He aha ka pilina o ka makemakika? Nā wehewehe a me nā hi'ohi'ona

Maopopo mea symmetry ma ka makemakika, ia mea pono e hoʻomau e aʻo i ka hoʻokumu a me ka holomua kumuhana apau loa o ka hōʻailona helu, anahonua. He nui no ka naauao o ka mea kakau, kuhikuhipuʻuone, rula o ke kūkulu nō. I loko nō o ka pili pilina me ka loa kiko'ī 'epekema - makemakika, symmetry mea nui no nā mea hana keaka, Artists, kanaka haku, a no ka poe i komo ma ka noiʻi hana, a ma kekahi kahua.

kekahi mau 'ike

'Aʻole wale nō makemakika, akā, i ka sciences maoli e pili kēia ma muli o ka manaʻo o ka symmetry. Eia hoʻi, ka mea, ua loaʻa i loko o maʻamau o ke ola, ka mea, o kekahi o na kumu oʻano o ko mākou ke ao holoʻokoʻa. He aha ka symmetry ma makemakika ke kālailai, ia mea pono i ka hōʻike i loaʻa i kekahi mauʻano o kēia kŰia. E kamailio e pili ana i kēia mau koho:

• ʻeluaʻaoʻao, i mea, e like me aniani symmetry. O kŰia i loko o ka 'epekema' ia, mau kapa "ʻeluaʻaoʻao".
• Al-Loipālākiō manawa. No kēia manaʻo ki kŰia - he kuapo makau pōpilikia mahele o ka 360 degere ma ka hoʻoholo ma mua waiwai. Eia hou kekahi, mālama '-i ho'ākāka' (axis) e pili ana i ke kuapo ia lŘlŘ.
• Padialnaya ka wā symmetry kŰia malama ina hana ana huli ma kekahi huikau ka lua huina. Axis ua i koho ma ka kūʻokoʻa ano. E wehewehe i kēia kŰia pili ¶ I pae (2).
• Spherical. Ma keia hihia mākou e kamailio ana ekolu Ana, ma a ka mea ua ke ka ao ka, koho ākeʻakeʻa kumu pana pua. Līkaia no kekahi hihia o ka isotropic, i ka wa a ka kŰia lilo he kūloko nona 'ia a me ka lewa.
• Rotational, hoʻohuiʻia ka mau hōʻike mua pūʻulu.
• Lorentz invariativnaya ka wā ma laila e ākeʻakeʻa kumu kuapo. No kēiaʻano o ka symmetry o ke ki manaʻo i "Minkowski wa-manawa."
• Super, hoakakaia ma ka hope o bosons, fermions.
• Higher hōʻike 'i pae Ka Ikepili.
• Ke'opi, i ka wa e haule ana na loli o ka lewa, no ka aʻepekema kuhikuhi i ke ala e hiki aku, mamao. Ma ke kumu o kaʻikepili loaa e hoʻomaka i kekahi mau Ikepili i hōʻike symmetry.
• Ana mālama i loko o ka hihia o ka moʻokūʻikena pähola 'o ke Kuokoa i loko o ka AYEIE loli'. Eia, ua uku a hiki i ka pähola 'ana o nā mahinaʻai kūikawā noonoo, a me ka pulakaumaka ma ka Yang-Mills manaʻo.
• Kaina, no a hiki i ka papa o ka huina'ine kŰia ke kau. I mea e like me ka symmetry, makemakika (Papa 6) mai aole lakou i ike, no ka mea, o ka 'epekema o ka lani kiekie loa kauoha. Ke kŰia ua kauoha ae la ia e ka haumāna alapine (frequency). Ua Ua ike i ka noiʻi E. Biron. Terminology C. Shchukarev hoʻolauna.

aniani

Oiai këia ma nā haumāna kula e kokoke mau noi, e hana i ka hana "Symmetry a puni mākou" (makemakika papahana). E like me ka rula, ka mea, ua? Aeiiaiaoaony e lawe mai i loko o ka ono o ka papa maʻamau kula me ka mau polokalamu o ke ao makaainana. E Makuakane me ka papahana, e pono mua i kama'āina i ka manaʻo o ka symmetry, i ka nui, ka mea he aniani ano me kekahi o ka hoʻokumu paʻa, a me ka hapanui keiki kao-aloha i ka hōʻike.

E kuhikuhi i na kumu o ka symmetry, noonoo iho la kekahi geometric kinona, a me ka pelane, ua koho. I ka kanaka olelo e pili ana i ka symmetry o ka mea? Mua, ka mea, ua koho 'o ka wahi, a laila, ua lewa ia ia. Ma waena o ka mau o ia ke lilo aku Hoʻohana a omaulia ana i ka huina ma i ka i koho pelane mea hala ae.

Ke kālailai ka mea symmetry ma ka makemakika, e hoomanao i waeia no ka ka loaʻaʻana o kēia kŰia e e haawiia i ka pelane o ka symmetry pelane, a me ka mea e ae. E paa ana ia Hoʻohana pono intersect mea i pono pana pua. Ka loihi mai ka wahi a hiki i keia pelane, a mai kaʻoi a hiki i ka lua o ka Hoʻohana e e like.

nuances

He aha hou aʻe hiki e hana hoihoi i ka ike, ina hookolokolo ke kŰia o ka symmetry? Makemakika (Papa 6) hai mai ai i nā kiʻiʻelua i manaoia 'O ke kaulike,ʻaʻole pono'ālike i kekahi i kekahi. I ka manaʻo o ka like ole ma ka puali ololi a me ka pālahalaha ano. No laila, symmetrical ukana ma ka puali ololi - i ka mea hookahi.

He aha mea he laʻana o ke ola ke alakai i ka? Elemetarny! He aha e kou manaʻo e pili ana i kā mākou Loan, mittens? Mākou nō a pau hoʻohana 'e komo ai lakou, a ua ike i ka hiki ole oe lilo, no ka mea, o ka lua o kekahi i loko o ka mau mea,ʻaʻole eʻohi mai, a laila, i ke kuai i elua hou. A me ke aha? No ka mea, o ka hui kaulua huahana, eia nae symmetrical, akā papahana no ka haʻalele a me ka lima'ākau. Kēia mea - he typical mamuli o ke aniani symmetry. Me ka pili ana i ka hoʻokolokolo pono, e like iauaeoia ike i ka "aniani-kaulike."

A me ka mea e pili ana i ka waena?

Noonoo kikowaena symmetry hoʻomaka ma ka wā o ka waiwai o ke kino, ma ka hoahanau i ka a ia mea e pono ke loiloi i ke kŰia. I mea e kapa ia he symmetrical, he wahi i koho mua, manaʻo nui ke aupuni '. Next wae wahi (e ka kapa ia A) a me ka imi ana i ka hui (conventionally denoted E) no ka mea.

Ma ka hoomaopopo ana i ka symmetry o na kumu i A a me ka E i interconnected ma ka pololei o ka laina, me ka pīhoihoi wahi o ke kikowaena kino. Next, e ana i ke kūpono laina. Inā kekahi laina mai ka wahi A hiki i ka waenakonu o ka mea, ua like me ka wā mawaena hookaawale ana i ka piko, mai ka wahi E, ua hiki ke olelo aku i ua loaʻa ai ka waenakonu o ka symmetry. Ke kikowaena symmetry ma ka makemakika - kekahi o na ki manaÿo e ae e hou möhala i ka kumumanaʻo o ka anahonua.

A ina oe ka ao ka?

He aha ka symmetry ma makemakika ke kālailai, i kekahi ke ole e hala i ka noonoo ana o ka manaʻo o rotational subtype o keia kŰia. I mea e maopopo i nā hua'ōlelo, e lawe i ke kino me he kikowaena wahi, a hoakaka helu.

Iloko o ka hoʻokolohua, i ke kino ua ke ka ao ma ka hoʻoholo ma mua huina like i ka hopena o ka mahele 360 degere ma ka wae ana. E hana i kēia, e pono i ka mea o ka iho (axis) o symmetry (2 papa, makemakika, ke kula polokalamu). Kēia (axis) - ka laina e ka mea koho i hōkeo 'nui elua. Ma kuapo symmetry hiki olelo, ina ma ka mea i koho huina o kuapo o ke kino, e ia i loko o ka ia kulana like ma mua o ka manipulations.

Ma ka hihia ma ka helu maoli 2 Ua wae mai ai, a loaa i ka kŰia o ka symmetry e olelo aku i iho symmetry ua ho'ākāka 'ia ma ka makemakika. He ano o ka helu o nā huahelu. A typical laʻana: he triangle.

About na examples hou

I ka hana ana o na makahiki o ke ao ana makemakika a me ka anahonua i loko o ke kula kiʻekiʻe hōʻike i ka easiest ala e maopopo i ka kŰia o symmetry, wehewehe ia me kekahi examples.

Mua, noonoo i ka laulā. No ka mea, he kino i ka mea ia manawa wehewehe aku ma ka kŰia o ka symmetry:

• kikowaena;
• aniani;
• rotational.

E like me ka papa kuhikuhiE wahi e e wae, Aia e like ma ka waena huahelu. Eʻohi i ka pelane ho'ākāka 'ia e kekahi hoa kanaka nui, a me ka ua ia e "oki" ia i loko o papa. He aha ke ano o ka makemakika? Ka ao ka a kikowaena symmetry i loko o ka hihia o ka poepoe - manaÿo e pili pū ana me ke anawaena o na huahelu, e malama i ka iho (axis) no ka kŰia.

Kekahi ahuwale hoʻohālike - he hoʻopoepoeʻohana. No keia shape hoʻomaopop 'ana i iho symmetry. I ka makemakika a me ka kuhikuhipuʻuone o keia kŰia ua lahaʻimi naʻauao a me ka pili ana. 'Ōlelo Aʻo: e like me ka iho (axis) no ka kŰia o hana i koe o kaʻohana iho (axis).

Ua hōʻike aʻo kŰia prism. Kēia huahelu He ano aniani symmetry. Pelane koho "kua", ia laua i ka waihona ipu huahelu, loihi mai ia i mauʻanuʻu. E pili ana geometric, ho'ākāka, kuhikuhipuʻuone manao (makemakika symmetry mea nui,ʻaʻole emi ma mua o kūlike loa a me ka ho'ākāka sciences), e malama i ka manao o ka mea hiki applicability a me ka waiwai i loko o ka hoʻolālā haawe-kona hanau ana o ka oihana mua specular loa.

A ina oi hana hoihoi 'ano?

He aha mākou ke haʻi aku Balanced (Papa 6)? Central symmetry mea,ʻaʻole wale nō i loko o ka noʻonoʻo a me ka maopopo e hoopii mai ai, e like me ka hoʻonui. He pono'ī nona, a me ka oi hana hoihoi a me ka luna 'kinona. No ka laʻana, keia mea i ka parallelogram. No ka mea, o kekahi mea, ke kikowaena wahi o ka kekahi ma i kela aoao diagonal.

Akā, inā i ka isosceles trapezoid mākou noonoo, ka mea, e lilo ia i aka me ka iho symmetry. E kuhikuhi i ka mea hiki ia ia ma ia hihia, ina e koho i ka iho (axis) akau. Ke kino Ua symmetrical me ka pili ana i ka laina p ÷ haku i ka honua, a hele ma ka mea pono i loko o ka waena.

Symmetry i ka makemakika a me ka kuhikuhipuʻuone pono lawe i loko no o ka daimana. Keia aka mea kupaianaha i ka poʻe hiehie mau ke ano o na symmetry:

• centerline;
• Central.

E like me ka iho (axis) o ka diagonal pono koho i ka mea. Ma ka wahi, kahi a na diagonals o ka rhombus intersect, ia mea he konu o ka symmetry.

About nani a me ka symmetry

Ho okumu i ka makemakika papahana, ke symmetry o ka i makemake e he kī kumuhana, i hookuu i loko o ka wahi mua e hoomanao i ka olelo akamai a o ka nui nä känaka 'epekema Weil: ". Symmetry - ka manao a no ka kenekulia imi e maopopo i ke kanaka, he pono, no ka mea, ua iho la ka mea hana i ka nani i hemolele ma o ka hanana mea"

E like me oe i ike, he 'ē aʻe mea e e nani loa, oiai kekahi poe lele aku, a hiki ina ka mea, e ole i ahuwale flaws. No ke aha la i keia ahaʻia nei? Ke pane i keia ninau hōʻike i ka pilina o ka kuhikuhipuʻuone a me ka makemakika ma ka symmetry, no ka mea, o keia kŰia, a lilo ae la ia i ke kumu no ka auhau ana i na kumuhana like aesthetically uʻi.

Kekahi o nā wāhine loa maikai ma ka Honua - ka mea, 'o ka supermodel Brushes Tarlikton. Heʻoiaʻiʻo e ua hiki mai i ka pomaikai ma ka mua wahi i ke aloha i kekahi hanana kŰia: kona mau lehelehe i symmetrical.

E like me uaʻike, i ke ano a me ka mālama i ka symmetry, a ua hiki ole hiki ia. Ia mea i ka mau rula, akā, e nānā i na kanaka a puni ia: i kanaka maka aneane e loaʻa nā aliʻi e kāpae symmetry, naʻe ka mea, Ua ike no ka makemake no ka mea. Ka oi symmetrical maka o ka interlocutor, no laila, e nana maikaʻi.

Pehea i ka manaʻo o ka symmetry o ka nani

Ka mea, Ua kahaha ko oukou naau i ma ka symmetry o na kanaka pokole o ka maikai, me ka nānā 'kona nā wahi a me nā mea i loko o laila. No ka nui kenekulia, kanaka lawelawe ka mea pono e maopopo, a me ka mea pushes ka ewaewa ole.

Ke symmetry, huliāmahi - i ka mea kōkua i visually ike i ka mea a me ka Loiloi i mea ikaika. All kumu mua, hapa e e 'O ke kaulike, a loko o ke kupono huliāmahi i kekahi i kekahi. Ua Ua lōʻihi ua ike ia asymmetric mea e like kanaka he nui emi. A pau keia ua ua hoʻopili i ka manaʻo o ka "lokahi". About ke kumu ia mea no laila, nui no kekahi kanaka me ka kahiko lōʻihi Puzzle sages, Artists.

Ka mea, e nana i ka geometric huahelu, a me ka kŰia o symmetry e e ahuwale a me ka oluolu, e ike. Ka loa typical symmetricalʻike manaʻo i loko o ka puni:

• pohaku;
• pua a me na lau o na mea kanu;
• hui kaulua mawaho nā loko hoʻomaopop 'ana i ka noho ana meaola.

Ka mea i ho'ākāka 'iaʻike manaʻo i ke kumu o ke ano. A eia ka mea e hiki keʻike symmetric, e nana ana kokoke i nā huahana o kanaka lima? Ua mea kekahi 'i kanaka gravitate ai i ka haku o ka pono kekahi inā ho'āʻo e e kekahi mea maikaʻi' ole iaea ooieoeiiaeuiiai (a me nā mea, a me ka mea ma ka ia manawa):

• lauana a me nā mea e nani ai, mahalo mai ka wā kahiko;
• hana oihana mua;
• ? ieoaeunoai hehee wale nōʻoe;
• humuhumu lopiʻano'ē.

About terminology

"Symmetry" - i ka olelo i hele mai i loko o kā mākou 'ōlelo, mai ka wa kahiko Helene i mua pili i keia kŰia noonoo, a ho'āʻo i ka makaikai ia. Ka manawa Hōʻike i ke alo o ke ano a me ka harmonious me ka hui pu ana o māhele o ke kiʻi. Unuhina o ka hua'ōlelo "symmetry", e hiki ke lawe ia i like synonyms:

• proportionality;
• sameness;
• proportionality.

Mai ka wā kahiko i ka symmetry mea nui ka manaʻo no ka hooulu ana o ke kanaka i loko o nā kula a me na hana. Kanaka, mai kahiko e i hoʻomaopopo like 'ana o kēia kŰia,ʻano nui e noonoo pono ia broadly. Symmetry ku iho la no ka lokahi a me ke koena. I ko kakou manawa, i ka terminology ua aʻo aku i loko o maʻamau kula. No ka laʻana, aha mea i ka iho (axis) o symmetry (2 papa makemakika) keiki kumu kūkaʻi'ōleloʻana i kaʻike mau papa.

E like me ka manaʻo o kēia kŰia pinepine i ka loiloi mua i hai mua ia o ka 'epekema hypotheses a me theories. No hanohano i loko o ka mua kenekulia, ka wā a pau ma luna o ka honua Kīwala'ō i ka manaʻo o ka makemakika lokahi hoʻomaopop 'ana i loko o ka loa'ōnaehana o ka ke ao holoʻokoʻa. Connoisseurs o ka manawa i hoomaopopoia ia symmetry mea he kīnā o ke kilokilo lokahi. Akā, ma ke kahiko Greece, ua koi poe akeakamai i ka ke ao holoʻokoʻa holoʻokoʻa mea symmetrical, a he hana a pau ma muli o ka postulate: ", ka symmetry Ua hemolele"

Great poe Helene a me ka symmetry

Symmetry kī i ka naau o na haumana loa kaulana o ka wa kahiko Greece. E ua ola ka hōʻike i Plato kapaia kaawale mahalo mau polyhedra. I kona manao, e like me na kii - he e ka kumu o ko mākou honua. Aia ke kēia Mea Maluna:

hehee ai	huahelu
ke ahi	Tetrahedron, e like me ka oioi o kona mau AIM skyward.
ka wai	Icosahedron. Choice mea ku pono i ka "katuchestyu" huahelu.
ea	Octahedron.
honua	I ka loa i ka pilina paʻa mea, i mea ke kupa.
ke ao holoʻokoʻa	Dodecahedron.

Pili kēia no ka mea, o keia kumumanaʻo ua ana kapaia regular polyhedra Platonic puaʻa hiwa.

Akā, i ka terminology hoʻolauna mua, a he mea ole ka mea hope a Mānoa hoʻokani ma ka sculptor Polycleitus.

Pythagoras a symmetry

Ma ke ola o Pythagoras, a ma hope, i ka wa o kona ao ana iʻike piʻi kona heyday, ka kŰia o ka symmetry ole e hoopuka maopopo. Ua Ua laila, malalo i ka 'epekema Ka Ikepili o ka symmetry, i haawi nui i ka pili ana o ka hopena.

E like me ka hopena:

• Symmetry ua nānā 'ana ma luna o ka manaÿo o ka like ana, uniformity a me ka like. I Ina o ka 'aʻe' ana i ka manaʻo i emi symmetrical huahelu, ke kiʻekiʻe o neʻe maila i ka oo asymmetric.
• Aia he 10 hui o kū'ē. E like me nā kānāwai, ka symmetry mea he kŰia i ho'ēmi i kā ma ke ku pono ana iʻaʻahu, a ma ia ho okumu i ka ke ao holoʻokoʻa me ka a pau. Kēia postulate no ka kenekulia i ka ikaika ma luna o ka helu o kiko'ī sciences like hoʻi me kālaiʻike, e like me maoli.

Pythagoras a me kona mau ukali i kaʻawale "loa symmetrical kino," i ke koko, e like me satisfying na ana:

• kēlā me kēia maka - iieeaii;
• facets i loaʻa i loko o nā kihi;
• huahelu E i like aoao a me ka pana pua.

Ka mea, ua Pythagoras ka mea mua, e olelo aku i ka poe kino, aia no elime wale. He He loaʻa nui ia i ka hoʻomaka o ka anahonua, a he mea nui ia no ke kālā no kuhikuhipuʻuone.

A me 'oe makemake eʻike maka i ka loa nani kŰia o ka symmetry? Hopu i kekahi snowflake hooilo. Malihini akā, oiaio - ia mea he wahi apana o ka hau e haule ana mai ka lani ua ole wale loa eiiieaen aniani 'ole, akā, i pono symmetrical. E hoomanao i ka mea pono: snowflake mea maoli nani, a me kona Ka Uluwehi O Ke laina manawa.