hlehla charm

Kunezinkulumo eziningi mayelana "ne-charm of opposites", hhayi kwizibalo kuphela. Khumbula ukuthi izinombolo eziphambene yilezo ezihluka ngophawu kuphela: hlanganisa 7 kanye nokususa 7. Isamba sezinombolo eziphambene nguziro. Kodwa kithi (okungukuthi osozibalo) ukuphindaphinda kuyathakazelisa kakhulu. Uma umkhiqizo wezinombolo ulingana no-1, lezi zinombolo ziphambene. Inombolo ngayinye inokuphikisana nayo, inombolo ngayinye engeyona i-zero inokuphikisana kwayo. I-reciprocal of the reciprocal yimbewu.

Ukuguqulwa kwenzeka noma yikuphi lapho amanani amabili ehlobene khona ukuze uma eyodwa ikhuphuka, enye yehle ngenani elihambisanayo. "Okufanelekile" kusho ukuthi umkhiqizo walezi zibalo awushintshi. Sikhumbula esikoleni: lokhu kuyingxenye ephambene. Uma ngifuna ukufika lapho ngiya khona ngokushesha kabili (okungukuthi, ukusika isikhathi phakathi), ngidinga ukuphinda kabili isivinini sami. Uma umthamo womkhumbi ovaliwe ngegesi uncishiswa ngezikhathi ze-n, khona-ke ukucindezela kwawo kuzokwanda ngezikhathi ze-n.

Emfundweni yaphansi, sihlukanisa ngokucophelela phakathi kokuqhathanisa okuhlukile nokuhlobene. "Kungakanani okunye"? - "Kukangaki ngaphezulu?"

Nansi eminye imisebenzi yesikole:

Ukuzivocavoca 1. Kumanani amabili amahle, elokuqala likhulu ngokuphindwe ka-5 kunelesibili futhi ngesikhathi esifanayo likhulu ngokuphindwe ka-5 kunelokuqala. Yiziphi izilinganiso?

Ukuzivocavoca 2. Uma inombolo eyodwa ingu-3 inkulu kuneyesibili, futhi eyesibili ingu-2 inkulu kuneyesithathu, inkulu kangakanani inombolo yokuqala kuneyesithathu? Uma inombolo yokuqala iphindwe kabili kuneyesibili, futhi inombolo yokuqala iphindwe kathathu kweyesithathu, inombolo yokuqala inkulu kangaki kuneyesithathu?

Ukuzivocavoca 3. Kumsebenzi wesi-2, izinombolo ezingokwemvelo kuphela ezivunyelwe. Ingabe ilungiselelo elinjalo elichazwe lapho lingenzeka?

Ukuzivocavoca 4. Kumanani amabili amahle, eyokuqala izikhathi ezi-5 kweyesibili, kanti eyesibili izikhathi ezi-5 kweyokuqala. Kungenzeka yini?

Umqondo othi "isilinganiso" noma "isilinganiso" ubonakala ulula kakhulu. Uma ngihamba ngebhayisikili amakhilomitha angama-55 ngoMsombuluko, amakhilomitha angama-45 ngoLwesibili, namakhilomitha angama-80 ngoLwesithathu, ngokwesilinganiso ngangihamba ngebhayisikili amakhilomitha angama-60 ngosuku. Sivumelana ngenhliziyo yonke nalezi zibalo, nakuba ziyaxaka ngoba angizange ngishayele u-60 km ngosuku olulodwa. Samukela kalula amasheya omuntu: uma abantu abangamakhulu amabili bevakashela indawo yokudlela phakathi nezinsuku eziyisithupha, isilinganiso sansuku zonke singama-33 kanye nabantu abathathu. Hm!

Kunezinkinga kuphela ngosayizi ojwayelekile. Ngithanda ukugibela ibhayisikili. Ngakho-ke ngathatha ithuba lokunikezwa kwe-ejensi yezokuvakasha "Ake sihambe nathi" - baletha imithwalo ehhotela, lapho iklayenti ligibela khona ibhayisikili ngezinjongo zokuzijabulisa. NgoLwesihlanu ngishayele amahora amane: owokuqala amabili ngesivinini esingama-24 km ngehora. Ngabe sengikhathala kangangokuthi kwabalandelayo ababili ngesilinganiso esingu-16 kuphela ngehora. Sasiyini isivinini sami esimaphakathi? Yebo (24+16)/2=20km=20km/h.

Nokho, ngoMgqibelo, imithwalo yashiywa ehhotela, ngase ngiyobona amanxiwa alesi nqaba, esiqhele ngamakhilomitha angu-24, futhi ngemva kokuwabona ngabuyela. Ngashayela ihora ohlangothini olulodwa, ngabuyela emuva kancane kancane, ngesivinini esingu-16 km ngehora. Sasiyini isivinini sami esimaphakathi kumzila wehhotela-castle-hotel? 20 km ngehora? Vele akunjalo. Phela ngihambe ibanga elingu-48 km kwangithatha ihora (“khona”) nehora nesigamu ukubuya. 48 km ngamahora amabili nesigamu, i.e. ihora 48/2,5=192/10=19,2 km! Kulesi simo, isivinini esimaphakathi akuyona incazelo ye-arithmetic, kodwa i-harmonic yamanani anikeziwe:

futhi le fomula yezindaba ezimbili ingafundwa kanje: incazelo ye-harmonic yezinombolo eziphozithivu iwukubuyelana kwencazelo ye-arithmetic yokuphindaphinda kwazo. I-reciprocal of the sum of the reciprocals ibonakala kumakhorasi amaningi ezabelo zesikole: uma isisebenzi esisodwa simba amahora, esinye - amahora angu-b, bese sisebenza ndawonye, ​​​​bamba ngesikhathi. ichibi lamanzi (elilodwa ngehora, elinye ngamahora b). Uma i-resistor eyodwa ine-R1 kanti enye ino-R2, khona-ke inokumelana okufanayo. 

Uma ikhompuyutha eyodwa ingaxazulula inkinga ngemizuzwana, enye ikhompuyutha ngemizuzwana engu-b, bese kuthi lapho isebenza ndawonye...

Ima! Yilapho isifaniso siphela khona, ngoba konke kuncike ejubaneni lenethiwekhi: ukusebenza kahle kokuxhumana. Abasebenzi bangakwazi futhi ukuvimbela noma ukusizana. Uma indoda eyodwa ikwazi ukumba umthombo ngamahora ayisishiyagalombili, ingabe izisebenzi ezingamashumi ayisishiyagalombili zingakwenza nge-1/10 yehora (noma imizuzu engu-6)? Uma abathwali bempahla abayisithupha beyisa upiyano esitezi sokuqala ngemizuzu engu-6, kuzothatha isikhathi esingakanani oyedwa wabo ukuletha upiyano esitezi samashumi ayisithupha? Ukungabi nangqondo kwezinkinga ezinjalo kusikhumbuza ukusetshenziswa okulinganiselwe kwazo zonke izibalo ezinkingeni "ezivela ekuphileni".

Mayelana nomthengisi wonke 

Izikali azisasetshenziswa. Khumbula ukuthi kwabekwa isisindo esitsheni esisodwa sezilinganiso ezinjalo, futhi izimpahla ezikalwayo zibekwe kwesinye, futhi lapho isisindo silingana, khona-ke izimpahla zazilingana nesisindo. Yiqiniso, izingalo zombili zomthwalo wesisindo kufanele zibe ubude obufanayo, ngaphandle kwalokho isisindo sizobe singalungile.

Kulungile. Cabanga ngomthengisi onesisindo esinamandla angalingani. Nokho, ufuna ukwethembeka kumakhasimende futhi akale izimpahla ngamaqoqo amabili. Okokuqala, ubeka isisindo epanini elilodwa, kanti kwelinye inani elihambisanayo lezimpahla - ukuze izikali zilingane. Khona-ke ulinganisa "ingxenye" ​​yesibili yezimpahla ngokulandelana okuphambene, okungukuthi, ubeka isisindo endishini yesibili, nempahla ekuqaleni. Njengoba izandla zingalingani, "ama-halves" awalingani. Futhi unembeza womdayisi ucacile, futhi abathengi badumisa ukwethembeka kwakhe: "Engikususile lapha, ngabe sengingeza."

Nokho, ake sibhekisise ukuziphatha komdayisi ofuna ukwethembeka naphezu kwesisindo esiyingozi. Izingalo zebhalansi mazibe nobude u-a no-b. Uma isitsha esisodwa silayishwe isisindo sekhilogremu kanti esinye sinezimpahla ezingu-x, khona-ke izikali ziyalingana uma i-ax = b okokuqala futhi bx = a okwesibili. Ngakho-ke, ingxenye yokuqala yezimpahla ilingana ne-b / ikhilogremu, ingxenye yesibili ngu-a / b. Isisindo esihle sine = b, ngakho umthengi uzothola u-2 kg wezimpahla. Ake sibone ukuthi kwenzekani uma ≠ b. Bese kuba u – b ≠ 0 kanye nefomula encishisiwe yokuphindaphinda esinayo

Sifike kumphumela ongalindelekile: indlela ebonakala ilungile "yokulinganisa" isilinganiso kuleli cala isebenza ukuze kuzuze umthengi, othola izimpahla eziningi.

Umsebenzi 5. (Kubalulekile, neze kuzibalo!). Umiyane unesisindo esingamamiligremu angu-2,5, kanti indlovu inesisindo esingamathani amahlanu (lokhu idatha enembile impela). Bala incazelo ye-arithmetic, incazelo yejiyomethri, kanye nencazelo evumelanayo yomiyane nezindlovu (izisindo). Hlola izibalo futhi ubone ukuthi ziyawenza yini umqondo ngaphandle kokuzivocavoca kwe-arithmetic. Ake sibheke ezinye izibonelo zezibalo zezibalo ezingenangqondo "empilweni yangempela". Ithiphu: Sesike sabheka isibonelo esisodwa kulesi sihloko. Ingabe lokhu kusho ukuthi umfundi ongaziwa umbono wakhe engawuthola ku-inthanethi wawulungile: “Izibalo zikhohlisa abantu ngezinombolo”?

Yebo, ngiyavuma ukuthi ngobukhulu bezibalo, "ungakhohlisa" abantu - isikhangiso ngasinye sesibili se-shampoo sithi kwandisa ukuguquguquka ngamaphesenti athile. Ingabe sizobheka ezinye izibonelo zamathuluzi awusizo ansuku zonke angasetshenziselwa izenzo zobugebengu?

Amagremu!

Isihloko salesi siqephu siyisenzo (umuntu wokuqala ubuningi) hhayi ibizo (ubuningi obuqanjiwe bengxenye eyinkulungwane yekhilogremu). Ukuvumelana kusho ukuhleleka nomculo. KumaGreki asendulo, umculo wawuyigatsha lesayensi - kufanele kuvunywe ukuthi uma sisho kanjalo, sidlulisela incazelo yamanje yegama elithi "isayensi" esikhathini esingaphambi kwenkathi yethu. UPythagoras wayephila ekhulwini lesi-XNUMX BC. Wayengazi nje ikhompyutha, umakhalekhukhwini kanye ne-imeyili, kodwa futhi wayengazi ukuthi uRobert Lewandowski, uMieszko I, uCharlemagne noCicero babengobani. Wayengazi izinombolo zesi-Arabhu noma zamaRoma (zaqala ukusetshenziswa cishe ngekhulu lesi-XNUMX BC), wayengazi ukuthi izimpi zamaPunic zaziyini ... Kodwa wayewazi umculo ...

Wayazi ukuthi ezinsimbini zomculo ezinezintambo ama-coefficients of vibration ayephikisana ngokuphambene nobude bezingxenye ezinyakazayo zezintambo. Wayazi, wayazi, wayengeke nje akwazi ukukuveza ngendlela esenza ngayo namuhla.

Amafrikhwensi ezintambo ezimbili zokudlidliza akha i-octave akwisilinganiso esingu-1:2, okungukuthi, imvamisa yenothi eliphezulu iphindwe kabili kuneyangaphansi. Isilinganiso sokudlidliza esilungile sesihlanu singu-2:3, eyesine ngu-3:4, ingxenye yesithathu enkulu ingu-4:5, ingxenye yesithathu encane ngu-5:6. Lezi izikhawu zongwaqa ezimnandi. Bese kuba khona okubili kokungathathi hlangothi, okuhambisana nokudlidliza okungu-6:7 no-7:8, bese kuba okungama-dissonant - ithoni enkulu (8:9), ithoni encane (9:10). Lezi zingxenyana (izilinganiso) zifana nezilinganiso zamalungu alandelanayo ochungechunge izazi zezibalo (ngaso kanye lesi sizathu) ezilubiza ngochungechunge lwe-harmonic:

iyisamba esingenasiphelo ngokomqondo. Isilinganiso sama-oscillations we-octave singabhalwa njengo-2:4 bese sibeka okwesihlanu phakathi kwakho: 2:3:4, okusho ukuthi, sizohlukanisa i-octave ibe ingxenye yesihlanu neyesine. Lokhu kubizwa nge-harmonic segment division kuzibalo:

Ilayisi. 1. Kumculi: ukuhlukanisa i-octave AB ibe yi-AC yesihlanu.Okwesazi Sezibalo: I-Harmonic Segmentation

Ngiqonde ukuthini uma ngikhuluma (ngenhla) ngesamba esingapheli ngokomqondo, njengochungechunge lwe-harmonic? Kuvela ukuthi isamba esinjalo singaba yinoma iyiphi inombolo enkulu, into eyinhloko ukuthi sengeza isikhathi eside. Kukhona izithako ezimbalwa futhi zincane, kodwa ziningi futhi ziningi zazo. Yini ephumelelayo? Lapha singena emkhakheni wokuhlaziya izibalo. Kuvela ukuthi izithako ziphelile, kodwa hhayi ngokushesha kakhulu. Ngizobonisa ukuthi ngokuthatha izithako ezanele, ngingafingqa:

ezinkulu ngokuzenzela. Ake sithathe "isibonelo" n = 1024. Ake siqoqe amagama njengoba kukhonjisiwe emfanekisweni:

Kubakaki ngamunye, igama ngalinye likhulu kunelangaphambili, ngaphandle, yiqiniso, elokugcina, elilingana nalo. Kubakaki abalandelayo, sinezingxenye ezingu-2, 4, 8, 16, 32, 64, 128 kanye nezingu-512; inani lesamba kubakaki ngamunye likhulu kuno-½. Konke lokhu kungaphezu kuka-5½. Izibalo ezinembe kakhulu zingabonisa ukuthi leli nani lilinganiselwa ku-7,50918. Hhayi okuningi, kodwa njalo, futhi ungabona ukuthi ngokuthatha n iyiphi enkulu, ngiyakwazi ukwedlula noma iyiphi inombolo. Lona uhamba kancane ngendlela emangalisayo (isibonelo, siphezulu kweshumi ngezithako zodwa), kodwa ukukhula okungapheli bekuhlale kubajabulisa osozibalo.

Uhambo oluya ku-infinity ngochungechunge lwe-harmonic

Nansi indida kwezinye izibalo ezibucayi kakhulu. Sinokunikezwa okungenamkhawulo kwamabhulokhi angunxande (ngingathini, unxande!) anobukhulu, yithi, 4 × 2 × 1. Cabangela isistimu ehlanganisa amaningana (ivuliwe umkhiwane. 2 - ezine) amabhlogo, ahlelwe ngendlela yokuthi owokuqala athambekele ngo-½ wobude bawo, owesibili ukusuka phezulu ngo-¼ njalonjalo, owesithathu ngesithupha. Hhayi-ke, mhlawumbe ukuze sizinze ngempela, ake sitshekise isitini sokuqala kancane. Akusho lutho ngezibalo.

Ilayisi. 2. Ukunquma isikhungo samandla adonsela phansi

Kulula futhi ukuqonda ukuthi njengoba isibalo esakhiwe amabhulokhi amabili okuqala (ukubala kusuka phezulu) sinesikhungo sokulinganisa endaweni engu-B, khona-ke u-B uyisikhungo samandla adonsela phansi. Ake sichaze ngokwejometri isikhungo samandla adonsela phansi esistimu, esakhiwe amabhulokhi amathathu aphezulu. Ukuphikisana okulula kakhulu kwanele lapha. Ake sihlukanise ngokwengqondo ukwakheka kwamabhlogo amathathu kube amabili aphezulu kanye nelesithathu eliphansi. Lesi sikhungo kufanele silale engxenyeni exhuma izikhungo zamandla adonsela phansi ezingxenyeni ezimbili. Kusiphi isikhathi kulesi siqephu?

Kunezindlela ezimbili zokuqoka. Okokuqala, sizosebenzisa ukuqaphela ukuthi lesi sikhungo kufanele silale phakathi kwephiramidi yamabhuloki amathathu, okungukuthi, emgqeni oqondile onqamula ibhulokhi yesibili, ephakathi. Ngendlela yesibili, siyaqonda ukuthi njengoba amabhulokhi amabili aphezulu enesisindo esiphelele esiphindwe kabili kunebhulokhi eyodwa #3 (phezulu), isikhungo samandla adonsela phansi kulesi sigaba kufanele sisondele kabili ku-B njengoba sisenkabeni. S yebhlokhi yesithathu. Ngokufanayo, sithola iphuzu elilandelayo: sixhuma isikhungo esitholakalayo samabhulokhi amathathu nesikhungo S sebhokisi lesine. Isikhungo salo lonke uhlelo siphakeme ngo-2 futhi sisendaweni ehlukanisa ingxenye ngo-1 kuya ku-3 (okungukuthi, ngo-¾ wobude bayo).

Izibalo esizozenza ziholela kancane kumphumela oboniswe ku-Fig. ikhiwa 3. Izikhungo ezilandelanayo zamandla adonsela phansi zisuswa emaphethelweni angakwesokudla webhulokhi engezansi ngokuthi:

Ngakho, ukuqagela kwesikhungo sokudonsela phansi kwephiramidi kuhlala kungaphakathi kwesisekelo. Umbhoshongo ngeke udilike. Manje ake sibheke umkhiwane. 3 futhi okwesikhashana, masisebenzise ibhulokhi yesihlanu ukusuka phezulu njengesisekelo (lena ephawulwe ngombala ogqamile). Okuthambekele okuphezulu:

ngakho-ke, unqenqema lwayo lwesokunxele luyi-1 ngaphezulu kunomkhawulo ongakwesokudla wesisekelo. Nakhu ukuphenduka okulandelayo:

Imuphi umjiko omkhulu? Sesiyazi! Akukho okukhulu! Ukuthatha ngisho namabhulokhi amancane kakhulu, ungathola i-overhang yekhilomitha elilodwa - ngeshwa, ngezibalo kuphela: Umhlaba wonke ubungeke wanele ukwakha amabhlogo amaningi kangaka!

Ilayisi. 3. Engeza amabhlogo engeziwe

Manje izibalo ukuthi sizishiye ngenhla. Sizobala wonke amabanga "ngokuvundlile" ku-x-eksisi, ngoba yilokho kuphela okukhona kuyo. Iphoyinti A (isikhungo sokudonsela phansi kwebhulokhi yokuqala) iyi-1/2 ukusuka onqenqemeni olungakwesokudla. Iphoyinti B (isikhungo sesistimu yebhulokhi ezimbili) ikude nge-1/4 ukusuka kwesokudla sebhulokhi yesibili. Vumela indawo yokuqala ibe ukuphela kwebhulokhi yesibili (manje sizodlulela kwesesithathu). Isibonelo, ikuphi isikhungo sokudonsela phansi kwebhulokhi eyodwa #3? Ingxenye yobude baleli bhulokhi, ngakho-ke, ingu-1/2 + 1/4 = 3/4 ukusuka endaweni yethu eyinkomba. Likuphi iphuzu C? Ezingxenyeni ezimbili kwezintathu zesegimenti ephakathi kuka-3/4 no-1/4, okungukuthi endaweni engaphambili, sishintsha iphoyinti lereferensi libe onqenqemeni olungakwesokudla lwebhulokhi yesithathu. Isikhungo se-gravity yesistimu ye-block-block manje isusiwe endaweni entsha yokubhekisela, njalonjalo. Isikhungo se-gravity C_n umbhoshongo owenziwe ngamabhulokhi angu-n ukude ngo-1/2n endaweni yereferensi esheshayo, okuwumkhawulo ongakwesokudla webhulokhi yesisekelo, okungukuthi ibhulokhi elingu-nth ukusuka phezulu.

Njengoba uchungechunge lwama-reciprocals luhlukana, singathola noma yikuphi ukuhluka okukhulu. Ingabe lokhu kungenziwa ngempela? Kufana nombhoshongo wezitini ongapheli - ngokushesha noma kamuva uzowa ngaphansi kwesisindo sawo. Kuhlelo lwethu, ukunganembi okuncane ekubekweni kwamabhulokhi (kanye nokwenyuka kancane kwesamba sezibalo zochungechunge) kusho ukuthi ngeke sifike kude kakhulu.