Fungidzira kuti bhora regoridhe riri muruoko rwupi
Kare munguva yepre-Covid (o, zvaive rini?) Ndakambokumbirwa kutora chikamu mu "chikoro chegirinhi". Mukuwedzera kune kuzorora kwakakodzera, musangano wacho wakatsaurirwa kumasvomhu, ndiko kuti nharaunda nezvinhu zvayo. Nyaya iyi inowanzosiiwa muchikoro nokuti... zvakanaka, handizivi kuti sei.
Mushure meizvi, kunyange vadzidzi ve geology havazivi kuti longitude chii (chinhu chaicho chakaitika kwandiri - ndakapa hurukuro padhipatimendi rakakodzera reyunivhesiti). Musangano wakabudirira zvakanyanya, kuombera hutungamiriri nevadzidzisi vatatu vakaronga zvese. Kudzidzisa hakusi kwekufambisa ruzivo chete mu45-maminetsi ekuwedzera kubva 8 AM kusvika XNUMX PM kana XNUMX PM. Zvakanaka, ikozvino zvese zvasiyana nekudzidza kure. Vadzidzisi vakawanda vari kukurukura kuti vangashandura sei tsika yekirasi yekirasi kuti ... saka chii? Yeuka kuti tiri kuedza pa "chipenyu" - vana. Ko bhora regoridhe rine hungwaru hwehupenyu riripi?
Ndiri kuongorora zvikumbiro zvevadzidzi zveNational Children's Fund scholarship yevana vane zvipo zvakasiyana. Paigara paine mameseji akawanda kubva kuLeszno. Vakanga vari mugore iroro, asi mwana wechipiri ari wose (mudzidzi wamagiredhi akaderera) akanyora, kuti: “Kubvira mudzidzisi wangu, Mai I., vakaenda, handichafariri masvomhu. Nekudaro, pakanga paine zvikumbiro zvakawanda kubva kuLublin, izvo kusvika parizvino zvishoma zvatumirwa. Chirahwe chevaverengi: Mai I. vanobva kuLeshno vakatamira kuguta ripi? KuLublin? Hongu, asi mauya sei nazvo vaverengi?
Musoro wedenderedzwa ibhora (kubva kuLatin sphere 'bhora, denga'). Iri izwi remasvomhu rapinda mumutauro wemakorokoza: tiri kutaura pamusoro pezvikamu zvesimba remasimba makuru, nzvimbo yezvido zvemunhu nemagariro evanhu. "Aa, haasi wedunhu redu," akadaro musikana uyu kumusikana akanaka wekumusha uyo aidanana naishe. Uye ipapo munhu wese aifungidzira nzanga semagomba akaomesesa, asingapindiki kune mumwe nemumwe: kune rumwe rutivi, isu tiri muboka rakanakisa, hongu, kune rimwe, musikana uyu murombo uye kunyange geometry anoti "Cinderella: gara pauri!".
Hazvina kuoma kufadzwa nechimiro chedenderedzwa. Zvakakwana kuva pasi pedenga rakazaruka usiku, kure nemaguta, zviri nani pagomo refu munguva yechando. Ngatitarisei kumusoro: hatisi kuona nzvimbo yedenga zvakajeka here? Nyeredzi dziri kure dzinoijoinha, pakatarisana nekwadziri zvisikwa zvemudenga zvinodzungaira zvinofamba zvichiswedera pedyo: mapuraneti. Ptolemy akadzidzisa kuti Nyika ndiyo iri pakati pechisiko chapose pose uye yakakomberedzwa nemapfumbamwe akakomberedzwa ekristaro mativi.
Mumanomwe ekutanga kune mapuraneti manomwe anozivikanwa: Diana (= Mwedzi), Mercury, Venus, Apollo (= Zuva), Mars, Jupiter uye Saturn. Denderedzwa rechisere raiva nenyeredzi dzisingachinji. Nguva yepfumbamwe yakanga yakaita semubato unodzora kufamba kwewachi: machirimo equinox akafamba navo. MuMiddle Ages, chikamu chegumi chakawedzerwa kune iyi hurongwa: Prime Mover, sechitubu, zvinhu zvose zvinofamba, simba rekufambisa, goko rakaoma rinoparadzanisa nyika kubva pakusavapo. VaPythagoreans vaitenda mukuwirirana kwemativi - kuti mapuraneti anofamba nepakati pawo anoburitsa ruzha rwakanyanya kunakidza. Mushure mezvose, nyika inhamba uye mimhanzi.
Mumakwikwi eMathematics Olympiad evana vechikoro, atakaronga muchikoro chegirinhi chambotaurwa, makwikwi acho aityisa. zvikwata zviviri. Zvakanaka, mumwe akakunda (33:31), mumwe akarasika. Sezviri mumitambo.
Iyo algorithm yekuparadzanisa vanotanga kuita zvikwata zviviri inonakidza kubva pamasvomhu maonero zvekuti ini ndichagara pairi zvakadzama. Dambudziko riri pano, hongu, kuenzana kwezvikwata zvakasimba uye zvisina simba. Asi chii chakatsiga? Sezviri pachena, sarudzo yakanakisa inongoitika: mutambi wega wega anotora bepa rine mazwi 1 kana 2 kubva mubhokisi uye anoenda kuchikwata chakakodzera. Asi… kana ukapeta coin ka10, 25% chete yenguva mhedzisiro inenge iri 5:5, inova misoro mishanu nemisoro mishanu. Saka, tinoona kuti nechikamu che75 percent zvikwata zvinenge zvisina kuenzana.
Pane nzira iri pachena isina kururama iyo vaviri vakambogadzwa vatungamiri vanosarudza nhengo dzechikwata chavo mumwe pashure pomumwe: kamwe iwe, ipapo ini. Mutungamiri wekutanga anogara aine mukana, anogona kusarudza akanakisa pane mamwe. Saizvozvo, munhabvu, anokunda mukombe wemukombe anotariswa kubva panzvimbo yechirango. Chikwata chimwe chinogara chichipfura pakutanga. Zvinhu zviri nani mutenisi uko sevha inogara iri munzvimbo yakanaka. Mumutambo we-tie-break, mushure mekutanga A kushumira, wechipiri anoshumira kaviri, kozoti A kaviri, uyezve maviri anoshumira, achichinjana B, A, ... kune mukana wemapoinzi maviri ekuhwina.
Iyi nzira hainawo kunyatsokodzera pakusarudza zvikwata zviviri zvevadzidzi. Nzira yandichatsanangura yakagadzirwa nenyanzvi dzemasvomhu pane imwe pfungwa yakatorwa kubva kune inonzi Steinhaus algorithm. Inowanzoshandiswa mumitambo yemasvomhu, senge pre-Olympic preliminaries. Sezvineiwo, isu takashandisa yakada kufanana system kuseri kwemba yangu pataida "kutamba nhabvu" munzvimbo isina chinhu kuseri kwemba. Paive nevakomana vazhinji (ini ndinobva kufungu rekutanga remashure ehondo mwana boom).
Iyo algorithm yakaita seizvi. Mari inosarudza kuti ndeupi wevakuru (A kana B) achatanga kusarudzwa. Ngazvive A. Anonongedza kumutambi, uye zvino (kuteerera!) Captain B anosarudza kana mutambi uyu achaenda kuboka rekutanga kana rechipiri. Uye saka alternately. Mumwe anosarudza mutambi, mumwe anomugadza. Yechipiri inoratidza kuti yekutanga inosimbisa.
Cherechedza matambudziko epfungwa. Kana kaputeni A akasarudza akanakisa, B anobva angomuwedzera kuchikwata chake. Kana akanongedza kune asina kusimba, B achati: "zvakanaka kwazvo, mutore" ... asi mushure mechinguva mabasa achadzorerwa. Saka unotamba sei?
Humwe huwandu hwesocial engineering uye social psychology inobatsira pano. Kunyanya apo vechidiki vanobatanidzwa mukusarudzwa, vanoda uye vasingadi zvakakosha zvikuru, uye kwete kungoita "nhanho" isingagumi. Kunyanya, mushure mekusarudza chero wevatambi sakaputeni A, kaputeni B anoongorora kuti waanoshanda naye (yakaratidza shamwari) ari pamusoro kana pasi pehafu yevatori vechikamu. Ndinomuda here kana kumurega aende kuA? Ndine sarudzo. Kana ndikaona nhengo yakataurwa muhafu yepamusoro, ndinomutora, uye kana ndikaona nhengo yakataurwa muhafu yepasi, ndinomusiya. Basa riri kuchinja, ikozvino B uye A zvibodzwa zvinokodzera. Anoita zvimwe chetezvo. Kana akaongorora munhu akaratidzwa zvakanaka, anomutora iye pachake, kana akakanganisa, anoenda. Nenzira iyi, kaputeni wese anova nani (kana kuti akaenzana!) nguva dzese. Munhu wose anofunga kuti akaita sarudzo yakanakisisa, kuti boka rake riri nani. Masvomhu anogona kufadza vanhu kunyange munyaya dzakaoma kudaro.
Yaiva nemibvunzo yakadai kuti vaikwikwidza muchikoro changu chegreen vakarwa. Sezvaunogona kuona, pane mimwe mibvunzo. dzisiri dzemasvomhu, dzinonetsa uye dzinonakidza.
- Chii chinonzi loxodrome?
- Une mabhora makumi maviri. Ndeipi urefu hwe tetrahedron inogona kugadzirwa navo? Mabhora mangani aunoda kune gumi-layer tetrahedron?
- Ndakabva patende. Ndakafamba kiromita kumadokero, kozoti kiromita kuchamhembe, kozoti kiromita kumaodzanyemba. Ndiwo maperero andakaita mutende rangu. Bere rakagara pamberi pake. Raive ruvara rwei?
- Mabhora mangani echidhayamita 1 achakwana mubhora redhayamita 2?
- Ronga kubva padiki kusvika pahombe bhora rinoshandiswa mumitambo inotevera: tenesi, tafura tennis, nhabvu, volleyball, basketball, polo yemvura.
- Ibhora ripi risina denderedzwa kana ovhari (semurugby kana nhabvu yekuAmerica)?
- Nyora tsumo nezvirevo zvine chekuita nebhora.
- Huya nejee rinotanga nemashoko okuti "Bullet flyes to the doctor."
- Sphere inonyorwa mucube ine divi re 1 mita. Pane nzvimbo yakakwana yebhora re20 cm mukona here?
- Ko cube ine divi re 1 inch ingakwana mubhora rine radius ye 1 centimita here?
- Sezvaunoziva, kare, cannonballs zvechokwadi denderedzwa. Nhasi havasi. Chii chakaita kuti uchinje chimiro chematombo?
- Huwandu hwenzvimbo ndeye p2 cubic centimita. Verenga pamusoro penzvimbo yayo.
- Iri idenderedzwa rine radius
inogona kurara panzvimbo yeradius
- Container B ine zana mabhora machena, mudziyo C une zana mabhora matema. Isu tinosarudza mabhora gumi kubva mumudziyo B uye tinodonhedzera muC. Pamabhora zana negumi ari muC iye zvino, tinosarudza 100 nekuadonhedza muB. Pane mamwe mabhora matema muB here kana machena muC?
- Ndeipi chimiro chinogona kuva mumvuri webhora?
- Ndeipi mirano paNyika ine hafu yehurefu hweequator?
- Planet T yakafukidzwa zvakaenzana nehuswa. Pane imwe nguva panyika, mbudzi inosungwa. Cheni inofanira kuva yakareba sei kuitira kuti mbudzi inyatsosvika hafu yeuswa hwepasi?
- Munhetembo, Pan Tadeusz Stolnik akapfurwa. Ko pfuti yakarohwa nebara ndeyani?
- Mangani mazwi ane mavara mana (anoreva kana kwete) anogona kuumbwa nekugadzirisazve mavara muizwi KULA?
- Pane bhora rinobata mativi ese ecube? Kana zvakadaro, verenga radius yayo. Kana zvisina kudaro, ruramisa.
Comments. Ini ndinofunga kutsvaga (kubva kupi Internet?) Chii chinonzi Loxodrome.
Basa rechipiri rakaoma chaizvo. Mabhora makumi maviri akafanana anogona kuitwa tetrahedron 2 + 10 + 6 + 3 (mabhora gumi ari pasi, ozoita matanhatu, matatu uye rimwe). Chivharo chakadaro chine mitsara ina, asi isingasviki kana kana dhayamita yechikamu chimwe nechimwe - mabhora anowira mumashure epasi pasi.
Ini ndichataura nezve dambudziko iri kunyangwe ... Ini handisi kuzosarudza. Ndichasiira muverengi anoda. Ndinoreva, pakati pevamwe, shamwari yangu Kazimierz anobva kuSzczecin. Kaziu - iwe zvechokwadi uchaifarira. Pashure pezvose, tinobatanidza basa racho nechikoro. Iri ndiro boka ratinoona mumufananidzo. Aya maranjisi aive akanaka kwazvo ... Chero mutengesi anoziva kuti zviri nani kuisa maapuro, maranjisi, marimu nemimwe michero yakaoma seizvi (matomatisi anogona kuputsika). Zvakanaka, pakupera kwezana remakore rapfuura apo dambudziko rakakonzerwa naJohannes Kepler muna 1610 rakagadziriswa, kureva, nzira yekuratidza masvomhu kuti iyi ndiyo nzira yakanakisisa. Zvakanyanya, maseferensi akaenzana anotora nzvimbo diki munzvimbo nehurongwa uhu. Izvi zvingori pasi pe75 muzana. Iri idambudziko remasvomhu rinonakidza nekuti rinoitika munzvimbo dzakakura, asi iyo zvakare inyaya yechimwe chinyorwa.
Chikoro chandakaenda, nguva refu yapfuura, ndakanga ndichiri nemakore gumi nerimwe. Mugiredhi rekupedzisira, regumi, gore rose rainyanya kuve geometry netrigonometry. Ndinorangarira matambudziko aHenryk Paśniewski - chii chakanga chisipo? Tetrahedra, prisms uye mapiramidhi anotemwa nenzira dzese dzinogoneka. Hongu, madondoro aiva mashoma. Nokuti zvakaoma, kunyange kudhirowa hakusi nyore.
Kubva ipapo, trigonometry kuchikoro yakaderedzwa zvakanyanya, yakaderedzwa. Kufanana neharahwa chero ipi zvayo, ndinowanzoyeuka kuti zvinhu zvose "ipapo" zvaive nani. Izvi, chokwadi, hazvisi zvechokwadi. Kwete zvose. Trigonometry haichadi zvakadaro mubasa rezuva nezuva reinjiniya uye muongorori. Shongwe dzemapuranga dziri pamusoro pemakomo hadzichadiwi. Imwe yezvivakwa zvakakura yaive muLyuban paKroshchenko Street. Aitove nezita remugomo rekuti "patria". Zvakanaka, zvakakwana zvezvipingamupinyi izvi. Ngatitarisei pamufananidzo. Kutanga, tinoona kureba kwechikamu s. Ndiyo 60 degree angle. Kubva pana AC tinowana BC, kozoti kureba BH. Asi uku ndiko kureba kwemadziro epadivi epiramidhi yedu yeorenji. Kubva pano, kureba kwepiramidhi kunowanikwa nekuwanda kweHV nesine yekona yekutenderera kwemadziro kusvika pachigadziko, iyo ... inodawo kuverengwa, asi izvi zviri nyore uye zvakajairika.
Ndingadaro here"dambudziko rakagadziriswa". Nehurombo, ini ndinosanganisa izvi nekuwedzera kupararira kudzidza kure. Ndinogara pamberi pechidzitiro uye "taura nemufananidzo", uye vadzidzi - nokuti ndinovadzidzisa - vanofanira kushanda maererano nemirairo yangu. Zvakadaro, ndiwo madzidzire andakaita Microsoft Teams, Inspery uye mamwe magajeti ekuitisa makirasi akadai. Murairidzi aive kumba, ini ndaiva kumba, munhu wese ainwa kofi yake, "aitaura nemufananidzo" uye ini ndaiedza kutevedzera.
→ Kuchikoro kwandinodzidzisa, vanotoziva kuti kunyange kana "tsika inodzoka", hurukuro dzichaenderera mberi mumweya mumwe. Iyi fomu ine zvakawanda zvakanakira. Uyu ndiwo musoro wechimwe chinyorwa. Izvi zvinoita kuti zvive nani kune avo vanoda kudzidza.
→ Nehurombo, hapana akawanda azvo sezvazvinoratidzika kwatiri, vadzidzisi. Ndakanonoka kuendesa chinyorwa ichi kumupepeti, asi kana uri kuverenga izvi, zvapera zvakanaka. Sezvineiwo, ndakaodzwa mwoyo nemaitiro evachangopedza kudzidza, vandakapa rusununguko rwakanyanyisa panguva yebvunzo. Ndichatora mhedziso uye nzira dze "mapurisa" dzichadzoka. Uye manzwiro angu aireva kuti panzvimbo pokupedza mashoko acho, ndakafamba nzendo refu nomuminda ine sinou pedyo neWarsaw. Kwaitonhora, ndaitonhora...
→ Ngatidzokerei kumakwikwi nebhora. Mubvunzo wechitanhatu unogona kupindurwa nehacksaw kana bhora rakapwanyika ping-pong. Joke yakanakisisa (basa rechi6) ndiyo iyo bullet inonyunyuta kuna chiremba: "Handizivi kuti chii chakaipa neni, asi ndakavhiringidzika zvachose." Paivewo nerakanaka, iro bara raigunun'una nemarwadzo aipenya uye kuti raiputika nepakati. Tsumo inobatanidzwa nebhora (basa rechinomwe) inoiswa mumusoro wechinyorwa, tinozivawo kuti bhora riri patsoka chii (iyi iNyika, handiti?). Basa rine ruvara rwebere rine ndebvu refu (zvechokwadi, bheya yakanga yakachena, nokuti nzira yakadaro inongogoneka munzvimbo dzepolar).
Macannonballs (dambudziko 11) haasisina denderedzwa nekuti tinokwanisa kugadzira madhiramu ane threaded, izvo zvinopa projectile rotational kufamba.
Mubvunzo wechi13 wakanakidza.Pave paye ndakatovapa vana vechikoro. Vakaedza kuita masvomhu akanga asina kunyatsonzwisisa, vakatyiswa nechinhu pa 17. Zvichakadaro, basa racho harina maturo. Dunhu rine radius yakapihwa idiki, ukuwo denderedzwa rakakura. Hazvina kukwana. Kumubvunzo wegumi nemasere, mhinduro chaiyo yaive: Muscovite ane pfuti Jacek Soplica yakabvutwa. Vadzidzi vakapindura zvisiri izvo: Jacek.
Ndichadzokera kusphere, nekuti inondikwezva zvakanyanya. Uye humbowo ndehunotevera "ode kune spherical".
Kulo! Iwe uri wangu! Zvikuru kana zvidiki
Wakangofanana kumagumo.
Ndinoda kuimba runako rwenyu rwese nhasi.
Ndinogona kuita equations. Asi ini ndichanyora ode!
Kukoshesa kwakawanda sei, achaziva chete
Ndiani akakuona. Asi kunaka kwako mukushongedza kwayo kwese
Avo vakadzidza pachikoro chegirini muSlavkov vachachikoshesa!
Runako rwako rwunobva pakati kusvika kumicheto!
Wese munhu anokwezvwa zvakaenzana kune yako geometry.
Ini ndinobva kumwana mudiki, kubva kupreschooler,
Ndagara ndichida kunzwisisa kuti sei wakadai.
Mazwi ababa aya airwadza sei:
“Uchaziva kana wakura. Nhasi uri mudiki!
Ndichiri mukomana uye mwana asina mhosva
Vana muzvitatu vaida kuziva zvakavanzika zvenyu
Uye kuti moyo wakadzika sei
Pandaida plaza yako yakavanzika ine nhurikidzwa ina.
Ndakamedza pwere zhinji dzinomhanya
Kubatanidza ako ekutanga kutenderera mukufunga,
Zvino chiso chejaya chakanga chafukidzwa namashanga;
Ndakaona triangle ine makona matatu ekurudyi
Akaita. Uye pakarepo ndakakwanisa kutsanangura kuti akanaka sei.
Iyo yepamusoro geometry ine elliptical.
Uye kuti jaya rakafurirwa sei naOscom,
Paakazondiratidza mutsara wake
Chii chinonzi meridian imwe neimwe?
Nekona imwechete yekucheka ... uye zvinotevera izvo
Kuti kureba kwecurve kukura kusvika kusingagumi,
Uye kuti matanda ese ari maviri akabatanidzwa nerudo.
Gare gare, uchitarisa yako Riemann tensor
Ndakaverenga nzvimbo dzeminda kusvika mangwanani
Uye pamusoro pechiso chako chinonzi sphere,
Macurves makuru haana kumboenda ku zero.
Saka ramba wakatendeka kwandiri, usingazununguki, une homogeneous,
Zvakangonaka uye zvinosetsa munzira dzese.
Gara uchisiya zvikamu zvakatenderera chete!
Kanopfuura kamwe mwoyo wangu unokushuvirai.
Regai majaya zvino, asingazivi vhudzi jena;
Vanodzidza macurves ako, asingazivikanwe naGauss.
