reverse charm
Kune zvakawanda zvekutaura nezve "charm yevanopesana", uye kwete mumasvomhu chete. Rangarira kuti nhamba dzakapesana ndidzo dzinongosiyana nechiratidzo: wedzera 7 uye kubvisa 7. Huwandu hwenhamba dzakapesana ndizero. Asi kwatiri (kureva masvomhu) kudzokorora kunonyanya kunakidza. Kana chigadzirwa chenhamba chakaenzana ne1, saka nhamba idzi dzinopesana kune imwe neimwe. Nhamba yega yega ine kupesana kwayo, nhamba imwe neimwe isiri zero ine inverse yayo. Kudzokororwa kwechitsinhano imbeu.
Inversion inoitika pese pese panobatana uwandu huviri kune umwe neumwe zvekuti kana imwe yakawedzera, imwe inodzikira pamwero unoenderana. "Relevant" zvinoreva kuti chigadzirwa chehuwandu uhu hachichinji. Tinorangarira kubva kuchikoro: ichi chikamu chakasiyana. Kana ndichida kusvika kwandinoenda kaviri nekukasira (kureva kucheka nguva nepakati), ndinofanira kupeta kumhanya kwangu. Kana huwandu hwemudziyo wakavharwa negasi wakaderedzwa nen nguva, ipapo kumanikidza kwayo kuchawedzera nen nguva.
Mudzidzo yepuraimari, tinonyatso kusiyanisa pakati pekusiyanisa uye kuenzanisa kuenzanisa. "Zvakawanda sei"? - "Kangani zvakare?"
Heano mamwe mabasa echikoro:
1 basa. Pakati pezvinhu zviviri zvakanaka, yekutanga inopfuura 5 nguva huru pane yechipiri uye panguva imwechete 5 nguva huru pane yekutanga. Zviyero ndezvipi?
2 basa. Kana nhamba imwe iri 3 huru pane yechipiri, uye yechipiri iri 2 huru pane yechitatu, nhamba yekutanga yakakura zvakadii pane yechitatu? Kana nhamba yekutanga iriposititi kaviri yechipiri, uye yekutanga nhamba katatu patatu, kangani nhamba yekutanga yakakura pane yechitatu?
3 basa. Mubasa rechipiri, nhamba dzakasikwa chete dzinobvumirwa. Kurongeka kwakadai sokurondedzerwa ikoko kunobvira here?
4 basa. Pakati pezvinhu zviviri zvakanaka, yekutanga ndeye 5 nguva yechipiri, uye yechipiri ndeye 5 nguva yekutanga. Zvinoita here?
Pfungwa ye "avhareji" kana "avhareji" inoita seyakapusa. Kana ndaichovha 55 km neMuvhuro, 45 km neChipiri, uye 80 km neChitatu, paavhareji ndaichovha 60 km pazuva. Isu tinobvumirana nemoyo wese nemaverengero aya, kunyangwe akatishamisa nekuti ini handina kutyaira 60 km pazuva rimwe. Isu tinongogamuchira nyore migove yemunhu: kana mazana maviri vanhu vakashanyira resitorendi mukati memazuva matanhatu, saka avhareji yemazuva ese ndeye makumi matatu nematatu uye chetatu vanhu. HM!
Pane matambudziko chete neavhareji saizi. Ndinoda bhasikoro. Saka ndakatora mukana wekupihwa kwesangano rekufamba "Ngatiendei nesu" - vanoendesa mikwende kuhotera, uko mutengi anotasva bhasikoro nekuda kwekunakidzwa. Musi weChishanu ndakatyaira kwemaawa mana: maviri ekutanga nekumhanya kwe24 km paawa. Ndakabva ndaneta zvekuti kwevaviri vaitevera ndaingoita 16 chete paawa. Speed yangu yaive yeavhareji yei? Chokwadi (24+16)/2=20km=20km/h.
Zvisinei, musi woMugovera mikwende yakasiiwa pahotera, uye ndakaenda kunoona matongo eimba yacho, iri makiromita 24 kubva ipapo, uye ndaaona, ndakadzokera. Ndakatyaira awa nedivi rimwe, ndichidzoka zvishoma nezvishoma, ndichimhanya 16 km paawa. Ndeipi avhareji yekumhanya munzira yehotera-castle-hotera? 20 km paawa? Chokwadi kwete. Mushure mezvose, ndakatyaira makiromita makumi mana nemasere uye zvakanditorera awa ("ikoko") uye awa nehafu kumashure. 48 km mumaawa maviri nehafu, i.e. awa 48/48=2,5/192=10 km! Mumamiriro ezvinhu aya, avhareji yekumhanya haisi iyo arithmetic zvinoreva, asi harmonic yeakapihwa kukosha:
uye iyi rondedzero yenyaya mbiri inogona kuverengwa sezvizvi: iyo harmonic zvinoreva yenhamba yakanaka ndeyekudzokororwa kwearithmetic zvinoreva kudzokorora kwavo. Kudzokororwa kwehuwandu hwekudzoka kunowanikwa mumakorasi akawanda emabasa echikoro: kana mumwe mushandi achichera maawa, imwe - b maawa, saka, kushanda pamwe chete, vanochera nenguva. dziva remvura (rimwe paawa, imwe paawa b). Kana imwe resistor ine R1 uye imwe iine R2, saka ivo vane parallel kuramba.
Kana komputa imwe ichigona kugadzirisa dambudziko mumasekonzi, imwe komputa mumasekonzi b, zvino kana vashanda pamwechete...
Mira! Apa ndipo panopera kuenzanisa, nokuti zvinhu zvose zvinoenderana nekumhanya kwetiweki: kushanda kwezvibatanidza. Vashandi vanogonawo kukanganisa kana kubatsirana. Kana murume mumwe achigona kuchera tsime mumaawa masere, vashandi makumi masere vanogona kurigona mu1/10 yeawa (kana kuti maminitsi matanhatu)? Kana vatakuri vatanhatu vakaendesa piyano pauriri hwekutanga mumaminitsi matanhatu, zvichatora nguva yakadii mumwe wavo kuendesa piyano pauriri hwemakumi matanhatu? Kusava nemusoro kwezvinetso zvakadaro kunounza mupfungwa kushandiswa kuduku kwemasvomhu ose kumatambudziko "kubva muupenyu".
Nezve mutengesi ane simba
Zviyero hazvichashandiswi. Yeuka kuti uremu hwaiiswa pandiro imwe yezvikero zvakadaro, uye zvinhu zvaiyerwa zvaiiswa pane imwe, uye kana uremu hwaienzana, zvinhu zvacho zvaibva zvayerwa zvinoenzana. Zvechokwadi, maoko ose emutoro unorema anofanira kunge akareba zvakafanana, kana zvisina kudaro kuyerwa kuchave kusina kururama.
Ah ndizvozvo. Fungidzira mutengesi ane uremu husina kuenzana. Nekudaro, anoda kuve akatendeseka kune vatengi uye anoyera zvinhu mumabheji maviri. Kutanga, anoisa uremu pane imwe pani, uye pane imwe chiyero chenhumbi - kuitira kuti zviyero zvienzane. Ipapo anoyera "hafu" yechipiri yezvinhu nenzira yakadzokera shure, ndiko kuti, anoisa uremu pandiro yechipiri, uye zvinhu pane yekutanga. Sezvo maoko asina kuenzana, "hafu" haina kumboenzana. Uye hana yomutengesi yakajeka, uye vatengi vanorumbidza kutendeseka kwake: "Zvandakabvisa pano, ndakabva ndawedzera."
Zvakadaro, ngatitarisei maitiro emutengesi anoda kutendeka kunyangwe uremu husina kunaka. Rega maoko echiyero ave nehurefu a uye b. Kana imwe yendiro yakaremerwa nehuremu hwekirogiramu uye imwe ine x zvinhu, ipapo zviyero zviri mukuenzanisa kana demo = b kekutanga uye bx = kechipiri. Saka, chikamu chekutanga chezvigadzirwa chakaenzana ne b / kilogram, chikamu chechipiri ndi / b. Huremu hwakanaka hune = b, saka mutengi achagamuchira 2 kg yezvinhu. Ngationei zvinoitika kana a ≠ b. Zvadaro a - b ≠ 0 uye kubva kune yakaderedzwa yekuwedzera formula yatinayo
Takasvika kumhedzisiro isingatarisirwi: iyo inoratidzika seyakanaka nzira ye "avhareji" kuyerwa muchiitiko ichi inoshanda kubatsira mutengi, anogamuchira zvimwe zvinhu.
Basa 5. (Zvakakosha, kwete mumasvomhu!). Umhutu hunorema 2,5 milligrams, uye nzou matani mashanu (iyi data chaiyo). Verenga masvomhu anoreva, geometric mean, uye harmonic zvinoreva mosquito nenzou (zviremu). Tarisa maverengero uye uone kana aine chero pfungwa kunze kwe arithmetic maekisesaizi. Ngatitarisei mimwe mienzaniso yekuverenga kwemasvomhu isingaiti mu "hupenyu chaihwo". Zano: Takatotarisa muenzaniso mumwe munyaya ino. Izvi zvinoreva here kuti mudzidzi asingazivikanwe ane maonero andakawana paInternet aive echokwadi: "Math inopusa vanhu vane nhamba"?
Hongu, ndinobvuma kuti muhukuru hwemasvomhu, unogona "kunyengedza" vanhu - sekondi yega yega shambuu yekushambadzira inoti inowedzera fluffiness neimwe muzana. Tichatsvaga here mimwe mienzaniso yezvishandiso zvemazuva ese zvinoshanda zvinogona kushandiswa kuita matsotsi?
Grams!
Musoro wechikamu ichi ishoko rechiito (munhu wekutanga muzvizhinji) kwete zita (nominative muzhinji wechuru chekirogiramu). Harmony zvinoreva kurongeka uye mimhanzi. Kune vaGiriki vekare, mimhanzi yaive bazi resainzi - zvinofanirwa kubvumwa kuti kana tikataura kudaro, tinotamisa zvinorehwa neshoko rekuti "sainzi" kune nguva isati yasvika. Pythagoras aigara muzana remakore rechiXNUMX BC. Kwete chete kuti aisaziva komputa, nharembozha uye email, asi zvakare aisaziva kuti Robert Lewandowski, Mieszko I, Charlemagne naCicero vaive ani. Akanga asingazivi kana nhamba dzechiArab kana dzechiRoma (dzakatanga kushandiswa kunenge muzana remakore rechishanu BC), akanga asingazivi kuti Hondo dzePunic dzaive dzipi ... Asi aiziva mimhanzi ...
Aiziva kuti pazviridzwa zvine tambo tsinhiro dzokudengenyeka dzaipesana nokureba kwezvikamu zvinorira zvetambo. Aiziva, aiziva, aisakwanisa kuzvitaura nenzira yatinozviita nayo nhasi.
Mafambiro etambo mbiri dzekuzunguzika dzinoita octave dziri muchiyero che1: 2, ndiko kuti, kuwanda kweinoti yepamusoro kaviri kuwanda kweiyo yepasi. Chiyero chevibration chaidzo chechishanu i2:3, yechina i3:4, huru huru yetatu i4:5, yetatu mudiki i5:6. Idzi nhanho dzemakonzonendi dzinonakidza. Ipapo kune maviri asina kwaakarerekera, ane vibration reshiyo ye6: 7 uye 7: 8, ipapo dissonant - toni hombe (8: 9), toni diki (9:10). Zvikamu izvi (retio) zvakafanana nereshiyo yenhengo dzinotevedzana dzenhevedzano iyo nyanzvi dzemasvomhu (nekuda kwechikonzero ichochi) dzinodaidza kuti harmonic series:
imari isingaperi. Reshiyo ye oscillations ye octave inogona kunyorwa se 2:4 toisa cheshanu pakati pawo: 2:3:4, kureva kuti tichakamura octave kuita cheshanu nechechina. Izvi zvinonzi harmonic segment division in mathematics:
Mupunga. 1. Kumuimbi: kupatsanura octave AB kuita yechishanu AC.YeMasvomhu: Harmonic Segmentation
Ndinorevei kana ndichitaura (pamusoro) yehuwandu husingaverengeki, senge harmonic series? Zvinoitika kuti nhamba yakadaro inogona kuva chero nhamba huru, chinhu chikuru ndechokuti tinowedzera kwenguva yakareba. Kune zvishoma uye zvishoma zvigadzirwa, asi kune zvakawanda uye zvakawanda zvacho. Chii chinokunda? Pano tinopinda munzvimbo yekuongorora masvomhu. Zvinoitika kuti zvigadzirwa zvinopera, asi kwete nekukurumidza. Ini ndicharatidza kuti nekutora zvakakwana zvinongedzo, ndinogona kupfupisa:
zvakakura zvisingaite. Ngatitorei "semuenzaniso" n = 1024. Ngatiisei mumapoka mazwi sezvakaratidzwa mumufananidzo:
Mumaparenthesis imwe neimwe, izwi rimwe nerimwe rakakura kudarika rakapfuura, kunze kwekuti, hongu, iro rekupedzisira, iro rakaenzana pacharo. Mumabhuraketi anotevera, tine 2, 4, 8, 16, 32, 64, 128 uye 512 zvikamu; kukosha kwechiverengero muvabereki chega chega chakakura kudarika ½. Zvese izvi zvinopfuura 5½. Kuverengera kwakaringana kungaratidza kuti mari iyi ingangoita 7,50918. Kwete zvakawanda, asi nguva dzose, uye iwe unogona kuona kuti nekutora n chero yakakura, ndinogona kupfuura chero nhamba. Izvi zvinononoka zvinoshamisa (somuenzaniso, isu tinotungamira gumi nezvigadzirwa chete), asi kukura kusingagumi kwagara kuchinakidza nyanzvi dzemasvomhu.
Rwendo rwekuenda kuinfinity neharmonic series
Heino dambanemazwi kune dzimwe svomhu dzakakomba. Tine huwandu husingagumi hwemakona emakona (chii chandingataure, rectangular!) Nezviyero, toti, 4 × 2 × 1. Funga nezvehurongwa hunosanganisira akati wandei (pa fig. 2 - mana) zvidhinha, zvakarongwa kuitira kuti yekutanga inorerekera nehafu yehurefu hwayo, yechipiri kubva kumusoro ne ¼ zvichingodaro, yechitatu neyechitanhatu. Zvakanaka, pamwe kuti zvinyatsogadzikana, ngatirerekedzei chidhinha chekutanga zvishoma. Hazvina basa nema calculations.
Mupunga. 2. Kusarudza pakati pesimba rinokwevera zvinhu pasi
Zviri nyore zvakare kunzwisisa kuti sezvo nhamba inoumbwa nematombo maviri ekutanga (kuverenga kubva kumusoro) iine nzvimbo yekuenzanisa panzvimbo B, ipapo B ndiye pakati pegiravhiti. Ngatitsanangurirei geometrically pakati pegiravhiti yegadziriro, inoumbwa nemabhuroko matatu epamusoro. Nharo yakareruka inokwana pano. Ngatigovane mumusoro chidimbu chetatu-block kuita maviri epamusoro uye chetatu chepasi. Nzvimbo iyi inofanira kurara pachikamu chinobatanidza nzvimbo dzegiravhiti yezvikamu zviviri. Panguva ipi muchikamu chino?
Pane nzira mbiri dzekusarudza. Mukutanga, tichashandisa kucherechedza kuti nzvimbo iyi inofanira kurara pakati pematatu-block piramidhi, kureva, pamutsara wakatwasuka unopindirana chechipiri, chepakati. Nenzira yechipiri, tinonzwisisa kuti sezvo mabhuroko maviri epamusoro aine huremu hwakapetwa kaviri hwechivharo chimwe #3 (pamusoro), nzvimbo yesimba rinokwevera zvinhu pasi pachikamu chino inofanira kunge iri padyo neB zvakapetwa kaviri pane pakati. S yechitatu block. Saizvozvowo, tinowana pfungwa inotevera: tinobatanidza nzvimbo inowanikwa yezvivharo zvitatu nechepakati S yechina. Pakati pehurongwa hwese huri pahurefu 2 uye panzvimbo inoparadzanisa chikamu ne1 kusvika 3 (kureva, ne ¾ yehurefu hwayo).
Iwo maverengero atichaita zvishoma kutungamira kune mhedzisiro inoratidzwa muFig. fig 3. Inotevedzana nzvimbo dzegiravhiti dzinobviswa kubva kumucheto wekurudyi wepazasi block ne:
Nokudaro, kuratidzwa kwepakati pegiravhiti yepiramidhi inogara iri mukati mechigadziko. Iyo shongwe haizokoromoke. Zvino ngatitarisei fig. 3 uye kwekanguva, ngatishandisei bhuroko rechishanu kubva kumusoro senheyo (iyo yakamisikidzwa neruvara rwakajeka). Top inclined:
saka, mupendero wayo wekuruboshwe uri 1 mberi kupfuura kumucheto kwekurudyi kwechigadziko. Heino nhanho inotevera:
Chii chinonzi swing? Tinotoziva! Hakuna mukuru! Kutora kunyange zvidhinha zvidiki, unogona kuwana overhang yekiromita imwe - zvinosuruvarisa, chete masvomhu: Nyika yese yaisazokwana kuvaka zvidhinha zvakawanda!
Mupunga. 3. Wedzera mamwe mabhuroki
Zvino masvomhu atasiya pamusoro. Tichaverenga madaro ese "akatarisana" pane x-axis, nekuti ndizvo chete zviripo kwazviri. Point A (pakati pesimba regiravhiti rekutanga) i1/2 kubva kumucheto kwekurudyi. Point B (pakati peiyo maviri block system) iri 1/4 kure nekurudyi kumucheto kwechipiri block. Rega pekutangira kuve kupera kweyechipiri block (ikozvino tichaenda kune yechitatu). Semuenzaniso, ndepapi nzvimbo yepakati yegiravhiti yeimwe block #3? Hafu yehurefu hwechivharo ichi, saka, i1/2 + 1/4 = 3/4 kubva pareferensi yedu. Ko point C iripi? Muzvikamu zviviri kubva muzvitatu zvechikamu chiri pakati pe 3/4 ne 1/4, kureva kuti, pane imwe nguva, tinoshandura nzvimbo yereferensi kumucheto wekurudyi wechitatu. Pakati pesimba regiravhiti retatu-block system ikozvino rabviswa kubva kune nyowani referensi point, zvichingodaro. Center of gravity Cn shongwe inogadzirwa ne n blocks ndeye 1/2n kubva ipapo ipapo referensi poindi, inova iyo yekurudyi mupendero weiyo base block, i.e. nth block kubva kumusoro.
Sezvo nhevedzano yekudzokororwa ichisiyana, tinogona kuwana chero mutsauko wakakura. Izvi zvinganyatsoitwa here? Zvakafanana neshongwe yezvidhinha isingaperi - nekukurumidza kana gare gare ichaputsika pasi pehuremu hwayo. Muchirongwa chedu, kushomeka kusarongeka mukuiswa kweblock (uye kuwedzera zvishoma nezvishoma kwezvikamu zvezvikamu) zvinoreva kuti hatizosvika kure.
