Famba uchipinda munyika isiri yechokwadi yemasvomhu

Ndakanyora chinyorwa ichi neChitatu mushure mehurukuro uye kudzidzira pakoreji yesainzi yekombuta. Ndinozvidzivirira kubva pakutsoropodza kwevadzidzi vechikoro ichi, ruzivo rwavo, mafungiro kune sainzi uye zvinonyanya kukosha: unyanzvi hwekudzidza. Izvi...hapana anovadzidzisa.

Sei ndichizvidzivirira kudaro? Nechikonzero chiri nyore - ndiri pazera apo, pamwe, nyika yakanditenderedza haisati yanzwisiswa. Pamwe ndinovadzidzisa masungiro nekusunungura mabhiza, pane kutyaira mota? Pamwe ndinovadzidzisa kunyora nechinyoreso? Kunyangwe ndine maonero ari nani emunhu, ndinotenda kuti "ndinotevera", asi ...

Kusvikira munguva pfupi yapfuura, muchikoro chesekondari vaitaura nezvenhamba dzakaoma kunzwisisa. Uye waive musi weChitatu ichi pandakauya kumba, ndikasiya - hapana kana mudzidzi anga asati adzidza kuti chii uye mashandisirwo enhamba idzi. Vamwe vanhu vanotarisa masvomhu ese kunge hanzi pamusuwo wakapendwa. Asi ndakashamiswawo zvechokwadi pavakandiudza nzira yokudzidza nayo. Zvichitaurwa zviri nyore, awa yega yega yehurukuro maawa maviri ekudzidza kumba: kuverenga bhuku, kudzidziswa kwekutanga kugadzirisa matambudziko pane yakapihwa musoro, nezvimwe. Takagadzirira nenzira iyi, tinouya kumitambo, apo tinovandudza zvinhu zvose ... Zvinofadza, vadzidzi sezviri pachena vakafunga kuti kugara pahurukuro - kazhinji kutarisa kunze nepahwindo - inotovimbisa kuti ruzivo ruchapinda mumusoro.

Stop! Zvakwana. Ndichatsanangura mhinduro yangu kumubvunzo wandakawana ndiri mukirasi nevamwe vaibva kuNational Children's Fund, sangano rinotsigira vana vane matarenda vanobva kumativi ose enyika. Mubvunzo (kana kuti chirevo) waive:

— Ungatiudza chimwe chinhu nezvenhamba dzisiri chaidzo here?

“Chokwadi,” ndakapindura kudaro. 

Chokwadi chenhamba

“Shamwari ndemumwe wangu, ushamwari ireshiyo yenhamba 220 ne284,” akadaro Pythagoras. Chiripo apa ndechekuti hwerengedzo yevapatsanuri venhamba 220 yakaenzana ne284, uye hwerengedzo yevapatsanuri venhamba 284 inokwana 220:

1 + 2 + 4 + 71 + 142 = 220

1 + 2 + 4 + 5 + 10 = 11 + 20 + 22 + 44 + 55 + 110 = 284. Ona nenzira iyo Jakobho womuBhaibheri akapa Esau makwai 220 nemakondohwe sechiratidzo choushamwari ( Genesi 32:14 ).

Chimwe chiitiko chinofadza pakati penhamba 220 ne284 ndeichi: gumi nenomwe dzepamusoro nhamba dzepamusoro ndi 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 , uye 59.

Huwandu hwavo ndeye 2x220, uye huwandu hwemakwere i59x284.

Chekutanga. Iko hakuna pfungwa ye "nhamba chaiyo". Zvakafanana mushure mekuverenga nyaya yenzou iwe unobvunza kuti, "Iye zvino tichakumbira kune vasiri nzou." Kune zvakakwana uye zvisina kukwana, zvine musoro uye zvisina musoro, asi hapana zvisizvo. Zvakananga: nhamba dzisiri chaidzo hadzinzi hadzina basa. Kune marudzi akawanda e "nhamba" mumasvomhu, uye akasiyana kubva kune mumwe nemumwe se-kutora kuenzanisa kwemhuka - nzou nevhu.

Chechipiri, tichaita maoparesheni aungatoziva kuti anorambidzwa: kutora masikweya midzi yenhamba dzisina kunaka. Eya, masvomhu achakunda zvipingamupinyi zvakadaro. Izvi zvine musoro here? Mumasvomhu, sezvakaita mune imwe sainzi: kana dzidziso ichapinda zvachose mudura reruzivo zvinoenderana ... nekushandiswa kwayo. Kana zvisingabatsiri, zvino zvinopera mumarara, zvino mune mamwe marara munhoroondo yezivo. Pasina nhamba dzandinotaura pamusoro pekupedzisira kwechinyorwa chino, hazvibviri kugadzira masvomhu. Asi ngatitange nezvimwe zvinhu zvidiki. Unoziva kuti nhamba chaidzo ndedzipi. Vanozadza mutsara wenhamba zvakasimba uye pasina mikaha. Unoziva zvakare kuti manhamba chaiwo ndeapi: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, …….. - ese haakwane chirangaridzo kunyange chikuru. Vanewo zita rakanaka: zvakasikwa. Vane zvinhu zvakawanda zvinofadza. Unoda sei izvi:

1 + 15 + 42 + 98 + 123 + 179 + 206 + 220 = 3 + 11 + 46 + 92 + 129 + 175 + 210 + 218

1² + 15² + 42² + 98² + 123² + 179² + 206² + 220² = 3² + 11² + 46² + 92² + 129² + 175² + 210² + 218²

1³ + 15³ + 42³ + 98³ + 123³ + 179³ + 206³ + 220³ = 3³ + 11³ + 46³ + 92³ + 129³ + 175³ + 210³ + 218³

1⁴ + 15⁴ + 42⁴ + 98⁴ + 123⁴ + 179⁴ + 206⁴ + 220⁴ = 3⁴ + 11⁴ + 46⁴ + 92⁴ + 129⁴ + 175⁴ + 210⁴ + 218⁴

1⁵ + 15⁵ + 42⁵ + 98⁵ + 123⁵ + 179⁵ + 206⁵ + 220⁵ = 3⁵ + 11⁵ + 46⁵ + 92⁵ + 129⁵ + 175⁵ + 210⁵ + 218⁵

1⁶ + 15⁶ + 42⁶ + 98³ + 123⁶ + 179⁶ + 206⁶ + 220⁶ = 3⁶ + 11⁶ + 46⁶ + 92⁶ + 129⁶ + 175⁶ + 210⁶ + 218⁶

1⁷ + 15⁷ + 42⁷ + 98³ + 123⁷ + 179⁷ + 206⁷ + 220⁷ = 3⁷ + 11⁷ + 46⁷ + 92⁷ + 129⁷ + 175⁷ + 210⁷ + 218⁷

“Ndokwomuzvarirwo kuva nefariro muzviverengero zvomusikirwo,” akadaro Carl Lindenholm, uye Leopold Kronecker (1823–1891) vakakutaura nenzira yakajeka: “Mwari akasika nhamba dzomusikirwo—chimwe chinhu chiri chose ibasa romunhu!” Zvidimbu (zvinodaidzwa kuti rational manhamba nenyanzvi dzemasvomhu) zvinewo zvinhu zvinoshamisa:

uye mukuenzana:

iwe unogona, kutanga kubva kuruboshwe, kukwiza ma pluses uye wotsiva iwo nezviratidzo zvekuwedzera - uye kuenzana kucharamba kuri kwechokwadi:

Etc.

Sezvinozivikanwa, kune zvikamu a/b, apo a na b ari manhamba uye b ≠ 0, vanodaro. nhamba inonzwisisika. Asi vanongozvidaidza ivo pachavo muchiPolish. Vanotaura Chirungu, French, German uye Russian. nhamba inonzwisisika. MuChiShona: manhamba akakwana. Nhamba dzisina musoro Hazvina musoro, hazvina musoro. Isu tinotaurawo muchiPolish pamusoro pedzidziso dzisina musoro, mazano nezviito - uku kupenga, kufungidzira, kusatsanangurika. Vanoti vakadzi vanotya mbeva - hazvina musoro zvakadii?

Kare, nhamba dzaiva nemweya. Imwe neimwe yaireva chimwe chinhu, chimwe nechimwe chaifananidzira chimwe chinhu, chimwe nechimwe chairatidza chikamu chetsinhirano iyoyo yeChisiko Chapose pose, ndiko kuti, muchiGiriki, Cosmos. Shoko rekuti “cosmos” pacharo rinoreva “kurongeka, kurongeka.” Chinonyanya kukosha chaiva chitanhatu (nhamba yakakwana) uye gumi, nhamba yenhamba dzakatevedzana 1 + 2 + 3 + 4, inoumbwa nedzimwe nhamba, iyo yekufananidzira yakasara kusvikira nhasi. Saka Pythagoras akadzidzisa kuti nhamba ndidzo mavambo uye bviro yezvose, uye kuwanikwa chete nhamba dzisina musoro akashandura kufamba kwePythagorean kugeometry. Tinoziva chikonzero kubva kuchikoro icho

√2 - nhamba isina musoro

Ngatitii pane: uye kuti chikamu ichi hachigone kudzikiswa. Kunyanya, ose p uye q haana kujairika. Ngatizvienzanise: 2q²=p². Nhamba p haigone kuve isinganzwisisike, kubva ipapo p² zvaizovawo, uye rutivi rworuboshwe rwekuenzana runowanda 2. Nokudaro, p is even, i.e., p = 2r, saka p.²= 4r². Isu tinoderedza equation 2q²= 4r² na2. Tinowana q²= 2r² uye tinoona kuti q inofanirawo kuenzana, uye takafunga kuti yakanga isiri. Iko kupokana kunoguma kunopedzisa humbowo - iyi fomula inogona kazhinji kuwanikwa mubhuku rega rega remasvomhu. Uhu humbowo husina kunanga inzira inodiwa yevasophist.

Uku kukura kwaisagona kunzwisiswa nevaPythagoras. Zvinhu zvose zvinofanira kukwanisa kutsanangurwa nenhamba, uye diagonal yechikwere, iyo chero munhu anogona kukwevera netsvimbo mujecha, haina, kureva, kuyerwa, kureba. “Kutenda kwedu kwakanga kusina maturo,” vaPythagorean vanoratidzika kuva vanodaro. Zvakadaro sei? Imhando ye ... isina musoro. Union yakaedza kuzviponesa nenzira dzemasekete. Chero ani zvake anotsunga kuratidza kuvapo kwavo nhamba dzisina musoro, aifanira kurangwa norufu, uye, sezviri pachena, mutongo wokutanga wakaitwa natenzi pachake.

Asi "pfungwa yakapfuura isina kukuvadzwa." Nguva yegoridhe yasvika. MaGiriki akakunda maPersia (Marathon 490, Plache 479). Democracy yakasimbiswa, nzvimbo itsva dzepfungwa dzeuzivi uye zvikoro zvitsva zvakabuda. Vateveri vePythagoreanism vakanga vachiri kunetseka nehuwandu husina musoro. Vamwe vakaparidza vachiti: Hatinganzwisisi chakavanzika ichi; isu tinogona chete kufungisisa uye kuyemura Uncharted. Iwo ekupedzisira aive akanyanya pragmatic uye aisaremekedza Chakavanzika. Panguva iyoyo, kuumbwa kwepfungwa kuviri kwakaoneka kwaiita kuti zvibvire kunzwisisa nhamba dzisina musoro. Icho chokwadi chekuti isu nhasi tinovanzwisisa chaizvo ndecheEudoxus (XNUMXth century BC), uye chete pakupera kwezana ramakore rechiXNUMX apo nyanzvi yemasvomhu yeGerman Richard Dedekind akapa dzidziso yeEudoxus 'yakakodzera budiriro maererano nezvinodiwa zvekusimba kwemasvomhu.

Nhamba dzakawanda kana kutambudzwa

Ungararama usina manhamba here? Kunyange kana, hupenyu hupi hungava ... Taizofanira kuenda kuchitoro kunotenga shangu netsvimbo, yatakamboyera nayo kureba kwetsoka. "Ndinoda maapuro, o, heino!" – taizoratidza vatengesi pamusika. "Kureba sei kubva kuModlin kuenda kuNowy Dwór Mazowiecki"? "Padyo!"

Nhamba dzinoshandiswa kuyera. Isu tinoashandisawo kutaura mamwe akawanda maconcepts. Semuenzaniso, chiyero chemepu chinoratidza kuti nzvimbo yenyika yadzikira sei. Chikero chembiri-kune-chimwe, kana kuti 2 chete, chinoratidza chokwadi chokuti chimwe chinhu chakapetwa kaviri. Ngatitii masvomhu: homogeneity imwe neimwe inoenderana nenhamba - chiyero chayo.

Basa. Isu takagadzira kopi yexerographic, tichikudza mufananidzo wacho kakawanda. Zvadaro chidimbu chakawedzerwa chakawedzerwa zvakare b nguva. Chii chinonzi general magnification scale? Mhinduro: a × b inopetwa na b. Zviyero izvi zvinoda kuwanzwa. Nhamba minus one, -1, inofambirana nechaizvo chiri pakati, ndiko kuti, kutenderera kwe180 degrees. Ndeipi nhamba inoenderana ne90 degree rotation? Hakuna nhamba yakadaro. Ndizvo, ndizvo ... kana kuti, zvichave munguva pfupi. Wagadzirira kutambudzwa mupfungwa here? Shingai uye tora sikweya mudzi we minus one. Ndiri kuteerera? Chii chausingagoni kuita? Handiti ndakakuudza kuti shinga. Bvisa kunze! Hei, zvakanaka, dhonza, dhonza... Ndichabatsira...Pano: −1 Zvatava nazvo, ngatiedzei kuishandisa... Hongu, zvino tinogona kutora midzi yenhamba dzose dzisina kunaka, nokuti. muenzaniso.:

√-4 = 2√-1, √-16 = 4√-1

- "zvisinei nekunetseka mupfungwa kunosanganisira." Izvi ndizvo zvakanyorwa naGirolamo Cardano muna 1539, achiedza kukunda matambudziko epfungwa akabatana nawo - sezvaakazodanwa nokukurumidza - uwandu hwekufungidzira. Akafunga seizvi...

...Basa. Gurai 10 muzvikamu zviviri, chigadzirwa chayo chakaenzana ne40. Ndinoyeuka kubva muchikamu chekare akanyora chimwe chinhu chakadai: Zviri pachena kuti hazvibviri. Zvisineyi, ngatiite izvi: patsanura gumi muzvikamu zviviri zvakaenzana, chimwe nechimwe chakaenzana na 10. Vawande - tinowana 5. Kubva pane zvabuda 25 tava kubvisa makumi mana, kana uchida, towana -25. Zvino tarisa: √-40 yakawedzerwa nekubviswa kubva pa15 inokupa chigadzirwa chemakumi mana. Nhamba idzodzo i15-√-5 uye 40 + √-5. Chigumisiro chakasimbiswa naCardano sezvinotevera:

“Pasinei nekunetseka mupfungwa kuri kuita izvi, wedzerai 5 + √-15 ne5-√-15. Tinowana 25 - (-15), iyo yakaenzana ne25 + 15. Saka, chigadzirwa chacho 40 .... Zvakaoma hazvo."

Zvakanaka, imarii: (1 + √-1) (1-√-1)? Ngatiwande. Rangarira kuti √-1 × √-1 = -1. Hukuru. Iye zvino dambudziko rakaoma: kubva pa + b√-1 kusvika ab√-1. Chii chaitika? Chokwadi, seizvi: (a + b√-1) (ab√-1) = a²+b²

Chii chinofadza paizvi? Semuenzaniso, chokwadi chekuti isu tinokwanisa kukonzeresa mataurirwo atakanga "taisaziva kare." Yakadimburirwa kuwanda formula ye²-b² pamwe unorangarira formula ye²+b² hazvina kuitika nekuti hazvaigona kuitika. Munzvimbo yenhamba chaidzo, iyo polynomial²+b² izvi hazvidzivisiki. Ngatiratidzei “yedu” square root ye” minus one” nebhii i.²= -1. Iyi i "unreal" prime number. Uye izvi ndizvo zvinotsanangura ndege inotendeuka 90 degrees. Sei? Shure kwezvose,²= -1, uye kubatanidza kutenderera kwe90-degree kumwe neimwe kutenderera kwakafanana kunoburitsa 180-degree rotation. Imhandoi yekutenderera iri kutsanangurwa? Zvakajeka - kutendeuka kwe45 degrees. Nhamba yacho inorevei? Zvakanyanya kuoma:

(-I)² = -i × (-i) = + i² = -1

Saka -ndinotsanangurawo kutenderera kwe90 degree, kungotarisana nekutenderera kwangu. Nderipi rinosara uye nderipi rakarurama? Unofanira kuita musangano. Isu tinofungidzira kuti nhamba i inotsanangura kutenderera munzira iyo nyanzvi dzemasvomhu dzinofunga kuti yakanaka: counterclockwise. Nhamba -i inotsanangura kutenderera munzira iyo inonongedza iri kufamba.

Asi pane nhamba dzakadai seni uye -i? Are! Takangoita kuti vave vapenyu. Ndiri kuteerera? Kuti varipo chete mumisoro yedu? Zvakanaka chii kutarisira? Dzimwe nhamba dzese dziripowo mupfungwa dzedu chete. Tinofanira kuona kana nhamba dzedu dzichangoberekwa dzichararama. Kunyanya, iyo dhizaini ine musoro uye ichave inobatsira kune chimwe chinhu? Ndokumbira utore izwi rangu pazviri kuti zvese zvakanaka uye kuti idzi nhamba nyowani dzinobatsira chaizvo. Nhamba dzakaita se3+i, 5-7i, mune imwewo nzira: a+bi dzinonzi nhamba dzakaoma. Ndakakuratidza kuti ungazviwana sei nekutenderedza ndege. Inogona kupinzwa nenzira dzakasiyana: semapoinzi endege, semamwe mapolynomials, semamwe manhamba arrays... uye pese paanenge akafanana: equation x.² +1=0 hapana chinhu... hocus pocus yatovapo!!!! Ngatifarei tifare!!!

Kupera kwerwendo

Izvi zvinopedzisa rwendo rwedu rwekutanga rwenyika yenhamba dzemanyepo. Pakati pedzimwe nhamba dzisiri dzepasi, ini ndichataura zvakare idzo dzine manhamba akawanda pamberi uye kwete kumashure (dzinonzi 10-adic, kwatiri p-adic inonyanya kukosha, apo p inhamba huru), semuenzaniso X = ... ... ... 96109004106619977392256259918212890625

Ngativerengei X ndapota². Nokuti? Ko kana tikaverenga sikweya yenhamba ine nhamba isingaperi yemanhamba kuseri kwayo? Zvakanaka, ngatiite zvimwe chete. Ngationei kuti X² = H.

Ngatitsvage imwe nhamba yakadaro ine nhamba isingaperi yemanhamba pamberi inogutsa equation. Ratidzo: Sikweya yenhamba inopera nenhanhatu inoperawo munhanhatu. Sikweya yenhamba inopera muna 76 inoperawo muna 76. Sikweya yenhamba inopera muna 376 inoperawo muna 376. Sikweya yenhamba inopera muna 9376 inogumawo muna 9376. Sikweya yenhamba inopera muna XNUMX... Kune zvakare nhamba idiki zvekuti, kunyangwe dziri positive, dzinoramba dziri diki pane chero imwe nhamba yakanaka. Iwo madiki zvekuti dzimwe nguva anokwana kuapeta kuti awane zero. Kune nhamba dzisingagutsi mamiriro a × b = b × a. Kunewo nhamba dzisingaperi. Ingani nhamba dzakasikwa dziripo? Zvisingaperi zvakawanda? Hongu, asi zvakadini? Ndeipi nhamba inogona kuratidzwa mune iyi? Mhinduro: diki pane nhamba dzisingaperi; yakanyorwa nebhii rakanaka: A uye inowedzerwa ne zero index A₀ , aleph-zero.

Kune zvakare nhamba dzatisingazive kuti dziriko ... kana dzatinogona kutenda kana kusatenda sezvaunoda. Uye kutaura nezvazvo: Ndinovimba iwe uchiri kuda Unreal Nhamba, Fantasy Species Nhamba.