Mabwalo amitundu ndi kadamsana wadzuwa
Nkhaniyi ikufotokoza za makalasi anga a ana asukulu zapakati omwe amalandila maphunziro a National Children's Fund. Maziko amafunafuna ana ndi achinyamata aluso (kuyambira giredi XNUMX kusukulu ya pulaimale mpaka kusekondale) ndipo amapereka "maphunziro" kwa ophunzira osankhidwa. Komabe, sizimaphatikizapo kuchotsa ndalama konse, koma chisamaliro chokwanira cha chitukuko cha talente, monga lamulo, kwa zaka zambiri. Mosiyana ndi mapulojekiti ena ambiri amtunduwu, ma ward a Foundation amatengedwa mozama ndi asayansi otchuka, anthu azikhalidwe, akatswiri odziwika bwino komanso anthu ena anzeru, komanso ndale.
Zochita za Foundation zimafikira kumaphunziro onse omwe ndi maphunziro oyambira kusukulu, kupatula masewera, kuphatikiza zaluso. Thumbali lidapangidwa mu 1983 ngati njira yothanirana ndi zomwe zidachitika panthawiyo. Aliyense angagwiritse ntchito thumba (nthawi zambiri kudzera kusukulu, makamaka kumapeto kwa chaka cha sukulu), koma, ndithudi, pali sieve inayake, ndondomeko yoyenerera.
Monga ndanenera kale, nkhaniyi idachokera kumaphunziro anga ambuye, makamaka ku Gdynia, mu Marichi 2016, pasukulu yasekondale ya 24 pasukulu yasekondale ya III. Navy. Kwa zaka zambiri, maseminawa akhala akukonzedwa mothandizidwa ndi Foundation ndi Wojciech Thomalczyk, mphunzitsi wachikoka chodabwitsa komanso wanzeru kwambiri. Mu 2008, adalowa khumi apamwamba ku Poland, omwe adapatsidwa udindo wa Pulofesa wa Pedagogy (zoperekedwa ndi lamulo zaka zambiri zapitazo). Pali kukokomeza pang'ono m'mawu akuti: "Maphunziro ndi gwero la dziko lapansi".
ndi mwezi nthawi zonse zosangalatsa - ndiye mutha kumva kuti tikukhala pa pulaneti laling'ono m'malo akulu, pomwe chilichonse chikuyenda, kuyeza ma centimita ndi masekondi. Zimandiwopsyezanso pang'ono, komanso chifukwa cha momwe nthawi ikuyendera. Tikuphunzira kuti kadamsana wotsatira, wowonekera kudera la Warsaw lero, adzakhala mu... 2681. Ndikudabwa kuti ndani aziwona? Miyezo yowoneka bwino ya Dzuwa ndi Mwezi m'mlengalenga mwathu ndi yofanana - ndichifukwa chake kadamsana amakhala waufupi komanso wodabwitsa kwambiri. Kwa zaka zambiri, mphindi zazifupizi ziyenera kukhala zokwanira kuti akatswiri a zakuthambo azitha kuwona korona wa dzuwa. Ndizodabwitsa kuti zimachitika kawiri pachaka ... koma izi zimangotanthauza kuti kwinakwake padziko lapansi amatha kuwonedwa kwa nthawi yochepa. Chifukwa cha kusuntha kwa mafunde, Mwezi ukuchoka pa Dziko Lapansi - m'zaka 260 miliyoni zidzakhala kutali kwambiri kotero kuti (ife ???) tidzangowona kadamsana wa annular.
Zikuoneka kuti woyamba kulosera kadamsana, anali Thales wa ku Mileto (zaka 28-585 BC). Sitingadziwe ngati zidachitikadi, ndiye kuti, ngati adaneneratu, chifukwa chakuti kadamsana ku Asia Minor kunachitika pa May 567, 566 BC ndi mfundo yotsimikiziridwa ndi mawerengedwe amakono. Zachidziwikire, ndimatchula zambiri zanthawi yamasiku ano. Ndili mwana, ndinkaganizira mmene anthu ankawerengera zaka. Ndiye izi, mwachitsanzo, XNUMX BC, Usiku wa Chaka Chatsopano ukubwera ndipo anthu akusangalala: zaka XNUMX zokha BC! Ayenera kuti anasangalala chotani nanga pamene “nyengo yathu” pomalizira pake inafika! Ndi kusinthika kotani nanga kwa zaka zikwi zambiri kumene tinakhala nako zaka zingapo zapitazo!
Masamu Owerengera Madeti ndi Magawo kadamsana, sizovuta kwambiri, koma zimadzaza ndi mitundu yonse ya zinthu zomwe zimagwirizanitsidwa ndi nthawi zonse komanso, zoipitsitsa, ndi kayendetsedwe kosagwirizana kwa thupi mumayendedwe. Ndikufuna ngakhale kudziwa masamu awa. Kodi Thales wa ku Mileto akanatha bwanji kuwerengera zofunika? Yankho lake ndi losavuta. Muyenera kukhala ndi mapu akumwamba. Mupanga bwanji mapu otere? Izi sizilinso zovuta, Aigupto akale ankadziwa momwe angachitire. Pakati pa usiku, ansembe aŵiri anatuluka padenga la kachisi. Aliyense amakhala pansi ndikujambula zomwe akuwona (monga mnzake). Pambuyo pa zaka XNUMX, tikudziwa zonse zokhudza kayendedwe ka mapulaneti ...
Zokongola za geometry, kapena zosangalatsa pa "rug"
Agiriki sankakonda manambala, adagwiritsa ntchito geometry. Izi ndi zomwe tidzachita. Zathu kadamsana zidzakhala zosavuta, zokongola, koma zosangalatsa komanso zenizeni. Timavomereza msonkhano kuti chithunzi cha buluu chimayenda motere kuti chiphimbe chofiira. Tiyeni titchule chithunzi cha buluu mwezi, ndi chithunzi chofiira dzuwa. Timadzifunsa mafunso awa:
- kadamsana kumatenga nthawi yayitali bwanji;
- pamene theka la cholinga chaphimbidwa;
Mpunga. 1 "Carpet" yamitundu yambiri yokhala ndi dzuwa ndi mwezi
- kuphimba kwakukulu ndi chiyani;
- ndizotheka kusanthula kudalira kwachitetezo cha chishango pa nthawi yake? M'nkhaniyi (ndili ndi malire ndi kuchuluka kwa malemba) ndidzayang'ana pa funso lachiwiri. Kumbuyo kwa izi pali geometry yabwino, mwina popanda kuwerengera kotopetsa. Tiyeni tione mkuyu. 1. Kodi tingaganize kuti zidzagwirizanitsidwa ndi ... kadamsana wa dzuwa?
Ndiyenera kunena moona mtima kuti ntchito zomwe ndikambirane zidzasankhidwa mwapadera, kusinthidwa kuti zigwirizane ndi chidziwitso ndi luso la ophunzira apakati ndi apamwamba. Koma timayesetsa kuchita zinthu monga ngati oimba amasewera masikelo, ndipo othamanga amachita masewera olimbitsa thupi kuti akule bwino. Kupatula apo, si chiguduli chokongola chabe (mkuyu 1)?
Mpunga. 2 "Blue" Moon ndi "Red" Dzuwa
Matupi athu akumwamba, poyamba, adzakhala mabwalo amitundu. Mwezi ndi buluu, dzuwa ndi lofiira (zabwino kwambiri zokongoletsa). ndi panopa kadamsana Mwezi umathamangitsa dzuwa kudutsa mlengalenga, kuligwira ... ndi kulitseka. Zidzakhalanso chimodzimodzi ndi ife. Chosavuta kwambiri, pamene Mwezi umayenda pafupi ndi Dzuwa, monga momwe tawonetsera mkuyu. 2. Kadamsana amayamba pamene nsonga ya diski ya Mwezi yakhudza nsonga ya Dzuwa (mkuyu 2) ndipo imatha pamene idutsa.
Mpunga. 3 Mwezi umayandikira dzuwa mozungulira
Tikuganiza kuti "Mwezi" umasuntha selo limodzi pa nthawi, mwachitsanzo, pamphindi. Kadamsanayu amatenga nthawi yokwana mayunitsi asanu ndi atatu, tinganene kuti mphindi. Theka kadamsana mdima kwathunthu Theka la kuyimba kwatsekedwa kawiri: pambuyo pa 2 ndi 6 mphindi. Chiwerengero cha obscuration graph ndichosavuta. Pamphindi ziwiri zoyambirira, chishango chimatseka mofanana pa mlingo wa zero mpaka 1, mphindi ziwiri zotsatira zimawonekera pamlingo womwewo.
Pano pali chitsanzo chochititsa chidwi (mkuyu 3). Mwezi ukuyandikira dzuwa mozungulira. Malinga ndi mgwirizano wathu wolipira mphindi imodzi, kadamsanayu amatha 8√2 mphindi - pakati pa nthawi ino tili ndi kadamsana wathunthu. Tiyeni tiwerengere gawo la dzuwa lomwe limaphimbidwa pambuyo pa nthawi t (mkuyu 3). Ngati mphindi t zadutsa chiyambireni kadamsana ndipo chifukwa chake Mwezi uli monga momwe zasonyezedwera mkuyu. 5, ndiye (tcheru!) Chifukwa chake chophimbidwa (dera la square APQR), lofanana ndi theka la diski ya solar, chifukwa chake chimakutidwa liti, i.e. mumphindi 4 (kenako mphindi 4 kadamsana usanathe).
Mpunga. 4 Chithunzi cha "shading" ntchito
Zonse imatha mphindi imodzi (t = 4√2), ndi graph ya "gawo lamthunzi" ntchito imakhala ndi ma arcs awiri a parabolas (mkuyu 4).
Mwezi wathu wabuluu udzakhudza ngodya ndi dzuwa lofiira, koma lidzaphimba, osati diagonally, koma diagonally pang'ono. Njira yoyendetsera tsopano ndi vector [6], ndiko kuti, "maselo anayi kumanja, maselo atatu mmwamba." Malo a Dzuwa ndi otero kuti kadamsana amayamba (malo A) pamene mbali za "zakumwamba" zimasinthana kufika pa kotala la utali wake. Mwezi ukafika pamalo B, udzaphimba gawo limodzi mwa magawo asanu ndi limodzi a Dzuwa, ndipo pamalo a C udzaphimbika theka. Pamalo D, timakhala ndi kadamsana wathunthu, ndiyeno zonse zimabwereranso, "monga momwe zinalili."
Mpunga. 5 Mbali ya Dzuwa yobisika pa nthawi t
Kadamsanayu amatha pamene Mwezi uli pamalo a G. Unatenga nthawi yaitali kutalika kwa gawo AG. Ngati, monga kale, titenga ngati gawo la nthawi nthawi yomwe Mwezi umadutsa "mzere umodzi", ndiye kuti kutalika kwa AG ndi kofanana. Ngati tibwerera ku msonkhano wakale kuti matupi athu akumwamba ndi 4 ndi 4, zotsatira zake zingakhale zosiyana (chiyani?). Monga n'zosavuta kusonyeza, cholingacho chimatseka pambuyo pa t <15. Chithunzi cha "peresenti ya chophimba chophimba" chikhoza kuwonetsedwa mkuyu. 6.
Mpunga. 6 Chithunzi cha "chitetezo chaperesenti" ntchito
Eclipse ndi kulumpha equation
Mpunga. 7 Kutsekereza diski ya dzuŵa pa kadamsana kosonyezedwa mkuyu. 6
Vuto la kadamsana lingakhale losakwanira ngati sitiganizira za mabwalo. Izi ndizovuta kwambiri, koma tiyeni tiyese kudziwa kuti bwalo limodzi likadamsana theka la linzake - ndipo m'njira yosavuta kwambiri, imodzi mwa izo ikasuntha m'mimba mwake kuwalumikiza onse awiri. Chojambulacho ndi chodziwika bwino kwa omwe ali ndi kirediti kadi.
Kuwerengera malo a minda kumakhala kovuta, chifukwa kumafuna, choyamba, chidziwitso cha chilinganizo cha gawo lozungulira, kachiwiri, chidziwitso cha arc ya ngodya, ndipo chachitatu (ndi choyipitsitsa kuposa zonse), luso. kuthetsa kulumpha kwa equation. Sindidzafotokozera kuti "transitive equation" ndi chiyani, tiyeni tiwone chitsanzo (mkuyu 8).
Mpunga. 8 Kadamsana wa "Spherical".
Gawo lozungulira ndi "mbale" yomwe imatsalira pambuyo podula bwalo ndi mzere wowongoka. Dera la gawo ili ndi S = 1/2r2(φ-sinφ), kumene r ndi malo ozungulira bwalo, ndipo φ ndi mbali yapakati yomwe gawolo limakhalapo (mkuyu 8). Izi zimapezedwa mosavuta pochotsa gawo la makona atatu kuchokera kudera la gawo lozungulira.
Ndime O1O2 (mtunda pakati pa malo ozungulira) ndiye wofanana ndi 2rcosφ/2, ndi kutalika (m'lifupi, "waistline") h = 2rsinφ/2. Kotero, ngati tikufuna kuwerengera pamene Mwezi udzaphimba theka la disk ya dzuwa, tiyenera kuthetsa equation: yomwe, itatha kuphweka, imakhala:
Mpunga. 9 Zithunzi za ntchito ziwiri
Yankho la equations wotere amaposa algebra yosavuta - equation ili ndi ngodya zonse ndi ntchito zawo trigonometric. Equation ndi yopitilira njira zachikhalidwe. Ndi chifukwa chake amatchedwa kulumpha. Tiyeni tiyang'ane kaye ma grafu a ntchito zonse ziwiri, mwachitsanzo, ntchito ndi ntchito.Titha kuwerenga yankho loyerekeza kuchokera pachithunzichi. Komabe, titha kupeza kuyerekezera kobwerezabwereza kapena… gwiritsani ntchito njira ya Solver mu Excel spreadsheet. Wophunzira aliyense kusekondale azitha kuchita izi, chifukwa ndizaka za zana la 20. Ndidagwiritsa ntchito chida chapamwamba kwambiri cha Mathematica ndipo nali yankho lathu lomwe lili ndi malo XNUMX olondola mosafunikira:
SetPrecision[FindRoot[x==Sin[x]+Pi/2,{x,2}],20] {x ⇒2.3098814600100574523}.
Mpunga. 10 Makanema a kadamsana mu matematica
Timatembenuza izi kukhala madigiri pochulukitsa ndi 180/π. Timapeza madigiri 132, mphindi 20, 45 ndi kotala la sekondi ya arc. Timawerengera kuti mtunda wapakati pa bwalo ndi O1O2 = 0,808 radius, ndi "chiuno" 2,310.
