Yintoni lohlukanisa zezibalo? Inkcazo kunye Imizekelo

Qonda ukuba ulingano kwimathematika, kuyimfuneko ukuqhubeka ukufunda izihloko ezingundoqo kunye phambili algebra, geometry. Kubalulekile ukuba ukuqonda kumzobo, izakhiwo, imithetho imizobo zokwakha. Nangona nolwalamano olusenyongweni kunye nenzululwazi kakhulu ngqo - kwimathematika, ulingano kubalulekile ukuba abadlali, amagcisa, kwabayili, kunye nabo bathatha inxaxheba kwimisebenzi ophando, kunye nayiphi na entsimini.

ulwazi jikelele

Nje kuphela imathematika, kodwa iinzululwazi zendalo zibethwa isekelwe phezu ingqiqo wolingano- macala. Ngaphezu koko, ifumaneka kubomi bemihla ngemihla, yenye ngemvelo esisiseko indalo yethu. Ukuhlalutya oko lohlukanisa kwimathematika, kubalulekile ukukhankanya ukuba kukho iintlobo ezininzi kule meko. Ukuze uthethe ngezi ndlela:

• Mazwe, oko kukuthi, ezifana njengesipili ulingano. Lo mkhwa kwindawo lwezenzululwazi, ezibizwa ngokuba "mazwe".
• Al-rated basis. Kuba ingqiqo nesenzeko iqhosha - kujikelezo engile division ebalwe degrees 360 kwi ixabiso kwangaphambili. Ukongeza, echazwe-axis malunga okwenzeka ukujikeleza.
• Padialnaya xa lohlukanisa nesenzeko waphawula ukuba enze lokungavinjwa amathuba kwezinye enkulu engile ejikelezayo. Axis nayo ezikhethiweyo ngendlela ezimeleyo. Ukuze achaza le meko isicelo SO Iqela (2).
• Ukulenza. Kule meko sithetha ezintathu dimensions, apho into esijikeleziswa, ngokukhetha engile esicalanye. Bucala kwimeko ethile isotropic, xa isenzeko uba bume yinqobo okanye indawo.
• Ukujikeleza, edibanisa amaqela amabini ochazwe ngaphambili.
• Lorentz invariativnaya xa kukho ukujikeleza ngokwesigqibo esicalanye. Ngokuba lo hlobo yolingano yengqiqo isitshixo uba "Minkowski isithuba-ixesha."
• Super, ichazwa ukutshintshwa bosons, fermions.
• Eliphezulu echongiweyo ngexesha uhlalutyo qela.
• Kuwa, xa kukho utshintsho va, apho izazinzulu ukuchonga indlela, umgama. Ngokwesiseko idata ifunyenwe ukuba ziqhube uphando lokujongisisa oluthelekisayo atyhila ulingano.
• YoLungiso-sandi lweSihambisi waphawula kwimeko kwingcamango gauge ukuzimela kwi zinguquko ahambelanayo. Apha, ingqalelo ekhethekileyo ihlawulwe kwithiyori amasimi, kuquka ingqwalasela kwiimbono Yang-Mills.
• UKayin, ukubayinxalenye udidi lobumbeko electron. Eso ulingano enjalo, kwimathematika (Grade 6) alazi, ngenxa yokuba inzululwazi ophum. Le meko ibangelwa amaza yesibini. Kwafunyaniswa ngethuba lokwenza uphando E. Biron. Kwamagama C. Shchukarev yaziswa.

isibuko

Ngoxa ukufunda abafundi esikolweni phantse lonke wacela ukuba benze lo msebenzi "Symmetry abasingqongileyo" (iprojekthi izibalo). Njengomgaqo, kucetyiswa ukuba enze kwindawo esabuvaranda kwibakala isikolo rhoqo kunye nenkqubo jikelele izifundo zokufundisa. Ukumelana nale projekthi, kufuneka kuqala uziqhelanise ingqiqo ulingano, ingakumbi, ukuchonga yintoni na uhlobo isipili njengomnye esisiseko kunye netakane-friendly kakhulu.

Ukuqaphela iimeko macala ingqalelo imilo ethile zejometri, kwaye moya ikhethiwe. Xa abantu bethetha malunga wolingano le nto? Okokuqala, kokuba ikhethwe ingongoma, baze emva koko kuboniswe kulo. Phakathi kwabo bobabini, bachithe icandelo nokubala i-engile apho moya ngaphambili uyikhethile igqitha.

Ukuhlalutya oko lohlukanisa kwimathematika, khumbula ukuba abakhethelwe ekufumanekeni le nto iya kuthunyelwa i-moya-moya wolingano- macala kunye akukho wumbi. ingxenye laqina kufuneka ahlangane oko engile. Umgama ukusuka kwindawo kule moya kwaye ukusuka kwindawo ukuya kwicandelo yesibini linokulingana.

bokuqonda

Yiyiphi enye umdla ukwazi, ukuhlolisisa isenzeko wolingano- macala? Mathematics (Grade 6) iyasixelela ukuba amanani amabini zithathwa elungeleleneyo, ngokuyimfuneko twatse omnye komnye. Ingcamango lokulingana olukhoyo ngengqiqo elimxinwa ibende. Ngoko ke, izinto macala kwindawo exineneyo - hayi into efanayo.

Yintoni ngumzekelo lobomi kungakhokelela? Elemetarny! Ucinga ntoni ngayo iiglavu zethu, mittens? Thina sonke kusetyenziswa ukunxiba kubo, yaye siyazi ukuba singalahlekani, ngenxa yokuba umntu wesibini ku pair akuthethi ukuba pick up, uze emva koko kufuneka ukuba bathenge zombini kwakhona. Yaye kutheni? Ngenxa yokuba imveliso bafundelane ngezibini, nangona macala, kodwa eyenzelwe ngesandla ekhohlo ne ekunene. Lo - ngumzekelo obabuthandwa kwisipili macala. Ngokuphathelele lokulingana, loo maziko bayaqonda i "esipilini-bayalingana."

Yaye kuthekani na iziko?

Izincomo lohlukanisa central iqale ngokuthi esicacisa iimpawu zomzimba, ngokunxulumene apho kuyimfuneko ukuhlola isenzeko. Ukuze ukubiza kuso macala, ingongoma ekhethiweyo kuqala, liphakathi. indawo ekhethiweyo Okulandelayo (masenze bayibiza A) kunye nokufuna isibini (ngokuqhelekileyo zibonakaliswe E) yona.

Ekumiseleni wolingano iingongoma A kunye E amaqhina oqhagamshelwano ngelayini ngqo, kwindawo ebangel umzimba engundoqo. Okulandelayo, ukulinganisa okukhokelela. Ukuba umgca ukusuka kwindawo A ukuya embindini into elingana lekhefu olwahlula iziko ukusuka kwindawo E, singatsho ukuba iziko wolingano- wafunyanwa. Le lohlukanisa esembindini kwimathematika - enye neengqikelelo ezingundoqo ezikuvumela ukuba baphuhle ngakumbi ngobhalo geometry.

Kwaye ukuba uphendule?

Ukuhlalutya oko lohlukanisa kwimathematika, umntu akakuphosi ingqalelo ingqikelelo uhlobo olunganeno ojikelezayo yale meko. Ukuze siqonde imiqathango, ethatha umzimba kokuba kwindawo esembindini, uze uchaze amanani apheleleyo.

Phakathi nokuhlola, umzimba esijikeleziswa yi engile kwangaphambili elingana umphumo yokwahlula degrees 360 ngeqondo ekhethiweyo. Ukuze wenze oku, kufuneka uyazi into esqwini wolingano-macala (2 iklasi, izibalo, inkqubo yesikolo). Le axis - kumgca osuka iingongoma ezimbini ezithile. Lokut- lohlukanisa na ongathi, ukuba kwi-engile ekhethiweyo ujikelezo komzimba iya kuba kwindawo efanayo phambi zazo.

Kwimeko apho inani yendalo 2 wakhethwa, wabutyhila isenzeko wolingano- bathi macala yezihlunu ichazwe kwimathematika. Oku uphawu eziliqela amanani. A Umzekelo: unxantathu.

Malunga imizekelo emininzi

Lo mkhwa iminyaka emininzi ukufundisa imathematika kunye nejiyometri kwisikolo samabanga aphakamileyo luveza ukuba eyona ndlela ilula ukuqonda isenzeko-macala, echaza ngayo ngemizekelo ethile.

Okokuqala, cinga ububanzi. Kuba umzimba okunjalo efanayo ixesha luphawulwa isenzeko-macala:

• iziko;
• esipilini;
• ukujikeleza.

Njengoko ingongoma ephambili ukuba ezikhethiweyo, ebekwe kanye kulo mzobo kwiziko. Makathathe moya buchazwa isangqa esikhulu, yaye kwabonakala ukuba "kunqunyulwa" ngayo ngomaleko. Ntoni na izibalo? Jikelezisa kunye lohlukanisa central kwimeko ibhola - amagama anxulumene kunye sangqa amanani aya kusebenza axis kuba isenzeko.

Omnye umzekelo izicacele - ikhowuni setyhula. Ngokuba lo isheyiphu semvelo yezihlunu ulingano. Kwimathematika bokwakha kwalo mmangaliso kwakuxhaphakile isicelo ithiyori kwaye aluncedo. Qaphela: njengoko axis kuba isenzeko yezenzo esqwini cone.

Oku kubonisa wafunda ngumkhuba prizim. Eli nani sisipili iimpawu ulingano. Plane ukhethe "kunqunyulwa", zibhekisela ngokomfanekiso isiseko, kude kubo rhoqo. Ukudala zejiyometri, esichazayo, uyilo bokwakha (izibalo ulingano kubalulekile, hayi ngaphantsi kwe inzululwazi ngqo nezichazayo), khumbula nokusebenza esebenzayo kunye nokusebenza kucwangciso umthwalo-ethwele izinto yeziphumo specular le.

Kwaye ukuba iimilo umdla ngakumbi?

Yintoni na onokumxelela Mathematics (Grade 6)? lohlukanisa Central ayikho kuphela into elula neqondakalayo, ngathi ibhaluni. Kuyinto iimilo abayinqobo, kunye nomdla ngakumbi ezintsonkothileyo. Umzekelo, oku ke parallelogram. Kuba into enjalo uba kwindawo engundoqo ye elinye awela oxwesileyo.

Kodwa xa siqwalasela trapezoid isosceles, kuya kuba umzobo macala yezihlunu. Chonga ukuba kungaba mzekelo, xa ukhetha esqwini ekunene. Umzimba macala malunga umgca nkqo emhlabeni watyhutyha ilizwe ncam phakathi.

Ulingano kwimathematika bokwakha kufuneka luthathele ingqalelo idayimani. Eli nani kuyamangalisa ukuba ngaxeshanye ngokudibanisa iintlobo ezimbini macala:

• ekumbindi;
• engundoqo.

Njengoko ezimanyeneyo diagonal kufuneka ukhethe into. Kwindawo apho idayagonali ye irhombus phambana, kuba liziko wolingano-macala.

Malunga ngobuhle ulingano

Ndiyila iprojekthi imathematika, lo wolingano kwalo kuba isihloko ephambili, ngokuqhelekileyo kwindawo yokuqala khumbula amazwi obulumko-nzulu enkulu Weil: ". Symmetry - ingcinga leyo kangangeenkulungwane bezama ukuqonda umntu esidlelana ngalo, kwafuneka ukuba ngenxa yokuba ngubani kudala ebuhleni ngokusebenzisa umyalelo ekhethekileyo"

Njengoko usazi, nezinye izinto ibonakala intle, ngoxa abanye bashenxise, nokuba ukuba ngaba iziphako ezicacileyo. Kutheni le nto isenzeka? Impendulo yalo mbuzo ibonisa ukuzalana izakhiwo kunye imathematika ulingano, kuba le meko kwaye uba isiseko sovavanyo njengesifundo nezamkelekileyo enomtsalane.

Enye abafazi ezintle kwi planethi - yeyona supermodel zobuciko Tarlikton. Yena ukuba impumelelo eze ndawo ngoncedo into yokuqala: imilebe zayo macala.

Njengoko yaziwa, uhlobo futhi kuyaphela ulingano, kwaye abakwazi ukufikelela kuyo. Asinto ulawulo jikelele, kodwa ujonge abantu abakufutshane kubo: ebusweni babantu phantse ukufumana isimetri elililo, nangona icacile umnqweno yona. Ubuso macala ngakumbi le interlocutor, ngoko ke abangcono.

Njani ingcamango wolingano kwendawo enhle

Kuyamangalisa ukuba lo wolingano yoluvo abantu ubuhle esekelwe kwindawo nezinto kulo yayo. Eminyaka, abantu badla ukuqonda oko kubonakala ofezekileyo, kwaye ugqithayo ngokungenamkhethe.

Le macala, ibathwana - yiloo nto inceda ukuqonda abangaboniyo into uze uvavanye ngayo kakuhle. Zonke izinto, izahlulo kufuneka ulungelelaniswe, phakathi olinganise ezifanelekileyo kunye nabanye. Kuye kudala kwafunyanwa ukuba izinto yezi ngathi ngabantu ngaphantsi kakhulu. Konke oku kunxulumene nengqiqo "ngokuvumelana". Malunga kutheni kubalulekile ukuba umntu zo emangalisiwe elide yamandulo, amagcisa.

Kufuneka sijonge amanani zejometri, kwaye isenzeko wolingano- macala iya kuba nezona lula ukuyiqonda. Le nesenzeko macala kakhulu kumba kwingingqi ezikufutshane:

• rocks;
• iintyatyambo kunye namagqabi kwezityalo;
• amalungu engaphandle nesithandwa ezendeleyo eziphilayo.

Ezi ngezenzeko ezichazwe ke umthombo indalo. Yaye nantsi into oyibona twatsa, wakhangela kufutshane iimveliso wezandla zabantu? Kuyinto lubonakale abantu eziphumela ekuyilweni nje omnye Ukuba uzama ukwenza into entle okanye esebenza (okanye zombini kukuthi, kwaye ngexesha elinye):

• iipatheni zobuhlalu, ethandwayo ukususela kumaxesha amandulo;
• izinto zokwakha;
• izinto zokwakha wena;
• womluki.

malunga kwamagama

"Ulingano" - eli gama kulwimi lwethu ukusuka amaGrike amandulo kuqala kule ngcaciso imfutshane senzeko uzame alikhangele. Lo gama ibonisa ubukho inkqubo kunye intlanganisela evumelanayo iinxalenye into. Translation of the elithi "ulingano", uyakwazi ukufumana njengoko ntonye:

• ukulingana;
• ngubo yobunye apho;
• ukulingana.

Ukususela kumaxesha amandulo le isimetri yi ingcamango ebalulekileyo kuphuhliso loluntu kwiinkalo ezahlukeneyo kunye namashishini. Izizwe adume ukuba banengqondo baye oqhelekileyo le meko, ucinga ikakhulu oko ngokubanzi. Symmetry wema ukuba imvisiswano eseleyo. Ekuhambeni kwexesha lethu, isigama sifundiselwa kwizikolo zesiqhelo. Ngokomzekelo, yintoni na esqwini wolingano-macala (2 iklasi izibalo) abantwana iintetho utitshala eklasini eqhelekileyo.

Njengoko ingcamango yale meko ntonje isithembiso sokuqala yeengcinga yenzululwazi kunye neengcamango. Ezithandwa kakhulu kwaba kwinkulungwane edlulileyo, xa ehlabathini lonke alawula ingcamango ukuvumelana lwemathematika azalwa ngawo kanye kwinkqubo iphela. Iingcali baloo maxesha babeqinisekile ukuba macala kubonisa ukuvumelana kaThixo. Kodwa Greece yamandulo, neengcamango bathi indalo yonke macala, kwaye zisekelwe phezu postulate: ". Le ulingano egqibelele '

AmaGrike Great kunye ulingano

Ulingano edubula iingqondo kubaphandi abadumileyo Greece yamandulo. Ukuze baye basinda bubungqina bokuba uPlato ekuthiwa eyahlukileyo om- ezimacala rhoqo. Ngokwembono yakhe, amanani ezinjalo - yomntu izinto ihlabathi lethu. Kukho ngezigaba ilandelayo:

element	figure
umlilo	Tetrahedron, njengoko eluchochoyini iinjongo zakhe esibhakabhakeni.
amanzi	Icosahedron. Choice kungenxa "katuchestyu 'nani.
umoya	Octahedron.
umhlaba	Eyona nto kakhulu oluzinzileyo, oko kukuthi ityhubhu.
yonke	Dodecahedron.

Ubukhulu becala ngenxa yale thiyori idla ngokuba ezimacala rhoqo eziqinileyo bulumko kaPlato.

Kodwa ke isigama waqalisa ngaphambili, yaye akukho indima lokugqibela eyadlalwa nomkroli Polycleitus.

KaPythagoras and lohlukanisa

Ngexesha ubomi Pythagoras yaye kamva, xa imfundiso yakhe amava ngexesha layo, isenzeko wolingano- yahlulekile ukukhuphela ecacileyo. ngoko yathotyelwa kwimeko uhlalutyo ulingano, leyo wanika ukubaluleka kwisicelo ngayo iziphumo zenzululwazi.

Ngokutsho izigqibo:

• Lohlukanisa isekelwe phezu iingqiqo zinkulu, ngokufanayo kunye nokulingana. Kwimeko sasiphikisana ingqiqo uba inani ngaphantsi macala, ngokuthe ngcembe ihamba ukuya yezi ngokupheleleyo.
• Kukho 10 izibini sokumelana. Ngokutsho iimfundiso, lo isimetri yi zesiganeko leyo kunciphisa iyunifomu eli uze ngokwenjenjalo oyinxalenye indalo xa iyonke. Le postulate eminyaka zibe nempembelelo ngamandla eziliqela wenzululwazi ngqo kwakunye bulumko, ngokunjalo zendalo.

KaPythagoras kunye nabalandeli bakhe sasikwanti "umzimba macala ngokupheleleyo," nto leyo zichongwe ekwaneziseni iimeko:

• ubuso ngalinye - polygon;
• facets ezifumaneka ezimbombeni;
• nani kufuneka babe amacala alingane kunye engile.

Yaba kaPythagoras kuqala ukuze bathi abo imizimba kukho ezintlanu kuphela. Le kwafunyaniswa enkulu laba sisiqalo geometry kwaye kubalulekile ngezakhiwo mihla.

Kwaye ufuna ukubona isenzeko eliligugu lawo macala? Catch a snowflake ebusika. Strange kodwa yinyani - undinike isiqwenga elincinane yomkhenkce eziwa isibhakabhaka nje entsonkothileyo kakhulu isakhiwo ngumkhenkce, kodwa ngokugqibeleleyo macala. Cinga ngocoselelo: snowflake Intle ngenene, kwaye imigca yayo ephambili obathandayo.