kashanu muziso

Pakupera kwa2020, zviitiko zvakati wandei zvakaitwa kumayunivhesiti nezvikoro, zvakamiswa kubva ... Kurume. Imwe yacho yaive "mhemberero" yezuva repi. Pachiitiko ichi, musi wa8 Zvita, ndakapa hurukuro iri kure kuYunivhesiti yeSilesia, uye chinyorwa ichi ipfupiso yehurukuro yacho. Bato rose rakatanga pa9.42, uye hurukuro yangu yakarongerwa 10.28. Kururama kwakadaro kunobva kupi? Zviri nyore: 3 nguva pi inosvika 9,42, uye π kune 2nd simba rinenge 9,88, uye awa 9 kusvika 88th simba 10 kusvika 28th ...

Tsika yekukudza nhamba iyi, ichiratidza chiyero chedenderedzwa kusvika padhayamita yaro uye dzimwe nguva inodaidzwa kuti Archimedes nguva dzose (pamwe chete netsika dzekutaura chiGerman), anobva kuUSA (onawo: ) 3.14 Kurume "American style" pa22:22, saka pfungwa. Kufanana nePolish kwakaenzana kungave kwaChikunguru 7 nekuti chikamu 14/XNUMX chinosvika π zvakanaka, izvo…Archimedes aitoziva. Zvakanaka, Kurume XNUMX ndiyo nguva yakanakisa yezviitiko zvepadivi.

Aya matatu negumi nemana mazana nderimwe remashoko mashoma emasvomhu akasara ainesu kubva kuchikoro kweupenyu hwose. Munhu wese anoziva zvazvinoreva"kashanu muziso". Zvakadzika midzi mumutauro zvokuti zvakaoma kuzvitaura zvakasiyana uye nenyasha dzakafanana. Apo ndakabvunza panzvimbo inogadziridza motokari kuti kugadzira kwaigona kuita marii, makanika akafunga nezvazvo ndokuti: “kashanu kanenge mazloty ane mazana masere.” Ndakasarudza kushandisa mukana wacho. "Unoreva rough approximation?". Makanika anofanira kunge akafunga kuti handina kunzwa zvisizvo, saka akadzokorora, “Handizivi kuti ingani chaizvo, asi kashanu ziso ringasvika 800.”

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Ndezvei? Hondo Yenyika Yechipiri isati yasvika yakashandisa "kwete" pamwe chete, uye ndakaisiya ipapo. Isu hatisi kubata pano nenhetembo yakasarudzika, kunyangwe ini ndinoda pfungwa yekuti "chikepe chegoridhe chinopomba mufaro." Bvunza vadzidzi: Pfungwa iyi inorevei? Asi kukosha kwechinyorwa ichi kuri kumwewo. Huwandu hwemavara mumazwi anotevera ndiwo manhamba ekuwedzera kwepi. Ngationei:

Π ≈ 3,141592 653589 793238 462643 383279 502884 197169 399375 105820 974944 592307 816406 286208 998628 034825 342117

Muna 1596, musayendisiti wechiDutch anobva kuGermany Ludolf van Seulen yakaverengera kukosha kwepi kusvika makumi matatu neshanu nzvimbo dzedesimali. Ipapo mifananidzo iyi yakanyorwa paguva rake. Akatsaurira nhetembo kune nhamba pi uye kune wedu Nobel mubairo, Vislava Shimborska. Szymborska akafadzwa nekusave-periodicity yenhamba iyi uye chokwadi chekuti paine mukana 1 imwe neimwe kutevedzana kwemanhamba, senge nhamba yedu yefoni, ichaitika ipapo. Nepo chivako chekutanga chiri munhamba yese isina musoro (iyo yatinofanira kurangarira kubva kuchikoro), yechipiri idi remasvomhu rinonakidza iro rakaoma kuratidza. Unogona kuwana mapurogiramu anopa: ndipe nhamba yako yefoni uye ini ndichakuudza kuti iripi mu pi.

Pane kutenderera, pane hope. Kana tiine dziva rakatenderera, saka kufamba-famba kwaro kwakareba 1,57 nguva kupfuura kushambira. Chokwadi, izvi hazvirevi kuti tichashambira zvishoma nekamwe nehafu kusvika kaviri pane zvatichapfuura. Ndakagovera rekodhi repasi re100m nerekodhi repasi re100m. Sezvineiwo, muvarume nevakadzi, mhedzisiro yacho inenge yakafanana uye ndeye 4,9. Tinoshambira ka5 zvishoma pane zvatinomhanya. Kukwasva kwakasiyana zvachose - asi idambudziko rinonakidza. Rine rungano rwakareba.

Achitiza Muponesi aidzingirira, Akanaka uye anokudzwa Akanaka akaenda kugungwa. Munhu akaipa anomhanya achitevedza mahombekombe uye anomirira kuti amuite kumhara. Zvechokwadi, anomhanya kupfuura Dobry rows, uye kana akamhanya zvakanaka, Dobry anokurumidza. Saka mukana wega weZvakaipa ndewekutora Zvakanaka kubva kumahombekombe - pfuti chaiyo kubva kupfuti haisi sarudzo, nekuti. Zvakanaka zvine ruzivo rwakakosha rwunoda kuziva Zvakaipa.

Yakanaka inonamatira kune inotevera zano. Anoshambira achiyambuka gungwa, zvishoma nezvishoma achisvika kumahombekombe, asi achigara achiedza kuva kune rumwe rutivi kubva kune Wakaipa, uyo anongomhanyira kuruboshwe, ipapo kurudyi. Izvi zvinoratidzwa mumufananidzo. Rega Kuipa kutange chinzvimbo kuve Z₁, uye Dobre iri pakati pegungwa. Kana Zly achienda kuZ₁, Zvakanaka achashambira kuenda kuD.₁apo Zvakaipa zviri muZ₂, zvakanaka D₂. Ichayerera nenzira yegzag, asi mukuteerera mutemo: kure sezvinobvira kubva kuZ. Zvisinei, sezvainofamba kubva pakati pegungwa, Yakanaka inofanira kufamba mumakwikwi makuru uye makuru, uye pane imwe nguva haigoni. vanoomerera kumusimboti wokuti “kuva kune rumwe rutivi rwaChakaipa.” Ipapo akakwasva nesimba rake rose akananga kumahombekombe, achitarisira kuti Wakaipa haasati aizopfuura negungwa. Ko Good achabudirira here?

Mhinduro yacho inobva pakuti Chakanaka chinogona kukurumidza sei kukwasva maererano nekukosha kwemakumbo eZvakaipa. Tomboti Munhu Akashata anomhanya nespeed s times the speed yeMunhu Akanaka padhamu. Naizvozvo, denderedzwa hombe, panogona kukwasva Akanaka kuti arambe Zvakaipa, ane radius idiki zvakapetwa kamwechete pane nzvimbo yedhamu. Saka, mukudhirowa tine. Panguva W, Rudzi rwedu runotanga kukwasva takananga kumahombekombe. Izvi zvinofanira kuenda 

 nekukurumidza

Anoda nguva.

Akaipa ari kudzingirira tsoka dzake dzose dzakanakisisa. Anofanira kupedza hafu yedenderedzwa, iyo inomutora masekonzi kana maminetsi, zvichienderana nezvikamu zvakasarudzwa. Kana izvi zvinopfuura kuguma kunofadza:

Akanaka achaenda. Maakaundi akareruka anoratidza zvazvinofanira kuva. Kana Munhu Akashata achimhanya kupfuura 4,14 nguva yeMunhu Akanaka, hazvipere zvakanaka. Uye pano, zvakare, nhamba yedu pi inopindira.

Chii chakatenderera chakanaka. Ngatitarisei pamufananidzo wemapuleti matatu ekushongedza - ndine iwo mushure mevabereki vangu. Ndeipi nzvimbo ye curvilinear triangle pakati pavo? Iri ibasa riri nyore; mhinduro iri mumufananidzo mumwe chete. Hatisi kushamisika kuti inoratidzika mufomura - shure kwezvose, apo pane kutenderera, kune pi.

Ndakashandisa izwi ringangove risingazivikanwe:. Iri ndiro zita renhamba pi mumutauro wekutaura chiGerman, uye izvi zvese nekuda kwechiDutch (chaizvoizvo muGerman aigara muNetherlands - nyika haina basa panguva iyoyo), Ludolf weSeoulen... Muna 1596 akaverenga manhamba makumi matatu nemashanu ekuwedzera kwake kusvika kudesimali. Rekodhi iyi yakabata kusvika 1853, apo William Rutherford vakaverenga zvigaro mazana mana nemakumi mana. Iyo inobata rekodhi yekuverenga kwemanyorero ndeye (zvichida zvachose) William Shanksuyo, mushure memakore mazhinji ebasa, akabudiswa (muna 1873) kuwedzera kusvika ku702 manhamba. Muna 1946 chete, nhamba dzekupedzisira 180 dzakawanikwa dzisina kururama, asi zvakaramba zvakadaro. 527 chokwadi. Zvainakidza kuwana tsikidzi pachayo. Nguva pfupi mushure mekuburitswa kwemhedzisiro yaShanks, vakafungidzira kuti "chimwe chinhu chaive chisina kumira zvakanaka" - pakanga paine mashoma manomwe aifungidzira mukusimudzira. Iyo ichiri isina kuratidzwa (Zvita 2020) hypothesis inotaura kuti nhamba dzese dzinofanirwa kuoneka neiyo frequency yakafanana. Izvi zvakakurudzira D.T. Ferguson kuti adzokorore kuverenga kwaShanks uye kuwana kukanganisa kwe "mudzidzi"!

Gare gare, makarukureta nemakombiyuta zvakabatsira vanhu. Iyezvino (Zvita 2020) rekodhi inobata Timothy Mullican (50 trillion decimal decimal nzvimbo). Kuverenga kwakatora ... 303 mazuva. Ngatitambe: inzvimbo yakawanda sei ingatore nhamba iyi, yakadhindwa mubhuku remazuva ese. Kusvika nguva pfupi yadarika, "divi" rakadhindwa rezvinyorwa raive nemavara 1800 (mitsetse makumi matatu nemitsara makumi matanhatu). Ngatidzikisei huwandu hwemavara uye micheto yepeji, cram mavara 30 papeji, uye tidhinde mabhuku makumi mashanu emapeji. Saka 60 matiririyoni emavara angatora mamirioni gumi mabhuku. Kwete zvakaipa, handiti?

Mubvunzo ndewokuti, chii chiri chinangwa chekurwa kwakadaro? Kubva pamaonero ehupfumi chete, nei muteresi achifanira kubhadhara "kuvaraidzwa" kwakadaro kwenyanzvi dzemasvomhu? Mhinduro haina kuoma. Chekutanga, kubva kuSeoulen akagadzira ma blanks ekuverenga, yobva yabatsira pakuverenga logarithmic. Dai akaudzwa kuti: ndapota, kuvaka ma blanks, angadai akapindura: sei? Saizvozvowo murayiro:. Sezvaunoziva, kuwanikwa uku hakuna kungoitika netsaona, asi zvakadaro ne-chigadzirwa chetsvakiridzo yerumwe rudzi.

Chechipiri, ngativerengei zvaanonyora Timothy Mullican. Heino kudhindwa kwekutanga kwebasa rake. Muzvinafundo Mullican ari mucybersecurity, uye pi ibasa diki zvekuti akangoyedza cybersecurity system yake nyowani.

Uye iyo 3,14159 muinjiniya inopfuura zvakakwana, ndiyo imwe nyaya. Ngatiite calculation iri nyore. Jupiter iri 4,774 Tm kure neZuva (terameter = 1012 metres). Kuti uverenge denderedzwa redenderedzwa rakadaro neradius yakadaro kune chaiyo isina musoro yemirimita imwe, zvingakwana kutora π = 1.

Mufananidzo unotevera unoratidza chikamu chechina cheLego zvidhinha. Ndakashandisa 1774 pads uye yaive ingangoita 3,08 pi. Kwete zvakanakisa, asi chii chekutarisira? Denderedzwa harigoni kugadzirwa nemakona.

Ndizvozvo. Nhamba pi inozivikanwa kuva denderedzwa square - dambudziko remasvomhu rave rakamirira mhinduro yaro kwemakore anopfuura 2000 - kubva panguva dzechiGiriki. Unogona here kushandisa kambasi uye kutwasanuka kugadzira sikweya ine nzvimbo yakaenzana nenzvimbo yedenderedzwa rakapihwa?

Izwi rokuti "square of the circle" rapinda mumutauro wekutaura sechiratidzo chechinhu chisingagoneki. Ini ndinodzvanya kiyi yekubvunza, iyi ndiyo imwe nzira yekuyedza kuzadza goronga reruvengo rinoparadzanisa vagari venyika yedu yakanaka? Asi ini ndinotonzvenga nyaya iyi, nekuti pamwe ndinongonzwa mumasvomhu.

Uye zvakare chinhu chimwe chete - mhinduro yedambudziko re squaring denderedzwa haina kuoneka nenzira yekuti munyori wemhinduro, Charles Lindemann, muna 1882 akagadzwa uye pakupedzisira akabudirira. Kusvika kumwero wakati hungu, asi wakanga uri mugumisiro wokurwiswa kwaibva pamberi pakafararira. Nyanzvi dzemasvomhu dzakadzidza kuti kune marudzi akasiyana enhamba. Kwete chete nhamba, zvinonzwisisika (kureva, zvikamu) uye zvisina musoro. Kusayera kunogonawo kuva nani kana kuipa. Tinogona kurangarira kubva kuchikoro kuti nhamba isina musoro i√2 - nhamba inoratidzira reshiyo yehurefu hwediagonal yechikwere kusvika pakureba kwedivi rayo. Kufanana nenhamba ipi neipi isina musoro, ine kuwedzera kusingagumi. Rega ndikuyeuchidze kuti kuwedzera nguva nenguva inzvimbo yenhamba dzinonzwisisika, i.e. private integers:

Pano nhevedzano yenhamba 142857 inodzokororwa nekusingaperi.Kuna √2 izvi hazvizoitiki - ichi chikamu chekusanzwisisa. Asi unogona:

(chikamu chinoenderera nekusingaperi). Isu tinoona pateni pano, asi yerudzi rwakasiyana. Pi haisati yakajairika. Haikwanise kuwanikwa nekugadzirisa algebraic equation - kureva, iyo isina square root, kana logarithm, kana trigonometric mabasa. Izvi zvinotoratidza kuti hazvigadzirike - kudhirowa madenderedzwa kunotungamirira kumabasa equadratic, uye mitsetse - mitsetse yakatwasuka - kune equations yedhigirii rekutanga.

Pamwe ndakatsauka kubva pakuronga kukuru. Kuvandudzwa kwemasvomhu chete ndiko kwakaita kuti zvikwanisike kudzokera kune zvakabva - kune masvomhu ekare akanaka evafungi vakatisikira tsika yekuEurope yekufunga, izvo zvisinganyatso zivikanwa nhasi nevamwe.

Pakati pemaitiro akawanda anomiririra, ndakasarudza maviri. Chekutanga chazvo tinochibatanidza nesurname Gottfried Wilhelm Leibniz (1646-1716).

Asi aizivikanwa (muenzanisiro, kwete Leibniz) kunyanzvi yekare yechiHindu Madhava yeSangamagram (1350-1425). Kuendeswa kweruzivo panguva iyoyo kwanga kusiri kukuru - kubatana kweInternet kwaigara kusinganzwisisike, uye pakanga pasina mabhatiri enharembozha (nekuti magetsi akange asati agadzirwa!). Iyo formula yakanaka, asi haina basa pakuverenga. Kubva kune zana zvigadzirwa, "chete" 3,15159 inowanikwa.

ari nani zvishoma Viète's formula (iyo kubva kuquadratic equations) uye fomula yacho iri nyore kuronga nekuti temu inotevera muchigadzirwa ndiyo square root yeyapfuura plus mbiri.

Tinoziva kuti denderedzwa rakatenderera. Tinogona kutaura kuti uku kutenderera kwe100%. Nyanzvi yemasvomhu inobvunza kuti: chingave chinhu chisiri 1 muzana kutenderera? Sezviri pachena, iyi inonzi oxymoron, mutsara une kupesana kwakavanzika, zvakadai, semuenzaniso, chando chinopisa. Asi ngatiedzei kuyera kuti maumbirwo angave akatenderedzwa sei. Zvinoitika kuti chiyero chakanaka chinopiwa nenzira inotevera, iyo S ndiyo nzvimbo uye L ndiyo denderedzwa yemufananidzo. Ngationei kuti denderedzwa rakanyatsotenderera, kuti sigma ndeye 6. Nzvimbo yedenderedzwa ndiyo denderedzwa. Isu tinoisa ... uye toona izvo zvakanaka. Sikweya yakatenderedzwa zvakadii? Macalculations akangoita simple, handichatombovape. Tora hexagon yenguva dzose yakanyorwa mudenderedzwa ine radius. Iyo perimeter iri pachena XNUMX.

Pole

Zvakadini nehexagon yenguva dzose? Denderedzwa rayo i6 uye nzvimbo yayo

Saka tine

iyo inenge yakaenzana ne0,952. Hexagon inopfuura 95% "round".

Mhedzisiro inonakidza inowanikwa pakuverenga kutenderera kwenhandare yemitambo. Zvinoenderana nemirairo yeIAAF, mitsetse uye macurves anofanirwa kureba makumi mana emamita, kunyangwe kutsauka kuchibvumidzwa. Ndinoyeuka kuti Bislet Stadium muOslo yaiva nhete uye yakareba. Ini ndinonyora "zvaive" nekuti ndakatombomhanya pazviri (kune amateur!), Asi anopfuura makore 40 apfuura. Ngatitarisei:

Kana arc ine radius yemamita zana, radius yearc iyoyo mita. Nzvimbo yelawn ine masikweya metres, uye nzvimbo iri kunze kwayo (pane maspringboards) inokwana masikweya metres. Ngatibatanidzei izvi mufomula:

Saka kutenderera kwenhandare yemitambo kune chekuita here nehutatu hwakaenzana? Nekuti kureba kwegonyonhatu yakaenzana inhamba imwe yenguva padivi. Iko kungosangana kwenhamba, asi yakanaka. Ndozvifarira. Uye vaverengi?

Zvakanaka, kuti rakatenderera, kunyangwe vamwe vangaramba nekuti hutachiona hunobata isu tese hwakatenderera. Ndokudhirowa kwavanozviita.