Tau Student me te ōwehenga koura: te hononga

I roto i te ao e tonu maha mea ngaro kāore, etahi o nei kua taea ki te tautuhi me te whakaahua pūtaiao. Student tau me te ōwehenga koura ko te pūtake o tīwhiri o te ao, te hanga o tona āhua me te tino arotau perception ataata tangata, ki e taea e ia ite i te ataahua me te au maite.

Wāhanga Golden

Ko te parau tumu o te rahi wāhanga koura ko te pūtake o te tino o te ao katoa, me ona wahi i roto i ona hanganga me te mahi, ka taea te kite i tona faaiteraa i roto i te āhua, toi me te hangarau. Kua te parau haapiiraa o te ōwehenga koura kua whakaurua rite ki te hua o te rangahau o te mau haapiiraa tahito o tau āhua.

Kei te hāngai te reira i runga i te ariā o hanganga me ngā ōwehenga o roa o wehenga i i meatia ki te philosopho tawhito, me te mathematician Pythagoras. whakamatauria e ia e te wehenga o te wāhanga ki e rua nga wahi: ko te X (iti) ko Y (nui), he rite ki te ōwehenga o te moni (te roa tapeke) te ōwehenga o nui ki te iti:

X: Y = Y: X + Y.

Ko te hua ko te whārite: x ² - x - 1 = 0, faatiti'aifarohia nei te rite x = (1 ± √5) / 2.

Ki te titiro tatou ki te ōwehenga o te 1 / x, na ko reira rite ki te 1.618 ...

E hoatu Taunakitanga o te whakamahi o te whakaaro tawhito o te ōwehenga koura i roto i te pukapuka o te Euclid "Elements", rite wawe rite 3 i tuhituhia. BC, i tono tenei ture ki te hanga i te tika 5-gon. Nga Pythagoreans, whakaaro tenei ahua te tapu no te mea he reira e rua hangarite, me te asymmetrical. Pentagram tohu ora me te hauora.

tau Student

whakaputaina te pukapuka Free abaci mathematician rongonui Leonardo Pizanskogo i Itari, i muri mai ka mohiotia rite Student, i roto i 1202. I roto i reira te tauira mata tuatahi pūtaiao o tau i roto i nei ia tau ko te moni o te maha o te 2 tau o mua. Student raupapa ko e whai ake:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, me ētahi atu

Hoki, kua arahina te kaipūtaiao, he maha o ture:

• Tetahi maha o nga rarangi wehea e te muri, ka waiho rite ki te uara i whangai ana ki te 0.618. A e kore e hoatu e te tau Student tuatahi he maha taua, engari rite i mua ia koutou i te timatanga o te raupapa, ka waiho atu pau te ōwehenga.
• Ki te wehe tatou te maha o ngā rārangi i runga i te tetahi o mua, na ka rere te hua ki te 1.618.
• Kotahi tau wehea e te tetahi i muri, ka whakaatu i te uara e whangai ana ki te 0,382.

Ka taea te kitea te whakamahi o te kōrero, me ngā tauira o te wāhanga koura, tau Student (0.618) kore anake i roto i te pāngarau, engari ano hoki i roto i te natura, hītori, hoahoanga me te hanganga, me te tokomaha atu pūtaiao.

tōrino Archimedean me te tapawhā koura

He tino noa koropetau i te natura, kua whakawakia reira e Archimedes, e ara arahina tona whārite. hāngai āhua Koru te i runga i nga ture o te wāhanga koura. I roto i tona roa taui i te whiwhi, e taea te tono, me te hanganga o ngā tau Student, puta te hua taahiraa kaupae.

Whakarara i waenganui i nga tau Student me te wāhanga koura, ka taea e kite koe, ka hanga i te "tapawhā koura", he hautanga rite 1.618 nei taha: 1. Kei te hangaia te reira, haere i iti ki te tapawhā nui kia ka rite ki nga tau o te raupapa i te roa o te taha. Ka taea te mahi te hanga i roto i te raupapa whakamuri, tīmata ki te tapawha "1". A, no te tūhono ngā rārangi, i whiwhi ai koki o te tapawhā i te pokapū o te whakawhitinga Student tōrino pākoki ranei.

Ko te hītori o te whakamahi o hanganga koura

i hanga tokomaha urupa hoahoanga Ihipa tahito whakamahi hanganga koura: ispolzoval rongonui Great Tara etc. Architects Ancient Greece ratou whānui i roto i te hanga o ngā hoahoanga, pērā i te mau hiero, te whare matakitaki, etu .. Hei tauira, kua oti taua hanganga whakamahia i roto i te hanga o te Parthenon tahito, whare tapere Dionysos (Atene), me ētahi atu taonga e riro faahiahia hoahoanga tawhito, whakaatu au maite, e hāngai ana i runga i te auautanga pāngarau.

I roto i ngā rau tau i muri mai, te moni i roto i te wāhanga koura mariri, a kua oti ture wareware, engari anō ano i roto i te Renaissance ki te pukapuka Franciscan moke L. Pacioli Di Borgo "ōwehenga Atua" (1509). Ngaahi tā fakatātā reira e Leonardo da Vinci kua kawea mai, me i noaa te ingoa hou o "wāhanga koura". He Kua hoki kua pūtaiao kï 12 ngā āhuatanga o te ōwehenga koura, korero te kaituhi e pā ana ki te pehea faaite te reira iho i roto i te natura, i roto i te toi me te huaina a reira "te parau tumu o te paturaa i te rongo, me te āhua."

a Leonardo Vitruvian te tangata

Figure e Leonardo da Vinci i 1492 whakaahua te pukapuka o Vitruvius, whakaatu ana te reira i te ahua tangata i roto i te 2-tūranga ki ringa whakarerea i roto i nga taha. Ko te ahua tuhituhi i roto i te porohita me te tapawha. whakaaro ana tēnei ahua te ki hei te hanganga kēnana o te tinana tangata (tane), whakaahuatia e Leonardo i te pūtake o to ratou ako i roto i te tuhinga whakapae o te kaihoahoa Roma Vitruvius.

tinana hub rite te wāhi equidistant i te pito o te ringa me waewae puku whakaaro, ringa roa rite ki te teitei o te tangata, pokohiwi mōrahi whanui = 1/8 teitei, te tawhiti i te tihi o te pouaka ki te huruhuru = 1/7, i te pouaka ki te tihi o te matenga runga = 1/6 etc.

Mai reira, whakamahia te pikitia kei te rite te tohu, e whakaatu ana i te te hangarite ā o te tinana tangata.

Ko te wā "Wāhanga Golden" Leonardo whakamahia ki te whakaahua i ngā hononga hautanga i roto i te ahua tangata. Hei tauira, te tawhiti i te hope ki te waewae o waewae hāngai ki te tawhiti taua i te pito ki te tihi te tupu o te roa tuatahi (i te hope ki raro) me te. E meatia enei tātaitanga i roto i te taua ōwehenga o te wāhanga i roto i te tātaitanga o te ōwehenga koura, me te whangai ana ki te 1,618.

Kei te maha enei hanganga pai katoa whakamahia toi ki te hanga mahi ataahua, me te mīharo te.

rangahau wāhanga koura i roto i 16-19 senituli

Mā te whakamahi i te ōwehenga koura me tau Student, te mahi rangahau i runga i nga hanganga tonu hoki mau tenetere. I roto i te whakarara ki te Leonardo da Vinci artist Tiamana Albrecht Dürer i whai wāhi i roto i te whanaketanga o te ariā o te hanganga tika o te tinana tangata ano hoki ia. Hoki tenei, ara i hanga e ratou kāpehu motuhake.

I roto i te rau tau 16. i oti rawa ki te mahi o te arorangi Kepler, e tono tuatahi enei ture ki te huaota i runga i te hononga o ngā tau Student me te wāhanga koura.

New "kitea" tūmanakohia i roto i te wāhanga koura 19. ki te whakaputanga o "Rerehua Studies" pūtaiao German Professor Tseyziga. whakaarahia e ia te rahi ki te tino ka kauwhautia e he ao mō ngā taiao katoa ratou. i ako ratou tokomaha nui o te iwi, ranei, kaua ratou hanganga tinana (e pā ana ki 2 mano.), I nei te whakatau o nga hua o nga regularities tatauranga whakapumautia i roto i te hanganga o ngā wāhanga rerekē tinana: roa ringa, ringa, ringa, maihao, me ētahi atu

hoki ahanoa toi (ipu, hanganga hoahoanga), i te uiui e pepe waiata, te āhuatanga i roto i te tuhituhi o ngā rotarota - katoa kua whakaaturia Tseyzig roto te roa o nga raina me whika, tapa ano ia te wā "rerehua pāngarau." I muri i te fariiraa i te hua whakakitea e whiwhi i te raupapa Student te.

tau Student me te wāhanga koura i roto i te natura

I roto i te ao huawhenua me te kararehe, i reira te mea he au ki auaha i roto i te puka o te hangarite, kitea nei i roto i te ahunga o te tupu, me te kaupapa. Ko te wehenga ki nga wahi hangarite, i haapa'o ki te wähanga koura - he he tauira noa ki maha tipu me ngā kararehe.

Nature a tawhio noa tatou kia whakaahuatia e te tau Student, hei tauira:

• wāhi o tetahi manga rau o ngā tipu ranei, me te te tawhiti hāngai ki te maha o ngā tau i homai 1, 1, 2, 3, 5, 8, 13, me te atu;
• purapura putirā (i runga i te tihi tauine, paināporo pūtau), e takoto ana e rua rarangi o koropetau miro i roto i ngā tohutohu rerekē i roto i;
• te ōwehenga o te roa o te hiku, me te tinana mokomoko;
• hua āhua, ki te iri i te aho puta noa i te wahi whanui o taua mea;
• te āhuatanga ōwehenga o te maihao i runga i te ringa tangata.

A, o te akoranga, te puka tino ngā he koropetau ngata tauira anga i runga i te tukutuku, te kaupapa o te hau i roto i te mata'i rorofa'i, te rua hanganga helix DNA, me ikarangi - ngā katoa o ratou te raupapa Student.

Mā te whakamahi i te wāhanga koura i roto i toi

Kairangahau whai wāhi i roto i te toi o te kimi tauira o te whakamahinga o te wāhanga koura, taipitopito tūhura rerekē ngā hoahoanga me mahi o te toi. Mohiotia hoki nga whakairo rongonui, nga kaihanga o e piri ki te hanganga koura, - te whakapakoko o Häkinakina Hupita, Apollona Belvederskogo ko Athena Parthenos.

Ko tētahi o nga mahi a Leonardo da Vinci - "Portrait o Mona Lisa" - kua roa kua he kaupapa o pūtaiao rangahau. kitea ratou e te hanganga o te mahi ngā katoa o te "Triangle Golden", hono i roto i te whetu auau taparima rite. mahi katoa da Vinci ko te kawenata ki te pehea hohonu ko tona mohio o te hanganga me te hanganga o te tinana tangata, a taea ia te hopu i te malimali enigmatic mīharo o te Mona Lisa.

hoahoanga Wāhanga Golden

Ka rite ki te tauira, kua ako kaipūtaiao te masterpieces o hoahoanga, hanga e nga tikanga o te "wāhanga koura": te koeko Ihipiana, te Pahiona, te Parthenon, Notre-Dame de Paris, St. Vasiliya Blazhennogo me ētahi atu.

Parthenon - tetahi o nga whare tino ataahua i roto i Ancient Greece (5 rau BC.) - e 8 tīwae me 17 i runga i taha ritenga, he rite ki te 0,618 te ōwehenga o tona tiketike ki te roa o te taha. Ko te haurangi ki runga ki tona kātakí hanga o "wāhanga koura" (whakaahua i raro nei).

(Pera-ka karanga "Modulor") e taha o nga pūtaiao e whakaaro me pai tono te whakapai ake o te pūnaha modular mo nga hanganga o ngā hoahoanga - ko te kaihoahoa French Le Korbyuze. Ko te pūtake o te Modulor hoatu te pūnaha ruri e pā ana ki te wehenga herenga ki nga wahi o te tinana tangata.

kaihoahoa Russian Mikhail Kazakov, nana nei i hanga e rave rahi whare noho i roto i Moscow, me te te whare kaumatua i roto i te Kremlin, me te Hospital Golitsyn (inaianei te 1 Clinical Pirogov.) - ko tetahi o nga kaihoahoa nei whakamahia nga ture hoahoa me te hanganga te wāhanga koura.

ōwehenga Taupānga i roto i te hoahoa

Ko te hoahoa o kaihoahoa kakahu katoa hanga whakapakoko hou me ngā tauira tango ki pūkete nga hanganga o te tinana tangata, me nga ture o te wāhanga koura, ahakoa i te natura, e kore e whai te iwi katoa nga hanganga pai.

A, no te whakamahere i te hoahoa whenua me te hanga o te tito rōrahi park te whakamahi i otaota (rākau me ngā mauwha), puna, me ngā hoahoanga iti me ngā tauira e taea te whakamahi "hanganga fakalangi". I muri i te katoa, kia hāngai te hanganga o te papa i hanga i te mana'o i runga i te manuhiri, noa e taea e whakatere te reira, ka kitea he pokapū hiato.

He āhuatanga katoa o te papa i roto i taua hanganga e na te tikanga o te hanganga āhuahanga, tūnga whanaunga, rama, marama, te whakaputa i te tangata i te ongo o te au maite, me te tino.

Ko te whakamahi o te wāhanga koura i roto i cybernetics me hangarau

puta hoki Ture o te tau Golden Wāhanga ko Student i roto i te whakawhitinga pūngao i roto i te tukanga tango wahi ki matūriki timatanga whakatu te pūhui matū, i roto i ngā pūnaha wāhi i roto i te hanganga ira o DNA.

tukanga e rite puta i roto i te tinana tangata, e faaite ake i roto i nga koiora o tona ora, i roto i whēkau mahi, pērā i roro kite ranei.

Kei te whānui hātepe me ngā tauira hanganga koura whakamahia i roto i cybernetics hou me Informatics. Ko tētahi o nga mahi ohie, e hoatu hötaka tauhou ki te whakaoti - ka tuhituhi i te tātai ki te whakatau i te moni o tau Student ki te tau etahi, mā te whakamahi i ngā reo hōtaka.

rangahau Modern i runga i te ariā o te ōwehenga koura

Mai te waenganui o te rautau 20, moni i roto i nga raruraru, me te pānga o te ture o nga hanganga koura o piki te ora o te tangata tino, me e maha pūtaiao o ngā ngaio: mathematicians, rōpū matawaka o kairangahau, ōmataora, philosopho, ngaio hauora, economists, kaiwaiata, me ētahi atu.

I roto i te US mai haamata 1970-hgodov ki te whakaputa i te buka aamu te Student Quarterly, e whakaputa pepa i runga i te tumu parau. I roto i te press reira he mahi i roto i nei te ture te whakatakiruatanga o o te wāhanga koura, me te raupapa Student e whakamahia i roto i mara ngā o te matauranga. Hei tauira, ki te whakawaehere mōhiohio, matū rangahau, koiora, me ētahi atu

tenei katoa fakapapau'i te kitenga o ngā pūkenga tawhito, me te hou e whānui hono te rahi koura ki ngā pātai taketake o te pūtaiao me te hangarite kitea i roto i mahi maha, me ari o te ao huri noa ia tatou.