sinthani chithumwa
Pali zokamba zambiri za "chithumwa cha otsutsana", osati masamu okha. Kumbukirani kuti manambala otsutsana ndi omwe amasiyana pachizindikiro chokha: kuphatikiza 7 ndi kuchotsera 7. Chiwerengero cha manambala otsutsana ndi ziro. Koma kwa ife (i.e. masamu) zobwezera ndizosangalatsa kwambiri. Ngati chiwerengero cha manambala chikufanana ndi 1, ndiye kuti manambalawa amatsutsana. Nambala iliyonse ili ndi zosiyana zake, nambala iliyonse yopanda ziro imakhala yosiyana. Chobwezerananso ndi mbewu.
Kutembenuka kumachitika paliponse pomwe kuchuluka kwawiri kumalumikizana wina ndi mzake kotero kuti ngati wina akuwonjezeka, winayo amachepetsa pamlingo wofanana. "Zoyenera" zikutanthauza kuti chopangidwa ndi miyeso iyi sichisintha. Timakumbukira kuchokera kusukulu: ichi ndi gawo losiyana. Ngati ndikufuna kupita komwe ndikupita kuwirikiza kawiri (ie kudula nthawi pakati), ndiyenera kuwirikiza kawiri liwiro langa. Ngati kuchuluka kwa chotengera chosindikizidwa ndi gasi kumachepetsedwa ndi n times, ndiye kuti kuthamanga kwake kumawonjezeka ndi n times.
M'maphunziro a pulayimale, timasiyanitsa mosamala pakati pa kufananitsa kosiyana ndi wachibale. "Muli bwanji"? - "Kawirikawiri bwanji?"
Nazi zina zomwe zimachitika kusukulu:
Ntchito 1. Pazigawo ziwiri zabwino, yoyamba ndi 5 nthawi zambiri kuposa yachiwiri komanso nthawi 5 kuposa yoyamba. Kodi miyeso yake ndi yotani?
Ntchito 2. Ngati nambala imodzi ndi 3 yaikulu kuposa yachiwiri, ndipo yachiwiri ndi 2 yaikulu kuposa yachitatu, kodi nambala yoyamba ndi yochuluka bwanji kuposa yachitatu? Ngati nambala yoyamba ndi yachiwiri ndi yachiwiri, ndipo nambala yoyamba ili katatu pachitatu, ndi kangati nambala yoyamba imakhala yaikulu kuposa yachitatu?
Ntchito 3. Mu ntchito 2, manambala achilengedwe okha ndi omwe amaloledwa. Kodi makonzedwe oterowo monga momwe akulongosoledwera pamenepo ndi otheka?
Ntchito 4. Pazinthu ziwiri zabwino, yoyamba ndi 5 nthawi yachiwiri, ndipo yachiwiri ndi 5 nthawi yoyamba. Ndizotheka kodi?
Lingaliro la "average" kapena "average" likuwoneka losavuta. Ngati ndimayenda panjinga 55 Km Lolemba, 45 km Lachiwiri, ndi 80 km Lachitatu, pa avareji ndimayenda 60 km patsiku. Timavomereza ndi mtima wonse mawerengedwewa, ngakhale kuti ndi achilendo pang'ono chifukwa sindinayendetse makilomita 60 tsiku limodzi. Timangovomereza mosavuta magawo a munthu: ngati anthu mazana awiri amapita kumalo odyera mkati mwa masiku asanu ndi limodzi, ndiye kuti pafupifupi tsiku lililonse ndi 33 ndi anthu atatu. Hm!
Pali mavuto okha ndi kukula kwapakati. Ndimakonda kupalasa njinga. Kotero ndinapezerapo mwayi woperekedwa ndi bungwe loyendetsa maulendo "Tiyeni tipite nafe" - amapereka katundu ku hotelo, kumene kasitomala amakwera njinga pofuna zosangalatsa. Lachisanu ndinayendetsa kwa maola anayi: awiri oyambirira pa liwiro la 24 km pa ola. Kenako ndinatopa kwambiri moti kwa aŵiri otsatirawo ndinali ndi 16 kokha pa ola limodzi. Liwiro langa linali lotani? Inde (24+16)/2=20km=20km/h.
Komabe, Loweruka katunduyo anasiyidwa kuhotela, ndipo ndinapita kukawona mabwinja a nyumba yachifumuyo, yomwe ili pamtunda wa makilomita 24, ndipo nditawaona, ndinabwerera. Ndinayendetsa ola limodzi mbali imodzi, ndikubwerera pang’onopang’ono, pa liwiro la makilomita 16 pa ola. Kodi pafupifupi liwiro langa linali lotani panjira ya hotelo-castle-hotelo? 20 km pa ola? Inde sichoncho. Pambuyo pake, ndinayendetsa makilomita a 48 ndipo zinanditengera ola limodzi ("kumeneko") ndi ola limodzi ndi theka kubwerera. 48 km mu maola awiri ndi theka, i.e. ola 48/2,5=192/10=19,2 km! Munthawi imeneyi, liwiro lapakati sikutanthauza masamu, koma ma harmonic a mfundo zomwe zaperekedwa:
ndipo ndondomeko ya nsanjika ziwiriyi ikhoza kuwerengedwa motere: tanthauzo la harmonic la manambala abwino ndilofanana ndi chiwerengero cha masamu omwe amafanana nawo. The reciprocal of the reciprocals of the reciprocals imapezeka m'makwaya ambiri a ntchito za sukulu: ngati wogwira ntchito akukumba maola, wina - maola a b, ndiye, akugwira ntchito limodzi, amakumba nthawi yake. dziwe lamadzi (limodzi pa ola, lina pa maola b). Ngati wotsutsa mmodzi ali ndi R1 ndipo winayo ali ndi R2, ndiye kuti ali ndi kukana kofanana.
Ngati kompyuta imodzi imatha kuthetsa vuto mumasekondi, kompyuta ina mumasekondi b, ndiye ikamagwira ntchito limodzi...
Imani! Apa ndi pamene fanizo limatha, chifukwa chirichonse chimadalira pa liwiro la intaneti: mphamvu ya maulumikizidwe. Ogwira ntchito angathenso kulepheretsa kapena kuthandizana. Ngati munthu m’modzi atha kukumba chitsime m’maola asanu ndi atatu, kodi antchito makumi asanu ndi atatu angachichite mu 1/10 ya ola (kapena mphindi 6)? Ngati onyamula limba asanu ndi mmodzi atengera limba pansanjika yoyamba m'mphindi 6, kodi m'modzi wa iwo adzatenga nthawi yayitali bwanji kuti apereke piyano kuchipinda cha XNUMX? Kupanda nzeru kwa mavuto oterowo kumabweretsa kukumbukira kuchepa kwa masamu onse ku mavuto "kuchokera ku moyo".
Wokondedwa wogulitsa
Mamba sagwiritsidwanso ntchito. Kumbukirani kuti mbale ina ya sikeloyo inkaikidwa m’mbale imodzi, ndipo katundu woyezedwayo ankaikidwa pa ina, ndipo pamene kulemera kwake kunali kofanana, ndiye kuti katunduyo ankalemera mofanana ndi kulemera kwake. Inde, mikono yonse yolemetsa iyenera kukhala yofanana kutalika, apo ayi kulemera kwake kudzakhala kolakwika.
O kulondola. Tangoganizirani munthu wogulitsa amene ali ndi kulemera kopanda mphamvu. Komabe, amafuna kukhala woona mtima kwa makasitomala ndi kuyeza katunduyo m’magulu awiri. Choyamba, amaika cholemera pa poto imodzi, ndipo pa chimzakecho amaika katundu wofanana - kuti miyesoyo ikhale yofanana. Kenako amapima “theka” lachiŵiri la katunduyo mosinthananso, ndiko kuti, amaika kulemera kwa mbale yachiŵiri, ndi katunduyo pa yoyamba. Popeza manja ndi osafanana, "mahafu" sakhala ofanana. Ndipo chikumbumtima cha wogulitsa ndi chomveka, ndipo ogula amatamanda kukhulupirika kwake: "Zimene ndinachotsa apa, ndiye ndinawonjezera."
Komabe, tiyeni tione bwinobwino khalidwe la wogulitsa amene amafuna kukhala woona mtima ngakhale kuti ali ndi kulemera koopsa. Lolani mikono yotsalira ikhale ndi kutalika kwa a ndi b. Ngati mbale imodzi yapakidwa kulemera kwa kilogalamu ndipo ina ili ndi x katundu, ndiye kuti sikelo imakhala yofanana ngati nkhwangwa = b nthawi yoyamba ndi bx = kachiwiri. Kotero, gawo loyamba la katundu ndi lofanana ndi b / kilogalamu, gawo lachiwiri ndi / b. Kulemera kwabwino kumakhala ndi = b, kotero wogula adzalandira 2 kg ya katundu. Tiyeni tiwone zomwe zimachitika ngati ≠ b. Kenako a - b ≠ 0 komanso kuchokera ku njira yochepetsera yochulukitsa yomwe tili nayo
Tinafika ku zotsatira zosayembekezeka: njira yowoneka ngati yabwino "yowerengera" muyeso mu nkhaniyi imagwira ntchito kuti ipindule ndi wogula, yemwe amalandira katundu wambiri.
Ntchito 5. (Chofunika, ayi mu masamu!). Udzudzu umalemera mamiligalamu 2,5, ndipo njovu imalemera matani asanu (izi ndi zolondola kwambiri). Werezerani tanthauzo la masamu, tanthauzo la geometric, ndi tanthauzo la udzudzu ndi njovu (zolemera). Yang'anani mawerengedwewo ndikuwona ngati ali ndi tanthauzo lililonse kupatula masamu. Tiyeni tiwone zitsanzo zina za mawerengedwe a masamu omwe samveka mu "moyo weniweni". Zokuthandizani: Taona kale chitsanzo chimodzi m’nkhaniyi. Kodi izi zikutanthauza kuti wophunzira wosadziwika amene maganizo ake ndinapeza pa intaneti anali olondola: "Masamu amapusitsa anthu ndi manambala"?
Inde, ndikuvomereza kuti mu kukula kwa masamu, mukhoza "kupusitsa" anthu - kutsatsa kwa shamposi iliyonse kumati kumawonjezera fluffiness ndi peresenti. Kodi tiyang'ane zitsanzo zina za zida zatsiku ndi tsiku zomwe zingagwiritsidwe ntchito pazachiwembu?
Ma gramu!
Mutu wa ndimeyi ndi mneni (munthu woyamba kuchulukitsa) osati dzina (mochulukitsitsa cha chikwi chimodzi cha kilogalamu). Kugwirizana kumatanthauza dongosolo ndi nyimbo. Kwa Agiriki akale, nyimbo inali nthambi ya sayansi - ziyenera kuvomereza kuti ngati titero, timasamutsa tanthauzo lamakono la mawu oti "sayansi" ku nthawi yathu isanafike. Pythagoras ankakhala m'zaka za m'ma XNUMX BC. Sanangodziwa makompyuta, foni yam'manja ndi imelo, komanso sankadziwa kuti Robert Lewandowski, Mieszko I, Charlemagne ndi Cicero anali ndani. Sankadziwa manambala achiarabu kapena achiroma (anayamba kugwiritsidwa ntchito cha m'zaka za m'ma XNUMX BC), sankadziwa kuti Nkhondo za Punic zinali zotani ... Koma ankadziwa nyimbo ...
Iye ankadziwa kuti pa zoimbira za zingwe mphamvu za kunjenjemera zimayenderana mosagwirizana ndi kutalika kwa mbali zonjenjemera za zingwezo. Iye ankadziwa, iye ankadziwa, iye sakanakhoza basi kufotokoza izo momwe ife timachitira izo lero.
Mafupipafupi a zingwe ziwiri zogwedezeka zomwe zimapanga octave ali mu chiŵerengero cha 1: 2, ndiko kuti, mafupipafupi a cholembera chapamwamba ndi kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawiri kawirizanikoloze kanu kukhale kocheperako. Kugwedezeka koyenera kwachisanu ndi 2:3, chachinayi ndi 3:4, chachitatu chenicheni ndi 4:5, chaching'ono chachitatu ndi 5:6. Awa ndi ma consonant intervals osangalatsa. Kenako pali awiri osalowerera ndale, omwe ali ndi ma vibration ratios a 6: 7 ndi 7: 8, kenako osagwirizana - toni yayikulu (8: 9), kamvekedwe kakang'ono (9:10). Tizigawo tating'onoting'ono tating'onoting'ono tating'onoting'ono (magawo) ndi ofanana ndi magawo otsatizana omwe akatswiri a masamu (pazifukwa zomwezi) amawatcha mndandanda wa harmonic:
ndi ndalama zopanda malire. Chiŵerengero cha oscillations cha octave chikhoza kulembedwa ngati 2: 4 ndikuyika chachisanu pakati pawo: 2:3:4, ndiko kuti, tidzagawaniza octave muchisanu ndi chachinayi. Izi zimatchedwa harmonic segment division mu masamu:
Mpunga. 1. Kwa oyimba: kugawa octave AB mu AC yachisanu.Kwa Katswiri wa Masamu: Harmonic Segmentation
Kodi ndikutanthauza chiyani ndikamalankhula (pamwambapa) za kuchuluka kopanda malire, monga mndandanda wa harmoni? Zikuoneka kuti kuchuluka koteroko kungakhale chiwerengero chachikulu, chinthu chachikulu ndi chakuti timawonjezera kwa nthawi yaitali. Pali zosakaniza zochepa komanso zochepa, koma pali zowonjezereka. Kodi chapambana n'chiyani? Apa tikulowa mu gawo la kusanthula masamu. Zikuoneka kuti zosakaniza zatha, koma osati mofulumira kwambiri. Ndiwonetsa kuti potenga zosakaniza zokwanira, nditha kufotokoza mwachidule:
chachikulu mopanda pake. Tiyeni titenge "mwachitsanzo" n = 1024. Tiyeni tigawane mawu monga momwe tawonetsera pachithunzichi:
M'makolo onse, liwu lirilonse ndi lalikulu kuposa lapitalo, kupatulapo, ndithudi, lomaliza, lomwe liri lofanana nalo lokha. M'mabulaketi otsatirawa, tili ndi zigawo 2, 4, 8, 16, 32, 64, 128 ndi 512; mtengo wa chiŵerengero m'mabungwe aliwonse ndi woposa ½. Zonsezi ndizoposa 5½. Kuwerengera kolondola kungasonyeze kuti ndalamazi ndi pafupifupi 7,50918. Osati zambiri, koma nthawi zonse, ndipo mutha kuwona kuti potenga n wamkulu, nditha kupitilira nambala iliyonse. Izi ndizochedwa kwambiri (mwachitsanzo, timakhala pamwamba khumi ndi zosakaniza zokha), koma kukula kosatha kwakhala kukopa akatswiri a masamu nthawi zonse.
Ulendo wopita ku infinity ndi mndandanda wa harmonic
Nayi chithunzithunzi cha masamu ena ovuta kwambiri. Tili ndi malire opanda malire a midadada amakona anayi (ndinganene chiyani, amakona anayi!) Ndi miyeso, kunena, 4 × 2 × 1. chith. 2 - zinayi) midadada, yokonzedwa kuti yoyamba ikhale ndi ½ ya kutalika kwake, yachiwiri kuchokera pamwamba ndi ¼ ndi zina zotero, yachitatu ndi chisanu ndi chimodzi. Chabwino, mwina kuti ikhale yokhazikika, tiyeni tipendeketse njerwa yoyambayo pang'ono. Zilibe kanthu kuwerengera.
Mpunga. 2. Kudziwa pakati pa mphamvu yokoka
N'zosavuta kumvetsetsa kuti popeza chiwerengero chopangidwa ndi midadada iwiri yoyamba (kuwerengera kuchokera pamwamba) chili ndi pakati pa symmetry pa mfundo B, ndiye B ndiye likulu la mphamvu yokoka. Tiyeni titanthauze geometric pakati pa mphamvu yokoka ya dongosolo, lopangidwa ndi midadada itatu yapamwamba. Kukangana kosavuta kwambiri kumakwanira apa. Tiyeni tigawe m'maganizo zomwe zili ndi mipiringidzo itatu kukhala ziwiri zapamwamba ndi zachitatu kutsika. Likululi liyenera kugona pagawo lomwe limalumikiza pakati pa mphamvu yokoka ya magawo awiriwa. Kodi muchigawo chino?
Pali njira ziwiri zopangira. Choyamba, tidzagwiritsa ntchito kuwonetseratu kuti malowa ayenera kugona pakati pa piramidi yazitsulo zitatu, mwachitsanzo, pamzere wowongoka wodutsa chipika chachiwiri, chapakati. Mwanjira yachiwiri, tikumvetsetsa kuti popeza midadada iwiri yapamwamba imakhala ndi kuchuluka kowirikiza kawiri kwa chipika chimodzi #3 (pamwamba), mphamvu yokoka yapakati pa gawoli iyenera kuyandikira kawiri ku B kuposa pakati. S wa chipika chachitatu. Mofananamo, timapeza mfundo yotsatirayi: timagwirizanitsa malo opezeka a midadada atatu ndi pakati S wa chipika chachinayi. Pakatikati pa dongosolo lonselo ndi pamtunda wa 2 ndipo pamapeto pake amagawaniza gawolo ndi 1 mpaka 3 (ndiko kuti, ndi ¾ kutalika kwake).
Kuwerengera komwe tidzachita kutsogola pang'ono ku zotsatira zomwe zikuwonetsedwa mkuyu. mku 3. Malo otsatizana a mphamvu yokoka amachotsedwa m'mphepete kumanja kwa chipika chakumunsi ndi:
Choncho, kuwonetsera kwapakati pa mphamvu yokoka ya piramidi nthawi zonse kumakhala pansi. nsanja sidzagwetsa. Tsopano tiyeni tione chith. 3 ndipo kwakanthawi, tiyeni tigwiritse ntchito chipika chachisanu kuchokera pamwamba ngati maziko (chimene chili ndi mtundu wowala). Zokonda kwambiri:
motero, m'mphepete mwake kumanzere ndi 1 kupitirira kumanja kwa maziko. Nayi kusintha kotsatira:
Kodi kugwedezeka kwakukulu ndi chiyani? Tikudziwa kale! Palibe wamkulu! Kutenga ngakhale midadada yaying'ono kwambiri, mutha kupitilira kilomita imodzi - mwatsoka, masamu: Dziko lonse lapansi silingakhale lokwanira kumanga midadada yambiri!
Mpunga. 3. Onjezani midadada ena
Tsopano mawerengedwe kuti tinasiya pamwamba. Tiwerengera mtunda wonse "mopingasa" pa x-axis, chifukwa ndizo zonse zomwe zilipo. Point A (pakati pa mphamvu yokoka ya chipika choyamba) ndi 1/2 kuchokera kumphepete kumanja. Point B (pakatikati pa block block) ndi 1/4 kutali ndi kumanja kwa chipika chachiwiri. Lolani malo oyambira akhale kumapeto kwa chipika chachiwiri (tsopano tipitilira chachitatu). Mwachitsanzo, pakatikati pa mphamvu yokoka ya single block #3 ndi pati? Theka la kutalika kwa chipikachi, choncho, ndi 1/2 + 1/4 = 3/4 kuchokera kumalo athu ofotokozera. Kodi point C ili kuti? Mu magawo awiri mwa magawo atatu a gawo pakati pa 3/4 ndi 1/4, mwachitsanzo, pa mfundo yapitayi, timasintha malo owonetsera kumphepete kumanja kwa chipika chachitatu. Pakatikati pa mphamvu yokoka ya katatu-block dongosolo tsopano amachotsedwa ku malo atsopano, ndi zina zotero. Pakati pa mphamvu yokoka Cn nsanja yopangidwa ndi n midadada ndi 1/2n kutali ndi malo ofotokozera pompopompo, yomwe ili m'mphepete kumanja kwa chipika choyambira, i.e. chipika cha nth kuchokera pamwamba.
Popeza mndandanda wa reciprocals umasiyana, titha kupeza kusiyana kwakukulu kulikonse. Kodi izi zingathekedi? Zili ngati nsanja ya njerwa yopanda malire - posakhalitsa idzagwa pansi pa kulemera kwake. Pachiwembu chathu, zolakwika zochepa pakuyika ma block (komanso kukwera pang'onopang'ono kwandalama pang'ono) kumatanthauza kuti sitifika patali.
