Essence ndi mitundu ya miyezo yodalirika mu ziwerengero ndi njira zoziwerengera izo. Mitundu yamtengo wapatali pa chiwerengero ndi yaifupi: zitsanzo, tebulo

Kuyambira kuphunzira za sayansi ngati ziwerengero, ziyenera kumveka kuti liri ndi (monga sayansi iliyonse) mawu ambiri omwe ayenera kudziwika ndi kumvetsa. Lero, tidzamvetsa lingaliro lofanana ndi la mtengo wapatali, ndikupeza mtundu umene umagawana, momwe ungawawerengere. Eya, musanayambe, tiyeni tiyankhule pang'ono za mbiriyakale, komanso za momwe zinalili komanso chifukwa chake panali sayansi ngati ziwerengero.

Mbiri

Mawu omwewo "ziwerengero" amachokera ku Chilatini. Amachokera ku mawu akuti "udindo", ndipo amatanthawuza "zinthu za zinthu" kapena "zochitika." Tsatanetsatane wamfupiyi ndikuwonetsa, tanthauzo lonse ndi cholinga cha chiwerengero. Amasonkhanitsa deta pazochitikazo ndikukulolani kuti musanthule mkhalidwe uliwonse. Ntchito ndi chiwerengero cha deta chinachitidwa ngakhale ku Roma wakale. Kumeneko nkhaniyi inatengedwa ndi nzika zaulere, katundu wawo ndi katundu. Kawirikawiri, ziŵerengero zinagwiritsidwa ntchito poyambirira kupeza deta pa chiwerengero cha anthu ndi phindu lawo. Motero, mu 1061 ku England chiwerengero cha anthu oyambirira padziko lonse chinachitika. Khans, yemwe analamulira ku Russia m'zaka za zana la 13, adachitiranso zofukiza kuti alandire msonkho kuchokera m'mayiko omwe anagwidwa.

Aliyense amagwiritsa ntchito ziwerengero zawo, ndipo nthawi zambiri izi zimabweretsa zotsatira zake. Anthu atazindikira kuti si masamu okha, koma sayansi yosiyana yomwe iyenera kuti iphunzire bwino, asayansi oyambirira omwe ali ndi chidwi ndi chitukuko chake anayamba kuonekera. Anthu omwe anayamba chidwi ndi dera lino ndikuyamba kulimbikira kumvetsetsa, anali otsatira a sukulu ziwiri zikuluzikulu: sukulu ya sayansi ya sayansi ya masamu a ndale komanso sukulu yachidule ya German. Yoyamba inayamba pakati pa zaka za zana la 17 ndipo cholinga chake chinali kupereka zochitika za chikhalidwe pogwiritsa ntchito zizindikiro. Iwo ankafuna kudziwa momwe angakhalire pa zochitika zokhudzana ndi chikhalidwe cha anthu pogwiritsa ntchito kufufuza deta. Otsatira a sukulu yowonetsera amafotokozeranso njira zokhudzana ndi chikhalidwe cha anthu, koma pogwiritsa ntchito mawu okha. Iwo sakanakhoza kulingalira mphamvu za zochitika kuti amvetse bwino izo.

M'zaka zoyambirira za m'ma 1800, njira ina yachitatu ya sayansi idakwera: chiwerengero ndi masamu. Chothandizira kwambiri kuti chitukukochi chitsogolere chinapangidwa ndi wasayansi wotchuka, wolemba mbiri ku Belgium Adolf Quetelet. Ndiye amene anadziwitsa mitundu ya maiko omwe ali ndi chiwerengero cha chiwerengero chake, ndipo payekha, misonkhano yadziko lonse yoperekedwa kwa sayansiyi inayamba kuchitika. Kuchokera kumayambiriro kwa zaka za zana la makumi awiri, njira zovuta kwambiri zamasamu zakhala zikugwiritsidwa ntchito muziwerengero, mwachitsanzo, mwinamwake lingaliro.

Masiku ano, sayansi ya chiwerengero ikukula kudzera mu makompyuta. Pothandizidwa ndi mapulogalamu osiyanasiyana, aliyense akhoza kupanga graph malinga ndi deta yomwe ikufunidwa. Pa intaneti, palinso zinthu zambiri zomwe zimapereka deta iliyonse ya chiwerengero cha anthu osati osati kokha.

M'chigawo chotsatira, tidzasanthula zomwe zikutanthawuza monga ziwerengero, mitundu ya zikhalidwe zenizeni komanso zotheka. Kenaka, tikukhudza funso la momwe tingagwiritsire ntchito chidziwitso chomwe tapeza.

Kodi ziwerengero ndi ziti?

Iyi ndi sayansi yomwe cholinga chake chachikulu ndichokwanitsa kufotokozera mfundo za kuphunzira malamulo omwe akuchitika m'dera. Motero, tingathe kuganiza kuti ziwerengero zomwe zimawerengera anthu komanso zochitika zomwe zikuchitika mmenemo.

Pali ziphunzitso zambiri za sayansi:

1) Chidziwitso chachiwerengero cha ziwerengero. Kukulitsa njira zosonkhanitsira deta yolongosola ndipo ndi maziko a mbali zina zonse.

2) Ziwerengero za chikhalidwe ndi zachuma. Amaphunzira zochitika zamakono kuchokera kumbali ya chilango choyambirira ndipo zimatanthauzanso kuti zikhalidwe zake zimakhala bwanji.

3) chiwerengero cha masamu. Sizinthu zonse zomwe zili m'dziko lino lapansi. Chinachake chiyenera kuwonedweratu. Ziwerengero za masamu zimaphunzira zosawerengeka mosavuta ndi malamulo a kugawidwa kwa zowerengeka.

4) Ziwerengero zamakampani ndi mayiko. Izi ndi malo ochepa omwe amaphunzira kuchuluka kwa zochitika zomwe zimachitika m'mayiko ena kapena m'madera ena.

Ndipo tsopano tiyang'ana mitundu ya zikhalidwe zowonongeka pa ziwerengero, kufotokozera mwachidule momwe ntchito yawo ikugwiritsidwira ntchito, osati malo ochepa ngati chiwerengero.

Mitundu yamtengo wapatali pa chiwerengero

Kotero ife tinabwera ku chofunikira kwambiri, kwenikweni, pa mutu wa nkhaniyo. Zoonadi, kuti zikhale zovuta komanso zogwirizana ndi mfundo zotere monga zofunikira ndi mitundu ya zikhalidwe zenizeni muziwerengero, chidziwitso china cha masamu n'chofunika. Choyamba, kumbukirani kuti ambiri ali masamu, harmonic, geometric ndi quadratic.

Tinachita masewera a masamu kusukulu. Ndi kosavuta kuwerengera: timatenga nambala zingapo, pakati pakati pazimene muyenera kuzipeza. Onjezani manambalawa ndikugawa malire ndi nambala yawo. Masamu, izi zikhoza kuimiridwa motere. Tili ndi nambala zingapo, monga chitsanzo, mndandanda wosavuta: 1,2,3,4. Tonse tiri ndi manambala 4. Ambiri mwa masamu amapezeka motere: (1 + 2 + 3 + 4) / 4 = 2.5. Ndi zophweka. Timayamba ndi izi, chifukwa ndi zophweka kumvetsetsa mitundu ya miyezo yamtunduwu mu ziwerengero.

Tiyeneranso kufotokozera mwachidule tanthauzo la chijerengero. Tengani manambala ofanana omwe ali mu chitsanzo choyambirira. Koma tsopano, kuti tiwerenge tanthauzo la chijerengero, tiyenera kuchotsa mizu ya digiri, yomwe ili yofanana ndi chiwerengero cha manambala awa, kuchokera ku mankhwala awo. Kotero, kwa chitsanzo choyambirira, timapeza: (1 * 2 * 3 * 4) ^1/4 ~ 2.21.

Tiyeni tibwerezebe lingaliro la harmonic yovuta. Monga momwe mungathe kukumbukira kuchokera ku sukulu ya masamu, kuti muwerenge mtundu umenewu, tifunikira kuti tipeze chiwerengero chomwe chikutsutsana ndi chiwerengero cha mndandanda. Izi ndizo, timagawaniza ndi chiwerengero ichi. Kotero ife timapeza ziwerengero zosiyana. Chiŵerengero cha chiwerengero chawo chiwerengero ndipo chidzakhala chikhalidwe cha harmonic. Tengani chitsanzo chofanana: 1, 2, 3, 4. Zotsatizana zowoneka ngati izi: 1, 1/2, 1/3, 1/4. Kenaka mtundu wa harmonic ukhoza kuwerengedwa motere: 4 / (1 + 1/2 + 1/3 + 1/4) ~ 1,92.

Mitundu yonseyi yamtengo wapatali paziwerengero, zitsanzo zomwe talingalira, ndi mbali ya gulu lotchedwa mphamvu yalamulo. Palinso malire ammwamba, omwe tidzakambirana pambuyo pake. Tsopano ife tiyima pa mawonekedwe oyambirira.

Mphamvu zamagetsi

Takhala tikufufuza kale masamu, zojambula ndi harmonic. Palinso malingaliro ovuta kwambiri, otchedwa zofunikira zedi. Ngakhale kuti sizingapite kusukulu, n'zosavuta kuwerengera. Ndikofunika kuwonjezera malo owerengeka a mndandanda, pagawani chiwerengerocho ndi chiwerengero chawo, ndi kuchotsa mizere ya square pa zonsezi . Zomwe timakonda kwambiri zikuwoneka ngati izi: ((1 ² +2 ² +3 ² +4 ² ) / 4) ^1/2 = (30/4) ^1/2 ~ 2.74.

Ndipotu, zonsezi ndizopadera chabe za mphamvu zambiri. Mwachizoloŵezi, izi zikhoza kufotokozedwa motere: mphamvu ya nth isana ndi mizu ya digiri n kuchokera ku chiwerengero cha nambala mu mphamvu nth yagawidwa ndi chiwerengero cha manambala awa. Ngakhale kuti zonse sizili zovuta momwe zikuwonekera.

Komabe, ngakhale mphamvuyo ikutanthauza mtundu wina wa mtundu umodzi - chiwerengero cha Kolmogorov. Ndipotu, njira zonse zomwe tapeza zikhalidwe zosiyana siyana izi zisanawonetsedwe ngati njira imodzi: y ^-1 * ((y (x ₁ ) + y (x ₂ ) + y (x ₃ ) + ... + Y (x _n )) / n). Nazi zonse zosiyana x ndi manambala a mndandanda, ndipo y (x) ndi ntchito yomwe timatenga mtengo wamtengo wapatali. Pachifukwachi, nenani, ndi malo ozungulira, uwu ndi ntchito y = x ² , ndipo ndi masamu amatanthauza y = x. Izi ndi zodabwitsa zina zomwe nthawi zina zimatipatsa ife. Tinasankha mitundu yamtundu wapatali kufikira mapeto. Kuwonjezera pa sing'anga palizomwe zimakhazikika. Tiyeni tiyankhule za iwo.

Miyezo ya chikhalidwe cha chiwerengero cha ziwerengero. Mafilimu

Apa chirichonse chiri chovuta kwambiri pang'ono. Kuti muwononge mitundu iyi ya mawerengero mu ziwerengero ndi momwe mungaziwerengere izo, muyenera kuganizira mosamala. Pali zigawo zikuluzikulu ziwiri: mafashoni ndi apakati. Tidzakumana ndi yoyamba.

Mafilimu amapezeka kwambiri. Amagwiritsidwa ntchito nthawi zambiri kuti adziwe kufunikira kwa chinthu china. Kuti mupeze phindu lake, muyenera kupeza nthawi yoyamba. Ndi chiyani? Nthawi yokhazikika ndizoyendera zamtengo wapatali pomwe chiwerengero chilichonse chili ndifupipafupi kwambiri. Kufunikira kufotokozera, kuti muyimire bwino mtundu ndi mitundu ya miyezo yeniyeni mu ziwerengero. Gome, limene timalingalira pansipa, ndilo gawo la ntchito yomwe ili:

Onetsetsani mafashoni molingana ndi deta ya msonkhano pa tsiku ndi tsiku.

Kwa ife, nthawi yamagulu ndi gawo la zochitika tsiku ndi tsiku ndi chiwerengero chachikulu cha anthu, ndiko, 40-44. Malire ake ndi 44.

Ndipo tsopano tikambirana momwe tingawerengere mafashoni. Njirayi si yovuta ndipo ingalembedwe motere: M = x ₁ + n * (f _M -f _{M -1} ) / (( _{M M} -f _{M -1} ) + (f _M- F _{M + 1} )). Pano f _M ndi nthawi yomwe nthawi yayitali, F _M-1 ndi nthawi yomwe nthawi yayitali isanayambe (mwa ifeyi ndi 36-40), f _{M + 1} ndi nthawi yomwe nthawi yayitali yatha (kwa ife - 44-48), n ndi nthawi Ndiko kusiyana kwake pakati pa malire apansi ndi apamwamba)? X ₁ ndi mtengo wa malire apansi (mwachitsanzo izi ndi 40). Kudziwa deta yonseyi, titha kudziwa bwinobwino momwe angapangidwire tsiku lililonse: M = 40 + 4 * (24-20) / ((24-20) + (24-19)) = 40 + 16/9 = 41, ( 7).

Miyezo yolingalira yachikhalidwe ndi ziwerengero. Zamkatikati

Tidzasanthulabe kukula kwake kwazomwe timapanga, mofanana. Sitidzapita mwatsatanetsatane, tidzangoyankhula za kusiyana ndi mtundu wakale. Mu geometry, wamkati amagawanika pang'onopang'ono. Sizinthu zopanda phindu kuti ziwerengero zimenezi zimatchedwa. Ngati tilembera mndandanda (mwachitsanzo, kukula kwa chiwerengero cha chiwerengero chimodzi kapena china cholemera kuti chiwerengero chikuwonjezeke), ndiye kuti wamkatiyo adzakhala wopindulitsa kwambiri omwe amagawaniza mndandanda wa magawo awiri, ofanana nambala.

Mitundu ina ya mawerengedwe mu ziwerengero

Mitundu ya chikhalidwe, pamodzi ndi magulu amphamvu, musapereke chilichonse chomwe chiyenera kuwerengedwa m'madera osiyanasiyana. Apatseni ndi mitundu ina ya deta iyi. Choncho, pali zolemera zolemera. Mtundu uwu umagwiritsidwa ntchito pamene manambala a mndandanda ali ndi "zolemera zenizeni" zosiyana. Izi zikhoza kufotokozedwa ndi chitsanzo chophweka. Tiyeni titenge galimotoyo. Zimayenda mofulumira mosiyana pa nthawi zosiyana. Pachifukwa ichi, zikhulupiliro za nthawi ndi nthawi zomwe zimayenda bwino zimasiyana. Kotero, izi zimakhala zolemera kwenikweni. Njira iliyonse yamagetsi ya mphamvu ikhoza kulemedwa.

Mu kukonza zamagetsi, mtundu wina wa mtengo wapatali umagwiritsidwanso ntchito: pafupifupi mtengo wa logarithmic. Icho chikufotokozedwa ndi njira yowopsya yovuta, yomwe ife sitidzaiigwira.

Kodi izi zikugwiritsidwa ntchito kuti?

Ziwerengero - sayansi yomwe sichimangiriridwa ku gawo limodzi. Ngakhale kuti inalengedwa monga gawo la chikhalidwe ndi zachuma, lero njira ndi malamulo ake amagwiritsidwa ntchito mufikiliya, chemistry, ndi biology. Kudziwa zambiri m'munda uno, titha kudziwa mosavuta zomwe anthu akuchita komanso nthawi yothetsera mantha. Kawirikawiri timamva mawu akuti "kuopseza ziŵerengero", ndipo awa si mawu opanda kanthu. Sayansi iyi imatiuza za ife tokha, ndipo mwa kuphunzira moyenera izo zingachenjeze za zomwe zingachitike.

Kodi njira zotsatila zikugwirizana bwanji?

Maubwenzi pakati pawo sakhalapo nthawi zonse, mwachitsanzo, machitidwe amtunduwu sagwirizana ndi njira iliyonse kwa wina ndi mzake. Koma ndi mphamvu zonse zimakhala zosangalatsa kwambiri. Mwachitsanzo, pali malo: zilembo zikutanthawuza za manambala awiri nthawizonse ndi zazikulu kapena zofanana ndi zilembo zawo. Masamu, akhoza kulembedwa monga: (a + b) / 2> = (a * b) ^1/2 . Kusalinganika kumatsimikiziridwa mwa kunyamula mbali yanja lamanja kumanzere ndi kumagulu. Zotsatira zake, timapeza kusiyana kwa mizu, mzere. Ndipo popeza chiwerengero chilichonse m'kati mwake chiri cholimbikitsa, motero, kusalinganika kumakhala koona.

Kuonjezerapo, pali mgwirizano wambiri wamakono. Zikuoneka kuti nthawi zambiri harmonic nthawi zonse imakhala yochepa kuposa chiwerengero cha masamu, omwe sali ovomerezeka. Ndipo zotsirizazo zimachokera, pambali pake, kuti zikhale zochepa kuposa zomwe zikutanthauza. Mukhoza kutsimikizira kuti zolingazi ndi zolondola, makamaka pa chitsanzo cha nambala ziwiri - 10 ndi 6.

Chosangalatsa ndi chiyani?

N'zochititsa chidwi kuti mitundu ya ma mtengo omwe amawoneka kuti akuwonetsa masewera apakati, angathe kumuuza munthu wodziwa zambiri. Tikayang'ana nkhaniyi, palibe amene amaganizira za tanthauzo la ziwerengerozi komanso momwe angapezere.

Ndipanso chiyani chomwe ndingachiwerenge?

Kuti tipititse patsogolo phunziroli, tikulimbikitsanso kuwerenga (kapena kumvetsera) maphunziro a ziwerengero ndi apamwamba masamu. Ndipotu, m'nkhaniyi tinkangolankhula za tirigu zomwe sayansiyi ili nazo, ndipo palokha zimakhala zosangalatsa kuposa momwe zikuwonekera poyamba.

Kodi chidziwitso ichi chingandithandize bwanji?

Mwina, zingakhale zothandiza kwa inu m'moyo. Koma ngati mufuna kudziwa kuti zokhudzana ndi chikhalidwe cha anthu ndizofunika bwanji, momwe zimakhalira ndi zomwe zimakhudza moyo wanu, ziwerengero zidzakuthandizani kumvetsa bwino izi. Mwachidziwitso, akhoza kufotokoza pafupifupi mbali iliyonse ya moyo wathu, ngati pali deta yoyenera yomwe ali nayo. Chabwino, ndiye, ndi liti zomwe zimaperekedwa kuti ziwerenge - mutu wa nkhani yapadera.

Kutsiliza

Tsopano tikudziwa kuti pali mitundu yosiyanasiyana ya mawerengero: mphamvu ndi zomangamanga. Tatsimikiza momwe tingawawerengere komanso mmene angagwiritsire ntchito.