Kuyini yesimethri izibalo? Incazelo kanye Izibonelo

Qonda lokho yesimethri wezibalo, kubalulekile ukuqhubeka ukufunda izihloko eziyisisekelo sezihambile algebra, geometry. Kubalulekile ukuqonda umdvwebo, ubungcweti, imithetho ukwakhiwa imidwebo. Naphezu ubuhlobo obuseduze isayensi ngqo kakhulu - izibalo, wesimethri Kubalulekile abalingisi, abaculi, abadali kanye labo abenza imisebenzi yocwaningo, futhi kunoma yimuphi umkhakha.

ulwazi olujwayelekile

Hhayi wezibalo kuphela, kodwa futhi ngesayensi yemvelo kuthiwa isekelwe umugca lohlukanisa emkhatsini. Ngaphezu kwalokho, butholakala zokuphila kwansuku zonke, ke ingenye uhlobo eziyisisekelo umkhathi wethu. Ukuhlaziya lokho ngewesimethri mathematics, kubalulekile ukusho ukuthi kukhona izinhlobo eziningana lesi simo. Ukukhuluma ngalezi ongakhetha:

• Bilateral, okungukuthi, ezifana esibukweni wesimethri. Lesi simo esiyingqayizivele sibangelwa imvelo yesayensi, evame ukubizwa ngokuthi "zamazwe amabili".
• Al-ukalwe isisekelo. Ngenxa yalesi umqondo mkhuba ukhiye - umjikelezo engela division ibalwa of 360 kunani kusengaphambili. Ngaphezu kwalokho, pre-echaziwe-eksisi mayelana nokuthi iziphi izinhlelo ukujikeleza kwenzeka.
• Padialnaya lapho wesimethri mkhuba waphawula uma enze ezinqumela sivuleka ezinye engela ngobukhulu okungahleliwe. Axis nayo ezikhethiwe ngendlela yokuzimela. Ukuchaza lesi simo isicelo SO iqembu (2).
• Eyisiyingi. Kulokhu sikhuluma ezintathu zobukhulu, lapho into ijikeleziswa, ngokukhetha engeli ezingafanele. Ukwabela icala ezithile isotropic, lapho lo mkhuba siba imvelo eyinqaba wendawo noma isikhala.
• Ukujikeleza, ngokuhlanganisa amaqembu amabili echazwe ngaphambilini.
• Lorentz invariativnaya lapho kukhona Ukujikeleza ezingafanele. Ukuze lolu hlobo wesimethri umqondo ukhiye iba "Minkowski isikhala esigcwele."
• Super, ichazwa ngokuthi esikhundleni bosons, fermions.
• Ephakeme ezikhonjwe phakathi ukuhlaziya iqembu.
• Ukuwa, uma kunezinguquko isikhala, okuyiwona ososayensi ukuhlonza isiqondiso, ibanga. Ngesisekelo idatha etholwe ekhaya azokuqhubela Luhlatiyo ezembula wesimethri.
• Isilawuli Samandla nasemkhakheni uma theory gauge wokuzibusa e kugucuka okuhambisanayo. Lapha, ukunakekelwa okukhethekile ikhokhelwa kuyinkolelo-mbono yokuziphendukela Amasimu, kuhlanganise focus on the imibono Yang-Mills.
• UKhayini, okuqondene ekilasini electron ukucupha. Lokho kuyinto wesimethri ezinjalo, izibalo (Libanga 6) alazi, ngoba isayensi esiseqophelweni eliphezulu. Lo mkhuba kubangelwa imvamisa yesibili. Kwatholakala phakathi ucwaningo E. Biron. Amatemu C. Shchukarev kwethulwa.

esibukweni

Ngesikhathi ngisafunda ngesikhathi abafundi basesikoleni Cishe njalo uma ucelwa ukuba wenze umsebenzi "kufanane abasizungezile" (izibalo project). Njengomthetho, kutuswa ukuba afeze lesithupha grade esikoleni njalo ngohlelo jikelele yokufundisa izifundo. Ukuze sibhekane nale phrojekthi, kuzomele uqale ukujwayelana umugca lohlukanisa emkhatsini, ngokukhethekile, ukubona ukuthi yini uhlobo esibukweni omunye eyisisekelo kanye icwecwe kakhulu.

Ukukhomba izimo wesimethri kubhekwe ukuma ethize weJiyomethri, futhi indiza kuyakhethwa. Lapho abantu khuluma ngezinto wesimethri into? Okokuqala, it is akhethiwe iphuzu, bese ziyabonakala kuso. Phakathi bobabili ukuchitha ingxenye futhi kubalwe i-engeli lapho indiza ngaphambilini sidlule.

Ukuhlaziya lokho ngewesimethri mathematics, khumbula ukuthi letikhetselwe ukuthola lesi simanga izobizwa indiza indiza wesimethri futhi akukho okunye. ingxenye ayeba kumelwe aphambana nganoma engeli kwesokudla. Ibanga kusuka iphuzu kule indiza futhi kusukela iphuzu kuya ingxenye yesibili kufanele alingane.

umehluko wemisindo nemiqondo yamagama

Yini enye kungaba ezithakazelisayo ukwazi, behlola lomkhuba wesimethri? Mathematics (Libanga 6) usitshela ukuthi izibalo ezimbili ezibhekwa olinganiselayo, hhayi ngempela efanayo nomunye. Umqondo ukulingana ukhona ngomqondo emincane futhi ebanzi. Ngakho, izinto zazo ziyalingana e emincane - hhayi into efanayo.

Kuyini isibonelo sokuphila kungaholela? Elemetarny! Ucabangani mayelana amagilavu yethu, amagilavu? Sonke esetshenziswa sizigqoke futhi siyazi ukuthi ngeke ukwazi ukulahlekelwa, ngoba umuntu wesibili ku pair akuyona eyolanda, bese ukuthenga kokubili futhi. Futhi kungani? Ngenxa yokuthi imikhiqizo abhanqiwe, nakuba ziyalingana, kodwa yakhelwe isandla kwesokudla noma kwesokunxele. Lena - yisibonelo esingokoqobo esibukweni wesimethri. Ngokuphathelene ukulingana, izikhungo ezinjengalezi aqaphele "mirror bayalingana."

Futhi kuthiwani isikhungo?

Kubhekwe emaphakathi wesimethri siqale ngokuchaza property umzimba, maqondana kuyo okudingekile ukuhlola lo mkhuba. Ukuze bakubiza ziyalingana, iphuzu lokuqala akhethiwe, emaphakathi. iphuzu Landelayo ekhethiwe (ake ukuyibiza A) futhi sifune bhangqa (evamile ezikhonjiswe E) ngoba.

Ekunqumeni wesimethri amaphuzu A no E zivumelane oxhumene by emgceni locondzile, iphuzu okuthakazelisayo ebusayo eyinhloko. Ngokulandelayo, ulinganise umugqa okuholela. Uma umugqa ukusuka endaweni A kuya maphakathi into uyalingana isikhawu esasihlukanisa isikhungo kusukela iphuzu E, singasho ukuthi isikhungo wesimethri kutholakala. Emaphakathi yesimethri wezibalo - omunye imiqondo esemqoka ezivumela ukuba kuphinde kuthuthukiswe imfundiso yokuziphendukela geometry.

Futhi uma uphendukisa?

Ukuhlaziya lokho ngewesimethri mathematics, umuntu akakwazi miss ukunakwa nomqondo subtype ukujikeleza zalesi simo. Ukuze uzwisise imigomo, ukuthatha umzimba kokuba endaweni eyodwa, kanye nokuchaza inombolo ephelele.

Ngesikhathi sokuhlola, umzimba ijikeleziswa ngumuntu engela predetermined ilingane yi sokuhlukanisa 360 ngesilinganiso ekhethiwe. Ukuze wenze lokhu, kumele wazi ukuthi yini eksisi wesimethri (2 ikilasi, izibalo, uhlelo esikoleni). Lokhu-eksisi - umugqa ohlanganisa amaphuzu amabili akhethiwe. On Ukujikeleza wesimethri ongathi, uma aqonde ngqo endaweni ekhethiwe ukuzungeza umzimba kuyoba endaweni efanayo njengoba phambi manipulations.

Esimweni lapho inani zemvelo 2 wakhethwa, futhi wathola lo mkhuba wesimethri bathi wesimethri Axial kuchazwa kwi-mathematics. Lena isici eziningi izibalo. Isibonelo esingokoqobo: unxantathu.

Mayelana izibonelo ezengeziwe

Umkhuba kweminyaka eminingi efundisa Tibalo kanye nebudlelwane lobukhona geometry esikoleni esiphakeme ebonisa ukuthi indlela elula ukuqonda lo mkhuba wesimethri, echaza ngayo izibonelo eziqondile.

Okokuqala, cabanga ngelithi ububanzi. Ukuze umzimba okunjalo ngesikhathi esifanayo libhekene lomkhuba wesimethri:

• isikhungo;
• esibukweni;
• ukujikeleza.

Njengoba iphuzu eliyinhloko ukuze kukhethwe, elise ncamashi figure isikhungo. Ukuze sithathe indiza kuchazwe embuthanweni omkhulu, futhi kwabonakala sengathi "usike 'ke zibe ugqinsi. Yini izibalo? Phendula futhi central wesimethri esimweni ibhola - imiqondo ehlobene ne ububanzi we izibalo ayokhonza njengamakhosi eksisi ngoba lo mkhuba.

Esinye isibonelo sobala - Isigaxa isiyingi. Ukuze lo mumo esingokwemvelo Axial wesimethri. Esifundweni sezibalo kanye izakhiwo zalesi simo kwaba isicelo okwandile-theory kanye nama-practical. Qaphela: njengoba eksisi ngoba lo mkhuba izenzo eksisi Isigaxa.

Kubonisa wafunda mkhuba nezibhebhe. Lesi sibalo sici esibukweni wesimethri. Plane khetha "usike ', zifana kuya isizinda sibalo, kude nabo ngezikhathi ezithile. Ukudala weJiyomethri, okuchazayo nemiklamo yokwakha (izibalo wesimethri kubalulekile, hhayi ngaphansi kuka wesayensi eqondile futhi achazayo), khumbula ukusebenza esiwusizo futhi iwusizo ekuhleleni umthwalo esindayo tincenye specular imiphumela.

Futhi uma Umumo mnandi?

Yini kufanele sitshele Mathematics (Libanga 6)? wesimethri Central akuyona kuphela into elula futhi kuyaqondakala, efana ibhaluni. Kuyinto Umumo eyinqaba, futhi ezithakazelisayo futhi eziyinkimbinkimbi ngokwengeziwe. Ngokwesibonelo, lena parallelogram. Ukuze into enjalo iba emnyombweni umuntu lapho sawela idayagonali.

Kodwa uma sicabangela trapezoid isosceles, kuyoba sibalo nge wesimethri Axial. Thola kungaba kulelo cala, uma ukhetha-eksisi engakwesokudla. Umzimba ziyalingana maqondana umugqa perpendicular phansi futhi edabula ke ncamashi phakathi.

Kufanane kwi-mathematics ne izakhiwo kufanele inake idayimane. Lesi sibalo Kuyaphawuleka ukuthi kanyekanye ihlanganisa izinhlobo ezimbili wesimethri:

• centerline;
• emaphakathi.

Njengoba ahlangene idayagonali Kufanele ukhethe into. Ngesikhathi phuzu lapho diagonals we rhombus aphambana, iyisikhungo wesimethri.

Mayelana ubuhle kanye wesimethri

Owenza iphrojekthi izibalo, i-wesimethri zazo kungaba ngesihloko ukhiye, ngokuvamile kwasekuqaleni ukukhumbula amazwi ahlakaniphile usosayensi omkhulu Weil: ". Kufanane - umbono okwaphela amakhulu eminyaka bezama ukuqonda abantu abavamile, ngoba kwaba esona kudala ubuhle ephelele ngokusebenzisa oda esiyingqayizivele"

Njengoba wazi, nezinye izinto Ubonakala enhle kakhulu, kuyilapho ezinye basunduze, ngisho noma abanayo amaphutha asobala. Kungani lokhu kwakwenzeka? Impendulo yalo mbuzo ubonisa ubuhlobo izakhiwo kanye izibalo wesimethri, ngoba lokhu mkhuba futhi uba isisekelo ukuhlolwa ezifana nokuthatha isifundo njengamaphuzu aesthetically ezikhangayo.

Omunye walaba besifazane enhle kakhulu kule planethi - kungcono supermodel emabhulashini Tarlikton. Nanguya isiqiniseko sokuthi impumelelo ifikile endaweni sibonga lokuqala esenzakalweni esiyisimangaliso esenzeka esiyingqayizivele: izindebe zakhe kukhona izinhlangothi zazo ziyalingana.

Njengoba yaziwa, isimo futhi avame wesimethri, futhi awukwazi ukufinyelela kuso. Akuyona ojwayelekile, kodwa sibheke abantu abaseduze kwabo: e nobuso bunjengobuso babantu cishe ukuthola wesimethri ngokuphelele, nakuba kusobala isifiso sokuba ke. Ubuso ziyalingana ngaphezulu interlocutor, ngakho-ke ubukeka kangcono.

kwaba kanjani umbono wesimethri amahle

Kuyamangalisa ukuthi phezu wesimethri we Umbono womuntu wobuhle based ezizungezile futhi izinto kuwo. Sekungamakhulu amaningi eminyaka, abantu bavame ukuba siqonde lokho kubonakala ephelele, futhi ukuthi odlulela ngokungakhethi.

I wesimethri, olinganise - yilokho kusiza ukuba zibukeke azibonayo into futhi ukuhlola ngendlela efanele. Zonke izici, izingxenye kufanele silinganisele futhi ngaphakathi olinganise ezinengqondo nomunye. Sekuyisikhathi eside wathola ukuthi izinto quin sengathi abantu ingasaphathwa. Konke lokhu kuhilela welithi "ngokuvumelana." Mayelana kungani kubalulekile kangaka ngomuntu zo eside lasendulo sidideke, abaculi.

Kufanele sibheke izibalo weJiyomethri, futhi lo mkhuba wesimethri kuyoba sobala futhi kulula ukuyiqonda. I ejwayelekile kakhulu izenzakalo ziyalingana eziluzungezile:

• amatshe;
• izimbali namaqabunga alesi izitshalo;
• abhanqiwe izitho yangaphandle esivela eziphilayo.

I izenzakalo ezichazwe kukhona umthombo uhlobo. Futhi nakhu ungabona lesinesitfombe-sibuko, ngifuna eduze imikhiqizo wezandla zomuntu? Kungokuphawulekayo ukuthi incwadi abantu gravitate ngokudalwa eyodwa nje uma uzama ukwenza into enhle noma obusebenzayo (noma kokubili kuba, futhi ngesikhathi esifanayo):

• amaphethini nemihlobiso, ethandwa kusukela ezikhathini zasendulo;
• izakhi isakhiwo;
• izakhi ukwakhiwa Nguwe;
• ngenalithi.

mayelana amagama

"Kufanane" - Kepha izwi lafinyelela olimini lwethu kusuka amaGreki asendulo owaqala kuyasetshenziswa kule ukunakwa mkhuba futhi zama ukuhlola ke. Igama elithi kubonisa khona uhlelo futhi inhlanganisela avumelanayo izingxenye into. Ukuhumusha izwi "wesimethri", ungakwazi sithathe amagama amqondo ofanayo:

• proportionality;
• sameness;
• proportionality.

Kusukela ezikhathini zasendulo wesimethri awusiwo umqondo obaluleke kakhulu sokuthuthukisa abantu emikhakheni ehlukahlukene kanye nezimboni. Abantu kusukela endulo ukuba nekucondza ngalokufanako lesi simanga, ikakhulukazi siyihlole ngobubanzi. Kufanane wema bayezwana nokulinganisela. Esikhathini sethu, itheminoloji okufundiswa ezikoleni ezejwayelekile. Ngokwesibonelo, yini eksisi wesimethri (2 ikilasi le-IiMbalo) izingane izinkulumo uthisha ukuze isigaba ezivamile.

Njengoba umqondo zalesi simo ngokuvamile nesithembiso kokuqala imicabango yesayensi nemibono. Ikakhulukazi ethandwa kwakunjalo ekhulwini langaphambilini, lapho wonke ezweni elibuswa umbono ongahambisani zezibalo esivela kakhulu ohlelweni universe. Ongoti ngalezo zikhathi ayeqiniseka ukuthi wesimethri siwukubonakaliswa ngokuvumelana saphezulu. Kodwa eGreece yasendulo, izazi zefilosofi nazo ziye umangalele ukuthi wonke umkhathi ziyalingana, futhi konke esekelwe postulate: ". Le wesimethri awusiwo ephelele"

AmaGreki Mikhulu wesimethri

Kufanane wadubula izingqondo izazi ezidumile kakhulu yeGrisi yasendulo. Ukuze ezisekhona kuwubufakazi bokuthi uPlato ngokuthi ahlukene bayahlonishwa polyhedra njalo. Ngokubona kwakhe, ezifana izibalo - ukwenziwa samuntu izici zezwe lethu. Kube ngezigaba ezilandelayo:

isici	sibalo
umlilo	Tetrahedron, njengoba esivelele izinjongo zakhe phezulu.
amanzi	Icosahedron. Ukukhetha kungenxa "katuchestyu" sibalo.
emoyeni	Octahedron.
umhlaba	Into esitebeleni kunazo, okungukuthi cube.
yonke	Dodecahedron.

Ngokuyinhloko, ngenxa yokuthi lo mbono Ivame ukubizwa polyhedra njalo ukudla okuqinile kaPlato.

Kodwa amagama owethulwa ngaphambili, futhi akukho indima yokugcina eyadlalwa umqophi Polycleitus.

Pythagoras futhi wesimethri

Phakathi nokuphila Pythagoras futhi kamuva, lapho ukufundisa kwakhe lalinenkinga nenkathi yokudlondlobala kwawo, lo mkhuba wesimethri kuhlulekile ukukhipha ecacile. Labe ngaphansi ukuhlaziywa yesayensi wesimethri, okwakunginika ukubaluleka ukuba ngokoqobo imiphumela.

Ngokusho iziphetho:

• Kufanane kusekelwe imiqondo Ingxenye, ukufana kanye nokulingana. Endabeni ka kwephulwe umqondo iba sibalo kancane ziyalingana, kancane kancane kokuthuthela quin ngokugcwele.
• Kukhona 10 namabhuzu eziphikisanayo. Ngokusho ezimfundisweni, le wesimethri iyisici esehlisa umfaniswano obuhlukile futhi kanjalo obumba yonke. Lokhu postulate amakhulu eminyaka ibe nethonya elinamandla inombolo wesayensi ngqo kanye nefilosofi, kanye yemvelo.

Pythagoras nabalandeli bakhe lalihlukene "umzimba ziyalingana ngokuphelele," okuyinto ubalwe njengenye wanelise izimo:

• ubuso ngamunye - ipholigoni;
• facets atholakala emakhoneni;
• sibalo kufanele abe amacala alingane nama-engeli.

Kwaba Pythagoras ngowokuqala bathi walemizimba kukhona ezinhlanu kuphela. Lena ukutholakala enkulu kwaphawula ukuqala geometry futhi ibalulekile ngobungcweti bokwakhiwa kwezindlu yesimanje.

Ingabe ufuna ukubona ngamehlo akho into ehle kunazo zonke yokulinganisa? Thola isibhamu seqhwa ebusika. Ngokumangazayo, iqiniso liwukuthi iqhwa elincanyana eliwela esibhakabhakeni alikona nje isakhiwo esiyinkimbinkimbi yekristal, kodwa futhi sinomlinganiso ophelele. Cabanga ngalokhu ngokucophelela: iqhwa leqhwa lihle ngempela, futhi imigqa yalo eyinkimbinkimbi iyamangalisa.