Zvikwere zvine mavara uye kuora kwezuva

Chinyorwa chinotsanangura makirasi angu evadzidzi vekusekondari - vane mabhezari eNational Children's Fund. Nheyo dzinotsvaga kunyanya vane zvipo zvevana uye vechidiki (kubva mugiredhi XNUMX rechikoro chepuraimari kusvika kuchikoro chesekondari) uye inopa "mabhezari" kuvadzidzi vakasarudzwa. Nekudaro, hazvibatanidzi zvachose mukubvisa mari, asi mukutarisira kwakazara kwekuvandudzwa kwetarenda, sekutonga, kwemakore mazhinji. Kusiyana nemamwe mapurojekiti mazhinji emhando iyi, masayendisiti anozivikanwa, vanhu vetsika, vanhu vane mukurumbira uye vamwe vanhu vakachenjera, pamwe nevamwe vezvematongerwo enyika, vanokoshesa mawadhi eSiseko.

Zviitwa zveNheyo zvinosvika kune zvese zvidzidzo zviri zvechikoro zvidzidzo, kunze kwemitambo, kusanganisira art. Homwe iyi yakagadzirwa muna 1983 semushonga wenguva iyoyo. Chero ani zvake anogona kunyorera kuhomwe (kazhinji kuburikidza nechikoro, zvichida risati rapera gore rechikoro), asi, hongu, kune imwe sefa, imwe nzira yekukodzera.

Sezvandambotaura, chinyorwa chakavakirwa pamakirasi angu tenzi, kunyanya muGdynia, muna Kurume 2016, pachikoro chepamusoro che24th pachikoro chepamusoro cheIII. Navy. Kwemakore akawanda, maseminari aya akarongwa pasi pechitsigiro cheSiseko naWojciech Thomalczyk, mudzidzisi weanoshamisira anoshamisa uye danho repamusoro rehungwaru. Muna 2008, akapinda pamusoro pegumi muPoland, uyo akapiwa zita rePurofesa wePedagogy (yakapiwa nemutemo makore akawanda apfuura). Pane kuwedzeredza kudiki muchirevo: "Dzidzo ndiyo axis yenyika".

uye mwedzi zvinogara zvichinakidza - ipapo iwe unogona kunzwa kuti isu tinogara pane diki pasi munzvimbo yakakura, umo zvese zviri kufamba, zvakayerwa mumasendimita nemasekondi. Izvo zvinotondityisa zvishoma, zvakare maonero enguva. Isu tinodzidza kuti kunotevera kwezuva kwakazara, kunoonekwa kubva munharaunda yeWarsaw yanhasi, kuchave mu ... 2681. Hameno kuti ndiani achazviona? Hukuru hunooneka hweZuva neMwedzi mudenga medu hwakada kufanana - ndosaka eclipses iri pfupi uye inoshamisa. Kwemazana emakore, iwo maminetsi mapfupi anofanirwa kukwana kuti vazivi venyeredzi vaone solar corona. Zvinoshamisa kuti zvinoitika kaviri pagore ... asi izvo zvinongoreva kuti pane imwe nzvimbo paNyika vanogona kuonekwa kwenguva pfupi. Nekuda kwekufamba kwemafungu, Mwedzi uri kufamba kubva paNyika - mumakore 260 miriyoni inenge iri kure zvekuti isu (isu ???) tichangoona eclipses.

Sezviri pachena wekutanga kufanotaura kupora, aiva Thales weMireto (28-585 mazana emakore BC). Isu pamwe hatizoziva kana zvakaitika chaizvo, kureva kuti, kana akazvifungidzira, nekuti nyaya yekuti kuora kwezuva muAsia Minor kwakaitika muna Chivabvu 567, 566 BC ichokwadi chakasimbiswa nekuverenga kwemazuva ano. Ehe, ini ndinotaura data remazuva ano account yenguva. Pandaiva mudiki, ndaifungidzira kuti vanhu vaiverenga sei makore. Saka izvi, semuenzaniso, XNUMX BC, Evha Idzva Idzva iri kuuya uye vanhu vari kufara: makore XNUMX chete BC! Vanofanira kuva vakafara sei apo “nguva yedu” yakazosvika! Kuchinja kwakadini kwemireniyumu kwatakava nako makore mashoma apfuura!

Iwo Masvomhu eKuverengera Mazuva uye Range eclipses, haina kunyanya kuoma, asi yakazadzwa nemhando dzose dzezvinhu zvine chokuita nekugara uye, zvakatonyanya, nekufamba kusina kuenzana kwemuviri mukutenderera. Ndinotoda kuziva masvomhu aya. Ko Thales weMireto aizoita sei maverengero aidiwa? Mhinduro iri nyore. Unofanira kuva nemepu yedenga. Nzira yekuita mepu yakadaro? Izvi zvakare hazvina kuoma, vaIjipita vekare vaiziva kuzviita. Pakati pousiku, vaprista vaviri vanobuda pamusoro pedenga retembere. Mumwe nemumwe wavo anogara pasi odhirowa zvaanoona (semumwe wake). Mushure mezviuru zviviri zvemakore, isu tinoziva zvese nezvekufamba kwemapuraneti ...

Yakanaka geometry, kana kunakidza pa "rug"

VaGiriki vaisada nhamba, vakashandura geometry. Izvi ndizvo zvatichaita. Yedu kupora dzichava dzakapfava, dzine mavara, asi dzinofadza uye dzechokwadi. Tinobvuma gungano rekuti chimiro chebhuruu chinofamba nenzira yekuti chinofukidza chitsvuku. Ngatidaidze mufananidzo webhuruu mwedzi, uye mufananidzo mutsvuku zuva. Tinozvibvunza mibvunzo inotevera:

1. Kuora kwezuva kunotora nguva yakareba sei;
2. apo hafu yechinangwa yakavharwa;

   Mupunga. 1 Multi-colored "carpet" ine zuva nemwedzi

3. chii chinonyanya kuvhara;
4. zvinokwanisika here kuongorora kutsamira kwechivharo chenhovo nenguva? Muchikamu chino (ini ndinogumira nehuwandu hwemashoko) ndichaisa pfungwa pamubvunzo wechipiri. Kuseri kweiyi yakanaka geometry, pamwe isina kufinha kuverenga. Ngatitarisei muonde. 1. Zvinogona kufungidzirwa here kuti ichabatanidzwa ne ... kunyura kwezuva?

Ndinofanira kutaura chokwadi kuti mabasa andichakurukura achave akasarudzwa, akachinjirwa kune ruzivo uye hunyanzvi hwevadzidzi vepakati nesekondari. Asi isu tinodzidzira mabasa akadai sevaimbi vanoridza zvikero, uye vatambi vanoita maekisesaizi ebudiriro. Kunze kwaizvozvo, hachiziri chigadziko chakanaka here (muonde 1)?

Mupunga. 2 "Blue" Mwedzi uye "Red" Zuva

Mitumbi yedu yekudenga, zvishoma pakutanga, ichave ine mavara masikweya. Mwedzi webhuruu, zuva rakatsvuka (yakanakira kuvera). nezvazvino kupora Mwedzi unodzingirira zuva mudenga, unobata ... worivhara. Zvichava zvimwe chete nesu. Iyo yakapfava nyaya, kana Mwedzi ukafamba uchienderana neZuva, sezvakaratidzwa muFig. 2. Kuora kwezuva kunotanga kana mupendero weDisiki reMwedzi unobata kumucheto kweDisiki reZuva (Fig. 2) uye rinopera kana rapfuura.

Mupunga. 3 Mwedzi unoswedera kuzuva nediagonal

Isu tinofungidzira kuti "Mwedzi" inofambisa sero rimwe pachikamu chenguva, semuenzaniso, paminiti. Kuora kwezuva kunobva kwatora zvikamu zvisere zvenguva, toti maminetsi. Hafu kuora kwezuva zvachose dimmed Hafu yedhiri yakavharwa kaviri: mushure me2 uye 6 maminitsi. The percentage obscuration graph iri nyore. Mukati memaminetsi maviri ekutanga, nhovo inovhara zvakaenzana pamwero we zero kusvika ku1, maminetsi maviri anotevera inoratidzwa pamwero wakafanana.

Heino imwe inonakidza muenzaniso (Fig. 3). Mwedzi unoswedera kuzuva diagonally. Maererano nechibvumirano chedu chekubhadhara paminiti yega yega, kuora kwezuva kunotora 8√2 maminetsi - pakati penguva ino tine eclipse yakazara. Ngativerengei kuti chikamu chipi chezuva chakafukidzwa mushure menguva t (Fig. 3). Kana t maminetsi apfuura kubva pakutanga kwekuora kwezuva, uye semhedzisiro Mwedzi unoratidzwa mumufananidzo. 5, ipapo (kutarisisa!) Naizvozvo, yakafukidzwa (iyo nzvimbo yechikwere APQR), yakaenzana nehafu yesolar disk; saka, yakafukidzwa apo, i.e. mushure memaminitsi mana (zvino 4 maminetsi kusati kwapera eclipse).

Mupunga. 4 Girafu ye "shading" basa

Totality inotora nguva imwe chete (t = 4√2), uye girafu ye "shaded chikamu" basa rinosanganisira maviri arcs eparabolas (Fig. 4).

Mwedzi wedu webhuruu uchabata kona nezuva dzvuku, asi ichaifukidza, isingaenderi diagonally, asi zvishoma diagonally.Inonakidza geometry inooneka patinoomesa kufamba zvishoma (Fig. 6). Nhungamiro yekufambisa ikozvino vector [4,3], kureva, "masero mana kurudyi, masero matatu kumusoro." Nzvimbo yeZuva ndeyekuti kunyura kwezuva kunotanga (chinzvimbo A) apo mativi e "mitumbi yekudenga" anobatana kusvika kuchikamu chechina chehurefu hwawo. Kana Mwedzi ukaenda pachinzvimbo B, unozodzika chikamu chimwe muzvitanhatu cheZuva, uye pachinzvimbo C unozonyura hafu. Muchinzvimbo D, tine kuora kwezuva rose, uye zvino zvose zvinodzokera shure, "sezvazvaiva."

Mupunga. 5 Chikamu cheZuva chakavigwa munguva t

Kuora kwezuva kunopera kana Mwedzi wava panzvimbo G. Kwakatora nguva yakareba chikamu urefu AG. Kana, sepakutanga, tinotora sechikamu chenguva nguva iyo Mwedzi unopfuura "imwe square", ipapo hurefu hweAG hwakaenzana. Kana tikadzokera kumusangano wekare kuti miviri yedu yekudenga ndeye 4 ne4, mugumisiro ungadai wakasiyana (chii?). Sezvo zviri nyore kuratidza, chinangwa chinovhara mushure me t <15. Girafu ye "percent of screen coverage" basa rinogona kuonekwa mufig. 6.

Mupunga. 6 Girafu ye "percent protection" basa

Eclipse uye kusvetuka equation

Mupunga. 7 Kuvharirwa kwesolar disk panguva yekuora kwezuva kunoratidzwa mufig. 6

Dambudziko rekuora kwezuva ringadai risina kukwana kana tikasatarisa nyaya yemadenderedzwa. Izvi zvakanyanya kuomarara, asi ngatiedzei kuona kana denderedzwa ranyura hafu yerimwe - uye mune yakapusa kesi, kana imwe yadzo ichifamba nepakati pedhayamita ichivabatanidza ese ari maviri. Mufananidzo wacho unozivikanwa kune vane kadhi rechikwereti.

Kuverenga nzvimbo yeminda kwakaoma, nekuti zvinoda, chekutanga, ruzivo rwefomati yenzvimbo yechikamu chedenderedzwa, chechipiri, ruzivo rwearc yekona, uye chechitatu (uye zvakanyanya kupfuura zvese), kugona. kugadzirisa imwe jump equation. Ini handisi kuzotsanangura kuti "transitive equation" chii, ngatitarisei muenzaniso (Fig. 8).

Mupunga. 8 "Spherical" eclipse

Chikamu chedenderedzwa ndicho "ndiro" inosara mushure mekucheka denderedzwa nemutsara wakatwasuka. Nzvimbo yechikamu chakadaro S = 1/2r²(φ-sinφ), apo r ndiyo nzvimbo yedenderedzwa, uye φ ndiyo yepakati pekona iyo chikamu chinogara (Fig. 8). Izvi zvinowanikwa zviri nyore nekubvisa nharaunda yetatu kubva munzvimbo yedunhu redunhu.

Chikamu O₁O₂ (kureba pakati pepakati pemadenderedzwa) inobva yaenzana ne2rcosφ/2, uye kureba (hupamhi, "waistline") h = 2rsinφ/2. Saka, kana tichida kuverenga kuti Mwedzi uchavhara riini hafu yesolar disk, isu tinofanirwa kugadzirisa iyo equation: iyo, mushure mekurerutsa, inova:

Mupunga. 9 Magirafu emabasa maviri

Mhinduro yemaequation akadaro inodarika algebra iri nyore - iyo equation ine makona ese uye mabasa avo etrigonometric. Equation haisviki nzira dzechinyakare. Ndosaka zvichinzi kusvetuka. Ngatitangei titarise magirafu emabasa ese ari maviri, i.e. mafunzo nemabasa.Tinogona kuverenga mhinduro kubva pamufananidzo uyu. Nekudaro, isu tinogona kuwana iterative fungidziro kana… shandisa iyo Solver sarudzo muExcel spreadsheet. Wese mudzidzi wepachikoro chesekondari anofanira kukwanisa kuita izvi, nekuti izana ramakore rechi20. Ndakashandisa yakaomesesa Mathematica chishandiso uye heino mhinduro yedu ine XNUMX decimal nzvimbo dzezvisina kufanira chaiyo:

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

Mupunga. 10 Mhuka ye eclipse mumatematica

Isu tinoshandura izvi kuita madhigirii nekuwanda ne 180/π. Tinowana 132 madhigirii, maminitsi makumi maviri, 20 uye chikamu chechina chearc sekondi. Tinoverenga kuti chinhambwe chepakati pedenderedzwa ndiO₁O₂ = 0,808 radius, uye "chiuno" 2,310.