Chii symmetry masvomhu? Definition uye Mienzaniso

Kunzwisisa, ndizvo chii symmetry mu masvomhu zvakafanira kuramba tichidzidza inokosha uye akura Nyaya nemasvomhu, geometry. Zvakakosha kuti kunzwisisa mufananidzo, mapurani, mitemo kuvakwa vanodhirowa. Pasinei noukama hwepedyo zvikuru chaiyo sayenzi - masvomhu, symmetry kunokosha kuti vatambi, vanodhirowa mifananidzo, creators, uye vaya vari kuita tsvakurudzo mabasa, uye chero munda.

Vhuṱanzi

Kwete chete masvomhu, asiwo sayenzi dzinongoitika vari zvikuru papfungwa yokuti symmetry. Uyezve, rinowanikwa muupenyu hwezuva nezuva, ndiyo imwe inokosha hunhu chechadenga chedu. Kuongorora zviri symmetry mu masvomhu, zvakakodzera kutaura kuti pane mhando wandei chiitiko ichi. Kutaura izvi zvaramba:

• Bilateral, kureva, akadai girazi symmetry. Ichi chinoshamisa mu zvesayenzi kwezvakatipoteredza, anowanzonzi "bilateral".
• Al-yavose sezvavakatarirwa hwaro. Nokuti pfungwa iyi inokosha chaiyo - mumwe kutenderera angled vakaverenga weboka 360 madhigirii pane akafanorongerwa ukoshi. Uyezve, pre-rinorondedzerwa akabatana pamusoro iyo kutenderera kunoitika.
• Padialnaya kana symmetry Fani aona kana kuita pamadiro Anovhura zvimwe chero pakukura angled. Akabatana ari zvakare vakasarudzwa muna yakazvimirira nenzira. Kutsanangura Fani iyi zvinoshandawo SO boka (2).
• Idenderedzwa. Muchiitiko ichi tiri kutaura pamusoro matatu kukura, umo chinhu ari zvayaitenderera paguyo, kusarudza zvemasanga pamakona. Govera zvakananga nyaya isotropic, apo Chiitiko rinova pachangu ezvinhu omunharaunda kana nzvimbo.
• Rotational, kubatanidza mapoka maviri kare kurondedzerwa.
• Lorentz invariativnaya kana paine zvemasanga kutenderera. Hworudzi urwu symmetry kiyi pfungwa anova "Minkowski nzvimbo-nguva."
• Super, rinorondedzerwa so yaitsiva bosons, fermions.
• Higher vanozivikanwa panguva boka kuongorora.
• Kuparara, kana pane kuchinja nzvimbo, iro masayendisiti kuziva gwara, daro. Pahwaro humboo vakawana kuti kuitisa kuenzaniswa ongororo dzinoratidza symmetry.
• Calibration kuchengetwa zvakaitika geji dzidziso kuzvimirira mune runoenzanirana transformations. Pano, pfungwa rwakabhadharwa kuna dzidziso neminda, kusanganisira pfungwa pamusoro Yang-Mills pfungwa.
• Kaini, kungova kirasi Erekitironi configurations. Ndizvo yakadaro symmetry, masvomhu (Grade 6) asina pfungwa, nokuti sayenzi wemandorokwati. Chiitiko anokonzerwa yechipiri maitikiro. Vakaziva panguva pakutsvakurudza E. Biron. Mazwi C. Shchukarev akatanga.

girazi

Pandaidzidza pachikoro vadzidzi vari dzinenge nguva dzose aite basa "Symmetry yakatipoteredza" (pamasvomhu chirongwa). Kazhinji, Zvinokurudzirwa kuti tiite rechitanhatu mugwaro dzose chikoro pamwe mukuru purogiramu yokudzidzisa nyaya. Kutsungirira basa, unofanira kutanga kuziva pfungwa symmetry, kunyanya kuziva chii girazi mhando somumwe inokosha uye chinonyanya nembudzana-ushamwari.

Kuziva mamiriro ezvinhu symmetry vaiona zvakananga geometric chimiro, uye ndege anosarudzwa. Kana vanhu vanotaura pamusoro symmetry ari chinhu? Kutanga, anosarudzwa pfungwa, uye ipapo zvinoratidzwa pariri. Pakati vaviri vanopedza chidimbu overenga pakona pa izvo ndege kare vakasarudzwa wakapfuura.

Kuongorora zviri symmetry mu masvomhu, yeuka kuti vakasarudzwa nokuda kuziva miedzo Fani ichi kunzi ndege ndiyo symmetry Ndege uye hapana chimwe. Wakaitwa chidimbu anofanira piringisha izvozvo kurudyi pamakona. The kure pfungwa kusvikira ndege iyi uye kubva pfungwa rechipiri chidimbu zvinofanira kuenzana.

nuances

Chiizve zvinogona dzinonakidza kuziva, kuongorora Chiitiko kuti symmetry? Masvomhu (Grade 6) rinotiudza kuti nhamba mbiri vanoonekwa nepakati, kwete hazvo kufanana nomumwe. Pfungwa vakaenzana chiri yakamanikana uye rakafara pfungwa. Saka, zvakafanana, ichibata zvinhu yakamanikana - kwete zvimwe chetezvo.

Ndeupi muenzaniso woupenyu kungaita kuti? Elemetarny! Unofungei pamusoro magiravhusi edu, Mittens? Tose inoshandiswa kudzipfeka, uye tinoziva kuti haugoni kurasikirwa, nekuti yechipiri muna vaviri hakusi tonotora, uye ipapo kutenga zvose zvakare. Uye nei? Nokuti aiwanzopiwa wokushanda zvigadzirwa, kunyange zvakafanana, ichibata, asi rakagadzirirwa kuruboshwe uye rworudyi. Ichi - chaiwo muenzaniso girazi symmetry. Panyaya vakaenzana, zvivako vakadaro vanoziva "girazi-vakaenzana."

Ko pakati?

Vaiona chakagadzirwa symmetry kutanga nokududza ehupfumi muviri, maringe izvo zvakafanira kuti vaongorore chinonakidza. Kuti vanouti zvakafanana, ichibata, pfungwa pakutanga vakasarudzwa, centrally iri. Next yasarudzwa pfungwa (ngatiendei kumutumidza A) uye kutsvaka vaviri (conventionally runotaurwa E) nokuti.

Pakusarudza symmetry pfungwa A uye E vari interconnected ne yakarurama mutsetse, rinonakidza pfungwa musimboti muviri. Next, uyere zvichiita mutsetse. Kana munhu mutsetse kubva nguva A kusvika nechepakati chinhu akaenzana penguva raiparadzanisa Nhongonya kubva pfungwa E, tinogona kutaura kuti pakati symmetry inowanikwa. The nechepakati symmetry mune masvomhu - mumwe anokosha pfungwa kuzobvumira mberi kutanga dzidziso geometry.

Uye kana iwe tenderera?

Kuongorora zviri symmetry mune masvomhu, mumwe anogona kurasikirwa pfungwa yokuti rotational subtype kuti chiitiko ichi. Kuti tinzwisise mashoko, achitora muviri ane nechepakati pfungwa, uye kutsanangura integer.

Munguva kuedza, muviri zvayaitenderera paguyo ne akafanorongerwa yorusvingo akaenzana mugumisiro kuparadzanise 360 madhigirii pamwero yakasanangurwa. Kuti aite izvi, unofanira kuziva zvinhu akabatana kuti symmetry (2 kirasi, masvomhu, chirongwa kuchikoro). akabatana ichi - mutsetse unobva mbiri pfungwa dzakasiyana. On kutenderera symmetry angati, kana panguva yasarudzwa kwekona pakati kutenderera muviri achava chete nzvimbo sezvo pamberi manipulations.

In Kana apo yepanyama nhamba 2 akasarudzwa, uye vawana Chiitiko pamusoro symmetry vanoti axial symmetry chinorondedzerwa masvomhu. Izvi manyorerwo dzinoverengeka nenhamba. Muenzaniso: netriangle.

About mienzaniso yakawanda

Tsika kwemakore akawanda kudzidzisa masvomhu uye geometry chesekondari kunoratidza kuti nyore nzira kunzwisisa Chiitiko pamusoro symmetry, achitsanangura paro mienzaniso yakananga.

Chokutanga, funga kukura. Nokuti muviri wakadaro panguva inozivikanwa nokuda Chiitiko pamusoro symmetry:

• centre;
• muchionioni;
• rotational.

Sezvo pfungwa huru kuti akasarudzwa, iri chaizvo pakati nhamba. Kuti atore ndege kunorondedzerwa hombe denderedzwa, uye airatidzika kuva "kucheka" kuva akaturikidzana. Ko yemasvomhu? Tenderera uye nechepakati symmetry kune bhora - pfungwa chokuita pamwe dhayamita nenhamba richava akabatana kuti chinonakidza.

Mumwe muenzaniso pachena - a tenderera cone. Nokuti ichi chimiro yokusafa axial symmetry. In masvomhu uye mavakirwo Fani iyi yakanga kwakapararira yokungotaura uye kushanda. Cherechedza: sezvo akabatana kuti Chiitiko mabasa ose cône akabatana.

Zvinoratidza aidzidza chinonakidza prism. Nhamba iyi ndiwo maitiro girazi symmetry. Ndege sarudza "kugurwa", noku nechigadziko nhamba kure navo panguva nenguva. Kusika geometric rairatidza, mapurani magadzirirwo (pamasvomhu symmetry kunokosha, kwete zvishoma pane sayenzi chaiwo uye rairatidza), yeukai inoshanda applicability uye richibatsira ari kuronga mutoro inobereka zvinhu specular migumisiro.

Uye kana kunakidza zvitarisiko?

Chii Tingaziva Mathematics (Grade 6)? Central symmetry hakusi chete ari nyore uye anonzwisisika chinhu, sezvinoita chibharuma. Hazvina chairwo, uye kunakidza uye dzakaoma zvitarisiko. Somuenzaniso, izvi ndizvo parallelogram. Nokuti vakadaro chinhu anova musimboti pfungwa imwe iyo akayambuka diagonal.

Asi kana isu funga isosceles trapezoid, ichava dimikira pamwe axial symmetry. Ziva chinogona kuva zvakadaro, kana iwe wasarudza zvakanaka akabatana. Muviri zvakafanana, ichibata noruremekedzo kuti mutsetse perpendicular pasi uye nepariri chaizvo pakati.

Symmetry mu masvomhu uye mavakirwo anofanira kufungawo nedhaimani. Nhamba iyi zvinoshamisa kuti panguva rinobatanidza marudzi maviri symmetry:

• centerline;
• nechepakati.

Sezvo akabatana ari diagonal vanofanira kusarudza chinhu. Panguva apo diagonals ane rhombus piringisha, ndiwo muzinda symmetry.

About runako uye symmetry

Wezvamatongerwe masvomhu chirongwa, iro symmetry izvo yaizova inokosha nyaya, kazhinji pakutanga yeuka vachenjeri mashoko musayendisiti mukuru Weil: ". Symmetry - imwe pfungwa iyo kwemazana emakore kuedza kunzwisisa vanhuwo murume, nekuti akanga iye uyo pave runako rwakakwana kuburikidza rakasiyana murayiro"

Sezvaunoziva, vamwe zvinhu zvinoita kuti yakaisvonaka, apo vamwe vasundire kure, kunyange kana vasina zvikanganiso pachena. Nei izvi zvichiitika? Mhinduro yomubvunzo uyu unoratidza ukama mapurani uye wemasvomhu mu symmetry, nokuti chiitiko ichi uye inova hwaro tinyatsonzwisisa nenyaya sezvo nemachira anoyevedza.

Mumwe wevakadzi yakaisvonaka panyika - ndiro supermodel Brushes Tarlikton. Iye chokwadi kuti kubudirira wakauya pakutanga panzvimbo nemhaka rakasiyana chakajairika: miromo yake vari zvakafanana, ichibata.

Sezvo chikazozikamwa, hunhu uye kunoita kuti symmetry, uye haigoni kusvika pairi. Haisi Kazhinji, asi tarira vanhu vakavapoteredza: mu zviso zvevanhu zvinenge kuwana Mhedziso symmetry, kunyange zviri pachena chido nokuti. The zvakawanda zvakafanana, ichibata chiso interlocutor, saka izvozvo anotarisa nani.

Sei pfungwa symmetry rakaisvonaka

Zvinoshamisa kuti pamusoro symmetry yevanhu maonero kworunako yakavakirwa nemakapoteredza uye zvinhu mairi. Kwemazana emakore akawanda, vanhu vanowanzofunga kunzwisisa chii sokuti akakwana, uye anomhanyira asingasaruri.

The symmetry, zvikuru - ndizvo zvinobatsira nemaziso kunzwisisa chinhu uye kuongorora nayo chokwadi. zvinhu zvose, nhengo vanofanira kuva pakati nepakati uye mukati zvine kukura pamwe nemumwe. Kwenguva yakareba zvave kuwanikwa kuti asymmetric zvinhu zvakafanana vanhu ndoda. izvi zvose rwakabatana pfungwa "maererano". About nei zvichikosha kuti munhu ane yekare refu kushamisika vakachenjera, vemifananidzo.

Zvinofanira kutarisa geometric nemifananidzo, uye Chiitiko kuti symmetry zvichava pachena uye nyore kunzwisisa. Chinonyanya chairwo zvakafanana, ichibata mananara munzvimbo dzakapoteredza:

• matombo;
• maruva uye mapenga zvinomera;
• aiwanzopiwa wokushanda dzokunze nhengo pakuona zvipenyu.

The zvinorondedzerwa zviitiko ndiwo anokonzera mamiriro. Uye pano ndizvo unogona kuona symmetric, akatarira pedyo zvibereko maoko evanhu? Zviri kuoneka kuti vanhu gravitate kuti kusikwa chete kana kuedza kuti chinhu chakanaka kana dzichipfekeka (kana vose ndiro, uye panguva imwecheteyo):

• mapatani nezvishongo, yakakurumbira kubva kare;
• chivakwa zvinhu;
• kuvaka zvinhu ndiwe;
• romuruki.

About mazwi

"Symmetry" - Shoko rakasvika mumutauro wedu kubva vaGiriki vekare uyo akatanga kushanda ichi chinonakidza kutarisirwa uye edza kuti kuongorora izvozvo. Izwi rinoratidza kuvapo nehurongwa uye rinopindirana mubatanidzwa zvikamu chinhu. Translation shoko "symmetry", unogona kunhonga sezvo anoreva zvakafanana:

• proportionality;
• sameness;
• proportionality.

Sezvo dzekare symmetry inokosha yokuti nokuda kukura vanhu muminda siyana uye maindasitiri. Peoples kubva kare kuti zvakakurumbira kunzwisisa Fani iyi, kunyanya kufunga nayo broadly. Symmetry raimirira Kuwirirana. Munguva yedu, kuti mazwi inodzidziswa zvavo kuzvikoro. Somuenzaniso, chii akabatana kuti symmetry (2 kirasi masvomhu) vana mudzidzisi hurukuro kwakajairika kirasi.

Sezvo pfungwa Fani iyi kazhinji chipikirwa kwokutanga hypotheses yesayenzi uye zvokufungidzira. Kunyanya yakakurumbira waiva yapfuura remakore, apo pasi rose vakatonga pfungwa kwemasvomhu kuwirirana kuri pakati chaipo ezvinhu zvakasikwa. Connoisseurs kakawanda iwayo nechokwadi kuti symmetry chinoratidza maererano naMwari. Asi muGirisi yekare, vazivi kwakauraya kuti yose nechadenga zvakafanana, ichibata, uye zviri zvose inobva uchapupu: ". The symmetry vakakwana"

VaGiriki Great uye symmetry

Symmetry airamba pfungwa yakakurumbira nyanzvi Greece yekare. To dzakararama kunoratidza kuti Plato akadana vakaparadzana rinoyemurwa dzose polyhedra. In zvaanofunga, nhamba dzakadaro - mumwe muenzaniso zvinhu edu nyika. Ikoko zvinotevera kupatsanura:

eremendi	maumbirwo
moto	Tetrahedron, sezvo porusvingo zvinangwa ake skyward.
mvura	Icosahedron. Choice imhaka "katuchestyu" nhamba.
mhepo	Octahedron.
pasi	Akatsiga zvikuru chinhu, kuti ndiye kuutio.
muchadenga	Dodecahedron.

Kunyanya nokuti dzidziso iyi inowanzodeedzwa dzose polyhedra Platonic nezvishoma.

Asi mazwi akasuma kwokutanga, uye hakuna yokupedzisira basa reDare nomuvezi Polycleitus.

Achibvuma pfungwa yaPythagoras uye symmetry

Panguva upenyu Achibvuma pfungwa yaPythagoras uye gare gare, apo kudzidzisa kwake kwakanga kuchiita ichatonga zvine mbiri yayo, mashoko Chiitiko kuti symmetry vakatadza ape zvakajeka. Zvakanga ipapo pasi nesayenzi Kuongorora symmetry, akapa kukosha kushandiswa chaikwo nemigumisiro.

Maererano mhedziso:

• Symmetry inobva Dzidziso zvinoenderana, zvakafanana uye kuenzana. Kana kutyora vanzwisise anova zvishoma zvakafanana, ichibata mufananidzo, zvishoma nezvishoma kutamira kune zvakazara asymmetric.
• Kune 10 yegwara wokushora. Maererano nedzidziso, kuti symmetry iri kutanga iyo kunoderedza iri pakatarisana yunifomu uye pakudaro achiumba zvakasikwa yose. Izvi uchapupu emakore aiva simba rokuchinja dzinoverengeka sayenzi chaiyo uyewo uzivi, uyewo dzinongoitika.

Achibvuma pfungwa yaPythagoras nevateveri vake vakanga with "zvachose zvakafanana, ichibata muviri," iyo semunhu kugutsa ezvinhu:

• mumwe chiso - polygon;
• kunobatanidza anowanikwa pamakona;
• Nhamba vanofanira vakaenzana mativi uye pamakona.

Yaiva Achibvuma pfungwa yaPythagoras wokutanga kutaura kuti miviri avo pane shanu chete. Izvi zvakawanikwa kukuru kwakaratidza kutanga geometry uye kunokosha kuti mapurani ano.

Uye uchida kupupurira kwazvo yakanaka chakajairika kuti symmetry? Mha snowflake muchando. Strange asi zvechokwadi - ndiko dukuduku piece chando kudonha kubva kudenga haasi chete zvikuru kunzwisisa sekristaro mamiriro, asiwo zvakakwana zvakafanana, ichibata. izvozvo nyatsocherechedza: snowflake zvechokwadi wakanaka, uye ayo vepamusorosoro yevanoda ruchiri kukangaidza.