Bwanji osangogawa ndi ziro?
Zamkatimu
Owerenga angadabwe kuti chifukwa chiyani ndimapereka nkhani yonse pankhani yoletsa? Chifukwa chake ndi kuchuluka kwa ophunzira (!) omwe akugwira ntchito movutikira pansi pa dzina. Ndipo osati ophunzira okha. Nthawi zina ndimagwiranso aphunzitsi. Kodi ophunzira a aphunzitsi otere adzatha kuchita chiyani pa masamu? Chifukwa chomwe chidalembera lembali chinali kukambirana ndi mphunzitsi yemwe kugawikana ndi ziro sikunali vuto ...
Ndi zero, inde, kupatulapo kuvutitsidwa konse, chifukwa sitiyenera kuigwiritsa ntchito pamoyo watsiku ndi tsiku. Sitipita kukagula ziro mazira. "Pali munthu m'modzi m'chipindamo" amamveka mwachibadwa, ndipo "ziro anthu" amamveka ngati ochita kupanga. Akatswiri a zinenero amanena kuti ziro ndi kunja kwa chinenero.
Titha kuchita popanda ziro mu maakaunti aku banki: ingogwiritsani ntchito - monga pa thermometer - yofiira ndi buluu pazotsatira zabwino ndi zoyipa (zindikirani kuti kutentha kwachilengedwe kumagwiritsa ntchito zofiira pa manambala abwino, komanso maakaunti aku banki. ndi njira ina, chifukwa debit iyenera kuyambitsa chenjezo, kotero kufiira kumalimbikitsidwa kwambiri).
Mwa kuphatikiza ziro ngati nambala yachilengedwe, timakhudza vuto la kusiyanitsa Manambala a Makadinala od banja. Mkati mwa 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ....
mphamvu ya chiwerengerocho ndi yofanana ndi chiwerengero cha malo pamene yaima. Apo ayi, ili kale mu ndondomeko 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ....
Chiwerengero cha seti za singleton chimabwera chachiwiri, chiwerengero cha seti ndi zinthu ziwiri chimabwera chachitatu, ndi zina zotero. Tiyenera kufotokoza chifukwa chake, mwachitsanzo, sitiwerengera malo a othamanga pamipikisano kuyambira pachiyambi. Ndiye wopambana woyamba adzalandira mendulo ya siliva (golide anapita kwa wopambana zero), ndi zina zotero. Njira yofanana ndi yomwe idagwiritsidwa ntchito mu mpira - sindikudziwa ngati Owerenga amadziwa kuti "league one" amatanthauza " kutsatira zabwino kwambiri." ", ndipo ligi ya zero imatchedwa "ligi yayikulu".
Nthawi zina timamva mkangano womwe tikufunika kuyambira pachiwonetsero, chifukwa ndi yabwino kwa anthu a IT. Kupitiliza malingaliro awa, tanthauzo la kilomita liyenera kusinthidwa - liyenera kukhala 1024 m, chifukwa ichi ndi chiwerengero cha ma byte mu kilobyte (ndinena nthabwala zomwe asayansi amapeza kuti: "Kodi pali kusiyana kotani pakati pa munthu watsopano ndi wophunzira wa sayansi ya makompyuta ndi wophunzira wachisanu wa sukuluyi? kuti kilobyte ndi 1000 kilobytes, chomaliza - kuti kilomita ndi 1024 mamita "!
Mfundo ina, yomwe iyenera kutengedwa mozama, ndi iyi: nthawi zonse timayesa kuyambira pachiyambi! Ndikokwanira kuyang'ana pamlingo uliwonse pa wolamulira, pamiyeso yapakhomo, ngakhale pa koloko. Popeza timayezera kuchokera ku ziro, ndipo kuwerengera kumatha kumveka ngati muyeso wokhala ndi gawo lopanda miyeso, ndiye kuti tiyenera kuwerengera kuyambira ziro.
Ndi nkhani yosavuta, koma ...
Tiyeni tisiye malingaliro onse ndi kubwerera ku magawano ndi ziro. Nkhaniyi ndi yophweka ndipo ikanakhala yophweka ngati sikunali ... ndiye chiyani? Tiyeni tiganizire ndikuyesera. Zingakhale zingati - imodzi yogawidwa ndi ziro? Tiyeni tiwone: 1/0 = x. Chulukitsani mbali zonse ziwiri ndi chowerengera cha kumanzere.
Timapeza 1 = 0. Chinachake chalakwika! Chinachitika ndi chiyani? Eya! Lingaliro lakuti pali quotient ya mgwirizano ndi zero kumabweretsa kutsutsana. Ndipo ngati wina sangathe kugawidwa ndi ziro, ndiye kuti nambala ina ikhoza. Ngati, Owerenga, mumagwedeza mapewa anu ndikudabwa chifukwa chake wolemba (ndiye, ine) akulemba za platitudes yotere, ndiye ... Ndine wokondwa kwambiri!
Fomu 0/0 = 0 ikhoza kutetezedwa mouma khosi, koma ikutsutsana ndi lamulo lakuti zotsatira za kugawa nambala palokha ndizofanana ndi imodzi. Mwamtheradi, koma zosiyana kwambiri ndi zizindikiro monga 0/0, °/° ndi zina zotero mu calculus. Sakutanthauza nambala iliyonse, koma ndi zilembo zophiphiritsira zamitundu ina.
M'buku laumisiri wamagetsi, ndidapeza kufananitsa kosangalatsa: kugawa ndi ziro ndikowopsa ngati magetsi okwera kwambiri. Izi ndi zachilendo: Lamulo la Ohm limanena kuti chiŵerengero cha voteji kukana ndi chofanana ndi chamakono: V = U / R. Ngati kukana kunali zero, mphamvu yopanda malire idzadutsa kupyolera mwa conductor, ikuwotcha onse oyendetsa zotheka.
Nthawi ina ndinalemba ndakatulo yonena za kuopsa kogawa ndi ziro tsiku lililonse la sabata. Ndikukumbukira kuti tsiku lochititsa chidwi kwambiri linali Lachinayi, koma ndi chisoni chifukwa cha ntchito yanga yonse m’derali.
Mukagawa chinthu ndi ziro
Lolemba kwambiri
Sabata zomwe zangochitika kumene
Mwalephera kale momvetsa chisoni.
Pamene Lachiwiri masana
Inu mumayika ziro mu denominator
Ine ndikuwuzani inu ndiye, inu mukulakwitsa
Katswiri woyipa wa masamu!
Mukadutsa zero, kupyolera mu kupotoza,
Ndikufuna kugawanika Lachitatu
Mudzapeza mavuto ambiri
Muli ndi udzu ndi madzi m'mutu mwanu!
Bartek wina anali nafe.
Iye ankasemphana ndi malamulowo.
Lachinayi, imagawidwa ndi ziro.
Salinso pakati pathu!
Ngati chilakolako chachilendo chikugwirani inu
Gawani ndi ziro Lachisanu
Ndikunena zoona, ndinena zoona:
Kuyamba koyipa kwa sabata ino.
Pamene ili ziro, kwinakwake Loweruka
Wogawayo adzakhala wanu (osati wolimba mtima)
Gwirani pansi pa mpanda wa tchalitchi.
Ichi ndi chiwukitsiro chanu.
Kodi mukufuna zero pansi pa dash,
Pangani tchuthi Lamlungu
Bweretsani choko, bolodi lakuda.
Lembani: sichigawidwa ndi ziro!
Zero amalumikizidwa ndi kupanda pake komanso zopanda pake. Zowonadi, adabwera ku masamu ngati kuchuluka komwe, kuwonjezeredwa kwa chilichonse, sikusintha: x + 0 = x. Koma tsopano ziro zikuwonekera muzinthu zina zingapo, makamaka ngati kuyambira pamlingo. Ngati kunja kwawindo kulibe kutentha kwabwino kapena chisanu, ndiye ... izi ndi zero, zomwe sizikutanthauza kuti palibe kutentha konse. Chipilala cha zero sichomwe chagwetsedwa kwa nthawi yayitali ndipo kulibe. M'malo mwake, ndi chinthu chonga Wawel, Tower Eiffel ndi Statue of Liberty.
Chabwino, kufunikira kwa ziro mu dongosolo lazigawo sikungayerekezedwe mopambanitsa. Kodi mukudziwa, a Reader, Bill Gates ali ndi ziro zingati mu akaunti yake yakubanki? Sindikudziwa, koma ndikufuna theka. Mwachiwonekere, Napoleon Bonaparte adawona kuti anthu ali ngati ziro: amapeza tanthauzo mwa udindo. Mufilimu ya Andrzej Wajda As the Years, As the Days Go by, wojambula wokonda kwambiri Jerzy akuphulika: "Mfilisti ndi zero, nihil, palibe, palibe, nihil, ziro." Koma ziro zikhoza kukhala zabwino: "zero kupatuka kwa chizolowezi" kumatanthauza kuti zonse zikuyenda bwino, ndipo pitirizani!
Tiyeni tibwerere ku masamu. Zero ikhoza kuwonjezeredwa, kuchotsedwa ndikuchulukitsidwa popanda chilango. “Ndinapeza ziro kilogalamu,” akutero Manya kwa Anya. "Ndipo izi nzosangalatsa, chifukwa ndinataya kulemera komweko," akuyankha Anya. Choncho tiyeni tidye ayisikilimu sikisi sikisi kasanu ndi kamodzi, sizingatipweteke.
Sitingathe kugawa ndi ziro, koma tikhoza kugawa ndi ziro. Mbale ya ziro dumplings ikhoza kuperekedwa mosavuta kwa iwo omwe akuyembekezera chakudya. Kodi aliyense adzalandira zingati?
Zero si zabwino kapena zoipa. Izi ndi nambala zopanda zabwinoи osatsutsa. Imakwaniritsa zosagwirizana x≥0 ndi x≤0. Kutsutsana "chinachake chabwino" si "chinachake choyipa", koma "chinachake choyipa kapena chofanana ndi ziro". Akatswiri a masamu, mosiyana ndi malamulo a chinenero, nthawi zonse amanena kuti chinachake ndi "chofanana ndi zero" osati "zero." Kuti tilungamitse mchitidwewu, tili ndi: ngati tiwerenga chilinganizo x = 0 "x ndi zero", ndiye x = 1 timawerenga "x ndi wofanana ndi mmodzi", omwe angamezedwe, koma bwanji "x = 1534267"? Simungathenso kugawira mtengo wa nambala kwa munthu 00kapena kukweza ziro ku mphamvu yoipa. Komano, mutha kuchotsa ziro mwakufuna kwanu ... ndipo zotsatira zake zidzakhala ziro nthawi zonse.
Ntchito yofotokozera y = ax, maziko abwino a a, sakhala ziro. Izi zikutsatira kuti palibe zero logarithm. Zowonadi, logarithm ya a to base b ndiye cholumikizira chomwe maziko ayenera kukwezedwa kuti apeze logarithm ya a. Kwa = 0, palibe chizindikiro choterocho, ndipo ziro sizingakhale maziko a logarithm. Komabe, ziro mu "denominator" ya chizindikiro cha Newton ndi chinthu china. Timaganiza kuti misonkhano imeneyi siyambitsa kutsutsana.
umboni wabodza
Kugawikana ndi ziro ndi nkhani yofala pa umboni wabodza, ndipo imachitika ngakhale kwa akatswiri odziwa masamu. Ndiroleni ndikupatseni zitsanzo ziwiri zomwe ndimakonda. Yoyamba ndi ya algebra. "Ndidzatsimikizira" kuti manambala onse ndi ofanana. Tiyerekeze kuti pali manambala awiri omwe sali ofanana. Choncho, mmodzi wa iwo ndi wamkulu kuposa mzake, tiyeni a > b. Tiyerekeze kuti c ndi kusiyana kwawo
c \uXNUMXd a-b. Chifukwa chake tili ndi - b = c, komwe a = b + c.
Timachulukitsa magawo onse awiriwa ndi a -b:
a2 – ab = ab + ac – b2 – bc.
Ndimamasulira ak kumanzere, ndithudi ndimakumbukira za kusintha chizindikiro:
a2 - ab - ac = ab - b2 - bc.
Sindikupatula zinthu zodziwika bwino:
A (a-b-c) \uXNUMXd b (a-b-c),
Ndimagawana ndipo ndili ndi zomwe ndikufuna:
ndi = b.
Ndipo kwenikweni ngakhale mlendo, chifukwa ndinaganiza kuti a> b, ndipo ndinapeza kuti = b. Ngati mu chitsanzo pamwambapa "kunyenga" ndikosavuta kuzindikira, ndiye mu umboni wa geometric pansipa sikophweka. Ndidzatsimikizira kuti ... trapezoid kulibe. Chiwerengero chomwe chimatchedwa trapezoid kulibe.
Koma tiyerekeze choyamba kuti pali chinthu monga trapezoid (ABCD mu chithunzi pansipa). Ili ndi mbali ziwiri zofananira ("maziko"). Tiyeni titambasule maziko awa, monga momwe tawonera pachithunzichi, kuti tipeze paralelogalamu. Ma diagonal ake amagawaniza diagonal ina ya trapezoid m'magawo omwe utali wake umatchulidwa x, y, z, monga mu chithunzi 1. Kuchokera pakufanana kwa makona atatu ofanana, timapeza magawo:
pomwe timatanthauzira:
Oraz
pomwe timatanthauzira:
Chotsani mbali zofananira zolembedwa ndi nyenyezi:
Kufupikitsa mbali zonse ziwiri ndi x - z, timapeza - a / b = 1, zomwe zikutanthauza kuti + b = 0. Koma manambala a, b ndi kutalika kwa maziko a trapezoid. Ngati kuchuluka kwawo ndi ziro, ndiye kuti nawonso ndi ziro. Izi zikutanthauza kuti chithunzi ngati trapezoid sichingakhalepo! Ndipo popeza ma rectangles, ma rhombuse ndi mabwalo ndi ma trapezoid, ndiye, Wokondedwa Reader, palibe ma rhombuses, makona ndi mabwalo mwina ...
Monga choncho
Kugawana zambiri ndichinthu chosangalatsa komanso chovutitsa pazochitika zinayi zofunika kwambiri. Pano, kwa nthawi yoyamba, timakumana ndi chodabwitsa chofala kwambiri akakula: "lingalirani yankho, ndiyeno fufuzani ngati munaganiza bwino." Izi zikufotokozedwa bwino kwambiri ndi Daniel K. Dennett ("Momwe Mungapangire Zolakwa?", mu How It Is - A Scientific Guide to the Universe, CiS, Warsaw, 1997):
Njira iyi ya "kulingalira" sikusokoneza moyo wathu wachikulire - mwinamwake chifukwa chakuti timaphunzira mofulumira ndipo kulingalira sikovuta. Mwachidziwitso, chodabwitsa chomwecho chimachitika, mwachitsanzo, mu masamu (yathunthu) induction. Pamalo omwewo, "timalingalira" fomula ndikuwunika ngati zomwe tikuganiza zili zolondola. Nthaŵi zonse ophunzira amafunsa kuti: “Tinadziŵa bwanji chitsanzocho? Angatulutsidwe bwanji?" Ophunzira akandifunsa funso ili, ndimasintha funso lawo kukhala nthabwala: "Ndikudziwa izi chifukwa ndine katswiri, chifukwa ndimalipidwa kuti ndidziwe." Ophunzira kusukulu angayankhidwe mwanjira yomweyo, mozama kwambiri.
Chitani masewera olimbitsa thupi. Dziwani kuti timayamba kuwonjezera ndi kulemba kuchulukitsa ndi gawo lotsika kwambiri, ndikugawa ndi gawo lapamwamba kwambiri.
Kuphatikiza kwa malingaliro awiri
Aphunzitsi a masamu nthawi zonse amanena kuti zomwe timatcha kulekana kwa akuluakulu ndi mgwirizano wa malingaliro awiri osiyana: Nyumba i kulekana.
Woyamba (Nyumba) zimachitika mu ntchito zomwe archetype ndi:
Gawani-gawikana Izi ndi ntchito monga:
? (Timasunganso mtundu wakale wa vutoli, wotengedwa m'buku la a Julian Zgozalewicz lofalitsidwa ku Krakow mu 1892 - złoty ndi Rhenish złoty, ndalama zomwe zinali kufalitsidwa mu Ufumu wa Austria-Hungary mpaka kumayambiriro kwa zaka za zana la XNUMX).
Tsopano ganizirani mavuto awiri ndi buku lakale kwambiri la masamu mu Chipolishi, bambo Tomasz Clos (1538). Ndi magawano kapena coupe? Konzani momwe ana asukulu m'zaka za zana la XNUMX ayenera:
(Kumasulira kwa Chipolishi kupita ku Polish: Mu mbiya muli quart ndi miphika inayi. Mphika ndi malita anayi. Wina anagula migolo 20 ya vinyo pa 50 zł pa malonda. Ntchito ndi msonkho (excise?) zidzakhala 8 zł. gulitsani lita imodzi kuti mupeze 8 zł?)
Sports, physics, congruence
Nthawi zina mumasewera mumayenera kugawa china chake ndi ziro (chiwerengero cha zolinga). Chabwino, oweruza mwanjira ina amachita nazo. Komabe, mu abstract algebra iwo ali pa ndandanda. kuchuluka kwa ziroomwe lalikulu lake ndi ziro. Ikhoza kufotokozedwa mosavuta.
Ganizirani ntchito F yomwe imagwirizanitsa mfundo (y, 0) ndi mfundo mu ndege (x, y). Kodi F2, ndiko kuti, kuphedwa kawiri kwa F? Zero ntchito - mfundo iliyonse ili ndi chithunzi (0,0).
Pomaliza, kuchuluka komwe sikuli ziro komwe masikweya ake ndi 0 ndi pafupifupi mkate watsiku ndi tsiku wa akatswiri a sayansi ya zakuthambo, ndi manambala a mawonekedwe a + bε, pomwe ε ≠ 0, koma ε.2 = 0, masamu amaimba manambala awiri. Amapezeka pakusanthula masamu komanso mu geometry yosiyana.
Kupatula apo, pali china chake mu masamu chomwe chimagawikana ndi ziro mu dzina. Ikuchokera kuphatikiza. Lolani Z asonyeze mndandanda wamagulu onse. Kugawa Z ndi p kumatanthauza kuti timafananitsa nambala iliyonse (integer) ndi ena, omwe ndi omwe kusiyana kwawo kumagawanika. Chifukwa chake, tikakhala ndi mitundu isanu ya manambala olingana ndi manambala 0, 1, 2, 3, 4 - zotsalira zomwe zingatheke pamene tagawidwa ndi 5. Njirayi yalembedwa motere:
mod pamene kusiyana kuli kochuluka.
Kwa = 2, tili ndi manambala awiri okha: 0 ndi 1. Kugawa manambala m'magulu awiri otere ndikofanana ndi kuwagawa kukhala ofananira ndi osamvetseka. Tiyeni tisinthe tsopano. Kusiyana kumagawika nthawi zonse ndi 1 (chiwerengero chilichonse chimagawika ndi 1). Kodi ndizotheka kutenga =0? Tiyeni tiyese: ndi liti pamene kusiyana kwa manambala awiri kuchulukitsa ziro? Pokhapokha pamene manambala awiriwa ali ofanana. Chifukwa chake kugawa magawo angapo ndi ziro ndizomveka, koma sizosangalatsa: palibe chomwe chimachitika. Komabe, ziyenera kutsindika kuti uku sikugawikana kwa manambala m'lingaliro lodziwika kuchokera kusukulu ya pulayimale.
Zochita zoterezi ndizoletsedwa, komanso masamu aatali komanso aakulu.
Mpunga. 2. Kuzindikiritsa manambala pogwiritsa ntchito kufananitsa
(mtengo 5 ndi mtengo 2)
