva masamu.

Ndipo kachiwiri chinthu chomwecho - yankho la vuto la squaring bwalo silinawonekere kotero kuti wolemba yankho, Charles Lindemann, mu 1882 adakhazikitsidwa ndipo pamapeto pake adapambana. Kumlingo wina inde, koma zinali zotsatira za kuwukira kochokera kutsogolo kotakata. Akatswiri a masamu aphunzira kuti pali mitundu yosiyanasiyana ya manambala. Osati zowerengeka zokha, zomveka (ndiko kuti, tizigawo) komanso zopanda nzeru. Kusayerekezeka kungakhalenso kwabwinoko kapena koipitsitsa. Tikhoza kukumbukira kuchokera kusukulu kuti nambala yopanda nzeru ndi √2, nambala yosonyeza chiŵerengero cha kutalika kwa diagonal ya sikweya mpaka kutalika kwa mbali yake. Monga nambala iliyonse yopanda nzeru, ili ndi chowonjezera chosatha. Ndiroleni ndikukumbutseni kuti kukulitsa nthawi ndi nthawi ndi katundu wa ziwerengero zomveka, i.e. Nambala zachinsinsi:

Apa kutsatizana kwa manambala 142857 kubwereza kosatha.Kwa √2 izi sizidzachitika - ichi ndi gawo la kusalingalira. Koma mukhoza:

(gawo likupitirira mpaka kalekale). Ife tikuwona chitsanzo apa, koma cha mtundu wina. Pi sichiri chofala chotero. Sichingapezeke pothetsa algebraic equation - ndiko kuti, imodzi yomwe mulibe muzu wa square, kapena logarithm, kapena trigonometric function. Izi zikuwonetsa kale kuti sizingapangidwe - zojambula zozungulira zimatsogolera ku ntchito za quadratic, ndi mizere - mizere yowongoka - ku ma equation a digiri yoyamba.

Mwina ndinapatuka pa chiwembu chachikulu. Kukula kokha kwa masamu onse kunapangitsa kuti zibwerere ku chiyambi - ku masamu akale okongola a oganiza omwe anatipangira ife chikhalidwe cha ku Ulaya cha kulingalira, chomwe chiri chokayikitsa lero ndi ena.

Mwa njira zambiri zoyimilira, ndinasankha ziwiri. Woyamba wa iwo timayanjana ndi surname Gottfried Wilhelm Leibniz (1646-1716).

Koma adadziwika (chitsanzo, osati Leibniz) kwa katswiri wachihindu wazaka zapakati Madhava wa Sangamagram (1350-1425). Kusamutsa zidziwitso panthawiyo sikunali kopambana - kulumikizana kwa intaneti nthawi zambiri kumakhala kovutirapo, ndipo kunalibe mabatire amafoni am'manja (chifukwa zamagetsi zinali zisanayambike!). Njirayi ndi yokongola, koma yopanda ntchito powerengera. Kuchokera ku zosakaniza zana, "kokha" 3,15159 imapezeka.

ali bwinoko pang'ono Fomula ya Viète (yochokera ku ma quadratic equations), ndipo chilinganizo chake ndi chosavuta kukonza chifukwa mawu otsatirawa ndi muzu wapakati wa zam'mbuyo kuphatikiza ziwiri.

Tikudziwa kuti bwalo ndi lozungulira. Titha kunena kuti uku ndi kuzungulira kwa 100%. Katswiri wa masamu adzafunsa: kodi china chake sichingakhale 1 peresenti yozungulira? Mwachiwonekere, iyi ndi oxymoron, mawu omwe ali ndi zotsutsana zobisika, monga, mwachitsanzo, ayezi otentha. Koma tiyeni tiyese kuyesa momwe mawonekedwewo angakhalire ozungulira. Zikuoneka kuti muyeso wabwino umaperekedwa ndi ndondomeko yotsatirayi, yomwe S ndi malo ndipo L ndi circumference ya chiwerengerocho. Tiyeni tiwone kuti bwalo ndilozungulira kwenikweni, kuti sigma ndi 6. Dera la bwalo ndilozungulira. Timayika ... ndikuwona chomwe chiri cholondola. Kodi square ndi yozungulira bwanji? Mawerengedwewo ndi ophweka, sindidzawapatsa. Tengani hexagon yokhazikika yolembedwa mozungulira ndi radius. Zozungulira mwachiwonekere ndi XNUMX.

Chipolishi

Nanga bwanji hexagon wamba? Kuzungulira kwake ndi 6 ndi malo ake

Kotero tili nawo

omwe ali pafupifupi ofanana ndi 0,952. Hexagon ndi yoposa 95% "yozungulira".

Chotsatira chosangalatsa chimapezedwa powerengera kuzungulira kwa bwalo lamasewera. Malinga ndi malamulo a IAAF, zowongoka ndi zokhotakhota ziyenera kukhala zazitali mamita 40, ngakhale kuti kupatuka kumaloledwa. Ndikukumbukira kuti Bislet Stadium ku Oslo inali yopapatiza komanso yayitali. Ndimalemba kuti "zinali" chifukwa ndidathamanganso (kwa amateur!), Koma zaka zopitilira XNUMX zapitazo. Tiyeni tiwone:

Ngati arc ili ndi utali wa mita 100, utali wa arcyo ndi mita. Dera la udzu ndi masikweya mita, ndipo malo omwe ali kunja kwake (komwe kuli ma boardboards) amakwana masikweya mita. Tiyeni tiphatikize izi mu fomula:

Ndiye kodi kuzungulira kwa bwalo lamasewera kuli ndi chochita ndi ma equilateral triangle? Chifukwa kutalika kwa makona atatu ofanana ndi nambala yofanana ya mbali. Ndi mwachisawawa manambala, koma ndi zabwino. Ndimachikonda. Ndi owerenga?

Chabwino, ndizabwino kuti ndi yozungulira, ngakhale ena angatsutse chifukwa kachilombo komwe kamakhudza tonsefe ndi kozungulira. Osachepera ndi momwe amajambula.