Izikwele ezinemibala kanye nokufiphala kwelanga

Isihloko sichaza amakilasi ami abafundi besikole esiphakathi - abanikazi bemifundaze Yesikhwama Sikazwelonke Sezingane. Isisekelo sifuna ikakhulukazi izingane ezinesiphiwo nentsha (kusuka ebangeni le-XNUMX lesikole samabanga aphansi kuya esikoleni esiphakeme) futhi sinikeza "imifundaze" kubafundi abakhethiwe. Kodwa-ke, azihlanganisi nhlobo ukuhoxiswa kwemali, kodwa ekunakekelweni okuphelele kokuthuthukiswa kwethalente, njengomthetho, eminyakeni eminingi. Ngokungafani namanye amaphrojekthi amaningi alolu hlobo, ososayensi abaziwayo, izibalo zamasiko, abantu abavelele nabanye abantu abahlakaniphile, kanye nabanye osopolitiki, bazithatha ngokungathi sína izigceme zeSisekelo.

Imisebenzi yeSisekelo idlulela kuzo zonke iziyalo eziyizifundo eziyisisekelo zesikole, ngaphandle kwezemidlalo, okuhlanganisa nezobuciko. Lesi sikhwama sasungulwa ngo-1983 njengekhambi leqiniso langaleso sikhathi. Noma ubani angafaka isicelo esikhwameni (ngokuvamile ngesikole, okungcono kakhulu ngaphambi kokuphela konyaka wesikole), kodwa-ke, kukhona isisefo esithile, inqubo ethile yeziqu.

Njengoba ngike ngasho, lesi sihloko sisekelwe emakilasini ami aphezulu, ikakhulukazi e-Gdynia, ngo-March 2016, esikoleni esiphakeme sama-24 esikoleni esiphakeme se-III. Navy. Iminyaka eminingi, lezi zifundo bezihlelwe ngaphansi kwesisekelo seSisekelo nguWojciech Thomalczyk, uthisha onekhono elimangalisayo nezinga eliphezulu lobuhlakani. Ngo-2008, wangena kwabayishumi abahamba phambili ePoland, abanikezwa isihloko sikaProfesa wePedagogy (esihlinzekwe ngumthetho eminyakeni eminingi edlule). Kukhona ihaba elincane esitatimendeni esithi: “Imfundo iwumgogodla womhlaba”.

kanye nenyanga zihlale ezithakazelisayo - khona-ke ungakwazi ukuzwa ukuthi siphila eplanethini encane endaweni enkulu, lapho yonke into ihamba khona, ilinganiswa ngamasentimitha nemizuzwana. Kuze kungithuse kancane, nombono wesikhathi. Sifunda ukuthi ukusitheka kwelanga okuphelele okulandelayo, okubonakalayo endaweni yase-Warsaw yanamuhla, kuzoba ngo-... 2681. Kazi ubani ozoyibona? Ubukhulu obubonakalayo beLanga neNyanga esibhakabhakeni sethu bucishe bufane - yingakho ukusitheka kwelanga kufushane futhi kumangalisa kangaka. Emakhulwini eminyaka, leyo mizuzu emifushane kufanele yanele ukuthi izazi zezinkanyezi zibone i-solar corona. Kuyamangaza ukuthi zenzeka kabili ngonyaka... kodwa lokho kusho ukuthi ndawana thize eMhlabeni zingabonwa isikhathi esifushane. Njengomphumela wokunyakaza kwamagagasi, iNyanga isuka kude noMhlaba - eminyakeni eyizigidi ezingama-260 iyobe ikude kangangokuthi thina (thina???) sizobona kuphela ukusitheka kwenyanga.

Ngokusobala owokuqala ukubikezela ukusitheka kwelanga, kwakunguThales waseMilethu (emakhulwini angama-28-585 BC). Cishe ngeke sazi ukuthi kwenzeka ngempela yini, okungukuthi, noma wakubikezela yini, ngoba iqiniso lokuthi ukusitheka kwelanga e-Asia Minor kwenzeka ngoMeyi 567, 566 BC kuyiqiniso eliqinisekiswe izibalo zesimanje. Yebo, ngicaphuna idatha ye-akhawunti yesikhathi yanamuhla. Lapho ngiseyingane, ngangicabanga indlela abantu ababebala ngayo iminyaka. Ngakho-ke lokhu, ngokwesibonelo, ngo-XNUMX BC, kuza usuku olwandulela uNcibijane futhi abantu bayajabula: iminyaka eyi-XNUMX BC kuphela! Yeka indlela okumelwe ukuba bajabula ngayo lapho ekugcineni “inkathi yethu” ifika! Yeka ukuguquka kwezinkulungwane zeminyaka esaba nakho eminyakeni embalwa edlule!

Izibalo Zokubala Izinsuku Nobubanzi ukusitheka kwelanga, ayiyona inkimbinkimbi ikakhulukazi, kodwa iminyene ngazo zonke izinhlobo zezinto ezihambisana nokujwayelekile futhi, okubi nakakhulu, nokunyakaza okungalingani komzimba emizileni. Ngingathanda nokwazi lesi zibalo. IThales yaseMilethu yayingakwazi kanjani ukwenza izibalo ezidingekayo? Impendulo ilula. Kufanele ube nemephu yesibhakabhaka. Indlela yokwenza imephu enjalo? Lokhu futhi akunzima, abaseGibhithe lasendulo babekwazi ukukwenza. Phakathi kwamabili, abapristi ababili baphumela ophahleni lwethempeli. Yilowo nalowo ahlale phansi adwebe akubonayo (njengozakwabo). Ngemva kweminyaka eyizinkulungwane ezimbili, sazi konke mayelana nokuhamba kwamaplanethi ...

Ijiyomethri enhle, noma kumnandi "kumaragi"

AmaGreki ayengathandi izinombolo, aphendukela ku-geometry. Yilokhu esizokwenza. Eyethu ukusitheka kwelanga zizoba lula, zibe nemibala, kodwa zithandeke futhi zibe ngokoqobo. Siyawamukela umhlangano wokuthi umdwebo oluhlaza okwesibhakabhaka uhamba ngendlela yokuthi usibekele obomvu. Ake sibize umfanekiso oluhlaza njengenyanga, nomfanekiso obomvu ngokuthi ilanga. Sizibuza le mibuzo elandelayo:

1. isikhathi esingakanani ukusitheka kwelanga;
2. lapho ingxenye yethagethi ikhaviwe;

   Ilayisi. 1 "Ukhaphethi" onemibala eminingi enelanga nenyanga

3. yikuphi ukufakwa okuphezulu;
4. kungenzeka yini ukuhlaziya ukuncika kokufakwa kwesihlangu ngesikhathi? Kulesi sihloko (nginqunyelwe inani lombhalo) ngizogxila embuzweni wesibili. Ngemuva kwalokhu kunejiyomethri enhle, mhlawumbe ngaphandle kwezibalo eziyisicefe. Ake sibheke umkhiwane. 1. Kungacatshangwa ukuthi kuzohlotshaniswa ... nokufiphala kwelanga?

Kumelwe ngisho ngokweqiniso ukuthi imisebenzi engizoxoxa ngayo izokhethwa ngokukhethekile, ihambisane nolwazi namakhono abafundi basesikoleni esiphakathi nabasesikoleni esiphakeme. Kodwa siziqeqeshela imisebenzi efana nabaculi abadlala izikali, futhi abasubathi benza izivivinyo ezijwayelekile zokuthuthuka. Ngaphandle kwalokho, akusiwo yini umata omuhle (umkhiwane 1)?

Ilayisi. 2 "Blue" Inyanga kanye "Red" Ilanga

Imizimba yethu yasezulwini, okungenani ekuqaleni, izoba yizikwele ezinemibala. Inyanga iluhlaza okwesibhakabhaka, ilanga libomvu (kungcono kakhulu ukufaka imibala). namanje ukusitheka kwelanga Inyanga ijaha ilanga esibhakabhakeni, ilibambe ... bese ilivala. Kuyoba njalo nakithi. Icala elilula, lapho iNyanga ihamba ngokuhlobene neLanga, njengoba kuboniswe ku-Fig. 2. Ukufiphala kwelanga kuqala lapho unqenqema lwediski yeNyanga luthinta unqenqema lwediski yeLanga (Fig. 2) futhi kuphele lapho seludlula.

Ilayisi. 3 Inyanga isondela elangeni ngokudayayo

Sicabanga ukuthi "iNyanga" ihambisa iseli eyodwa ngeyunithi yesikhathi, isibonelo, ngomzuzu. Ukusitheka kwelanga kube sekuthatha amayunithi esikhathi ayisishiyagalombili, ake sithi imizuzu. Ingxenye ukufiphala kwelanga dimmed ngokuphelele Ingxenye yokudayela ivalwe kabili: ngemva kwemizuzu emi-2 neyesi-6. Igrafu yephesenti yokufiphaza ilula. Phakathi nemizuzu emibili yokuqala, isihlangu sivala ngokulinganayo ngesilinganiso se-zero kuya ku-1, imizuzu emibili elandelayo ivezwa ngesilinganiso esifanayo.

Nasi isibonelo esithakazelisayo (Fig. 3). Inyanga isondela elangeni diagonally. Ngokwesivumelwano sethu sokukhokha ngomzuzu ngamunye, ukusitheka kwelanga kuthatha 8√2 imizuzu - phakathi nalesi sikhathi sinokufiphala okuphelele. Ake sibale ukuthi iyiphi ingxenye yelanga embozwe ngemva kwesikhathi t (Fig. 3). Uma sekudlule imizuzu emi-t kusukela ekuqaleni kokusitheka kwelanga, futhi ngenxa yalokho iNyanga injengoba kukhonjisiwe ku-Fig. 5, bese (ukunaka!) Ngakho-ke, imbozwe (indawo ye-APQR yesikwele), ilingana nengxenye yediski yelanga; ngakho-ke, yahlanganiswa lapho, i.e. ngemva kwemizuzu emi-4 (bese kuba imizuzu emi-4 ngaphambi kokuphela kokusitheka kwelanga).

Ilayisi. 4 Igrafu yomsebenzi "wokufiphaza".

Ingqikithi ihlala umzuzwana owodwa (t = 4√2), futhi igrafu yomsebenzi "wengxenye enomthunzi" iqukethe ama-arcs amabili we-parabolas (Fig. 4).

Inyanga yethu eluhlaza okwesibhakabhaka izothinta ekhoneni ngelanga elibomvu, kodwa izoyimboza, ingahambi nge-diagonally, kodwa kancane nge-diagonally.I-geometry ethakazelisayo ibonakala lapho sihlanganisa ukunyakaza kancane (Fig. 6). Isiqondiso sokunyakaza manje sekuyi-vector [4,3], okungukuthi, "amaseli amane kwesokudla, amaseli amathathu phezulu." Ukuma kweLanga kuyindlela yokuthi ukufiphala kwelanga kuqala (indawo A) lapho izinhlangothi "zezinkanyezi" zihlangana zibe ingxenye yesine yobude bazo. Lapho iNyanga isuka iye endaweni engu-B, izositha ingxenye eyodwa kwesithupha yeLanga, futhi endaweni C izosibekela uhhafu. Esimeni D, sinokufiphala okuphelele, bese yonke into ibuyela emuva, "njengoba yayinjalo."

Ilayisi. 5 Ingxenye yeLanga ifihlwe ngesikhathi t

Ukusitheka kwelanga kuphela lapho iNyanga isendaweni engu-G. Yahlala isikhathi eside ubude besigaba AG. Uma, njengangaphambili, sithatha njengeyunithi yesikhathi isikhathi lapho iNyanga idlula "isikwele esisodwa", khona-ke ubude be-AG buyalingana. Uma sibuyela emhlanganweni omdala wokuthi imizimba yethu yasezulwini i-4 by 4, umphumela wawuyoba ohlukile (ini?). Njengoba kulula ukukhombisa, okuqondiwe kuvalwa ngemva kwe-t <15. Igrafu yomsebenzi "wephesenti lokumbozwa kwesikrini" ingabonakala kumfanekiso. 6.

Ilayisi. 6 Igrafu yomsebenzi "wokuvikela amaphesenti".

I-Eclipse kanye ne-jump equation

Ilayisi. 7 Ukuvinjwa kwediski yelanga phakathi nokusitheka kwelanga okuboniswe emkhiwaneni. 6

Inkinga yokusitheka kwelanga izobe ingaphelele uma singacabangi indaba yemibuthano. Lokhu kuyinkimbinkimbi kakhulu, kodwa ake sizame ukuthola ukuthi umbuthano owodwa usibekela nini ingxenye yomunye - futhi esimweni esilula, lapho omunye wabo uhamba ngobubanzi obuxhumanisa bobabili. Umdwebo ujwayelekile kubanikazi bamakhadi athile esikweletu.

Ukubala indawo yamasimu kuyinkimbinkimbi, ngoba kudinga, okokuqala, ulwazi lwefomula yendawo yengxenye eyindilinga, okwesibili, ulwazi lwe-arc ye-angle, futhi okwesithathu (futhi okubi kakhulu kunakho konke), ikhono. ukuxazulula i-jump equation ethile. Ngeke ngichaze ukuthi "i-equation transitive" iyini, ake sibheke isibonelo (Fig. 8).

Ilayisi. 8 Ukufiphala kwelanga "okuyisiyingi".

Ingxenye eyisiyingi "isitsha" esisala ngemva kokusika isiyingi ngomugqa oqondile. Indawo yengxenye enjalo yi-S = 1/2r²(φ-sinφ), lapho i-r iyi-radius yombuthano, futhi φ i-engeli emaphakathi lapho ingxenye ihlezi khona (Fig. 8). Lokhu kutholakala kalula ngokukhipha indawo kanxantathu endaweni yomkhakha oyindilinga.

Isiqephu O₁O₂ (ibanga eliphakathi kwezikhungo zemibuthano) bese lilingana no-2rcosφ/2, nobude (ububanzi, “umugqa okhalo”) h = 2rsinφ/2. Ngakho-ke, uma sifuna ukubala ukuthi iNyanga izovala nini ingxenye yediski yelanga, sidinga ukuxazulula i-equation: okuthi, ngemva kokwenza lula, ibe:

Ilayisi. 9 Amagrafu emisebenzi emibili

Isixazululo salezi zibalo sidlulela ngale kwe-algebra elula - i-equation iqukethe womabili ama-engeli kanye nemisebenzi yawo ye-trigonometric. I-equation ingaphezu kokufinyelela kwezindlela zendabuko. Yingakho ibizwa gxuma. Ake siqale sibheke amagrafu ayo yomibili imisebenzi, okungukuthi imisebenzi nemisebenzi.Singafunda cishe isixazululo kulo mfanekiso. Nokho, singathola ukulinganisa okuphindaphindayo noma... sebenzisa inketho ye-Solver kusipredishithi se-Excel. Wonke umfundi wesikole samabanga aphezulu kufanele akwazi ukwenza lokhu, ngoba ikhulunyaka lama-20. Ngisebenzise ithuluzi le-Mathematica eliyinkimbinkimbi futhi nasi isisombululo sethu esinezindawo zamadesimali eziyi-XNUMX zokunemba okungadingekile:

SetPrecision[FindRoot[x==Sin[x]+Pi/2,{x,2}],20] {x ⇒2.3098814600100574523}.

Ilayisi. 10 Izithombe ze-eclipse kumatematica

Lokhu sikwenza amadigri ngokuphindaphinda ngo-180/π. Sithola ama-degree angu-132, amaminithi angu-20, ama-45 kanye nengxenye yesine ye-arc yesibili. Sibala ukuthi ibanga eliya enkabeni yesiyingi ngu-O₁O₂ = 0,808 irediyasi, kanye "nokhalo" 2,310.