Kulesi sihloko uzokwazi ukwazi ngamunye izethulo ezakha okuqinile kwe-platonic, izibalo zabo zejiyomethri zihlukile futhi azifani nomlando. Ngakho-ke, sizokunikeza ulwazi olubalulekile noluthakazelisayo mayelana nezakhi ezinhlanu ze-polygonal eziyingxenye yaleli qembu eliyinqaba.
Ayini ama-Platonic Solids?
Ziyizinto eziqinile ezihlanganisa izinhlangothi eziningana ngokusho kwesibalo, lapho ungazi khona inhloso yazo kanye nokulingana ezinakho ebusweni babo ngamunye. Okusho ukuthi, zonke izinto eziqinile ze-platonic zaziwa ngokuthi ama-polygons ahlanganisa zonke izingxenye zawo ezinezindawo ezivamile, okuzenza zibe izethulo ezikhangayo kakhulu. Ngaphezu kwalokho, banama-engeli abo okhonkolo alinganayo.
Ngakolunye uhlangothi, kufanele sikhulume ngemvelaphi yaleli gama elithakazelisa kakhulu elihlanganisa lezi zibalo ikakhulukazi, ngoba "Plato” Leso sazi sefilosofi esingumGreki sasendulo saba nethuba lokuhlola leli qembu lezinto eziqinile zikaplatonic ngaphambili. Ngenxa yalesi sizathu, igama lashintshwa ukuze kuhlonishwe lo mlingiswa omkhulu, isithonjana somlando emkhakheni wocwaningo nokutholwa.
Ngaphezu kwalokho, lezi izethulo eziqinile zaziwa kuwo wonke umlando wesintu ngamagama ahlukene, ezihlanganisa nokusetshenziswa okuhlukahlukene kanye nokuxhumana ezindaweni zokuphila, ukufunda nokuziphendukela kwemvelo. Ngakho-ke, izinto eziqinile ze-platonic zibe nohambo oluthakazelisayo kakhulu nolubanzi, lapho ziye zakwazi ukuhlanganisa nezindaba zezibalo, ezingokomoya, zesakhiwo kanye nobunye ubudlelwano obuthakazelisa kakhulu.
Ngenxa yalezi zibalo ezinhle, namuhla kuneziqondiso ezihlukene ngezihloko ezithile, ezisize ekusungulweni kwemithetho yezibalo ebaluleke kakhulu njengokwakhiwa kwezibalo eziningi, njengoba zisebenze njengesikhuthazo sokuziphendukela kwemvelo nentuthuko.
Izinto eziqinile zikaplatonic zaziwa ezifundweni nasezimeni ezahlukahlukene, ezinikeza usizo ekuqondeni okujulile kunokujwayelekile noma okujwayelekile, njengoba kuyizethulo eziveza ukuthi kungenzeka ukuba khona kwezakhi ezingaqukatha izinhlangothi ezilinganayo futhi, zibe lusizo Ngokuphelele empilweni yansuku zonke. , kufanele nje wazi ukuthi ungazibona kanjani.
Ngenxa yalesi sizathu emlandweni kuye kwenzeka ukuqaphela izindawo ezibalulekile zalezi zinto eziqinile, ezincishiselwa emaphethelweni, izinhlangothi kanye nama-vertices, olwazi lwazo alushintshi, ubukhulu bazo noma ukusetshenziswa kungaba yizinhlobonhlobo ezikhona kulezi zibalo ezikhethekile. musa abanalo ukungalingani. Uma uthanda izibalo, ungase futhi ube nentshisekelo yokwazi i-cube ye-metron
Namuhla, izibalo ezi-5 zingabonwa njengeziqinile ze-platonic ezivame ukuvame kakhulu empilweni yansuku zonke yomuntu. Ngaphezu kwalokho, ngokuvamile ziyizindlela zokuqala umuntu afundiswa ngazo ukunikeza isiqalo sokuqonda, ukuthuthukiswa, ukuziphendukela kwemvelo okunempilo nokugcwele ukuqonda.
Ngenxa yalesi sizathu, kunezifundo eziningi ezenziwa maqondana nalezi zinto eziqinile zikaplatonic, ezinedatha yasendulo, kanye neyamanje, lapho ukusetshenziswa kanye nezinzuzo zokuba khona kwalezi zimele kusanwetshwa, okunikeza umoya kalula. kokutholakele, uphenyo kanye nezinkinga zesayensi.
Kusukela ezikhathini zasendulo kuze kube namuhla, kungashiwo ukuthi azikho izindlela ezilinganayo kwezinye izibalo eziqukethe ukujwayela okufanayo noma isici esingavamile njengalezo eziqinile ze-platonic. Hhayi-ke, akunakwenzeka ukwakha ukuqina okusha okufana nalezi, njengoba zingekho izitudiyo ezingazakha, yingakho kukhona okuqinile okungu-5 kuphela.
Lezi yizibalo ezaziwa kakhulu emhlabeni, ezinikeze ulwazi oluningi kanye nokuhambisana nokutholakele okuhlukahlukene, kanye nocwaningo lwesayensi nezibalo ikakhulukazi. Izakhi zawo zibalulekile ekuqondeni izindikimba okufanele zisekelwe ngalezi zethulo zikaplatonic.
Amathwithi abo anomthwalo wemfanelo wokuhlanganisa uhlangothi ngalunye lwe-platonic solids ukuze kwakhiwe ipholigoni enokujwayela kanye nobukhulu obunembile, okubenza babe ngokoqobo futhi bavelele uma kuqhathaniswa nezinye izibalo ezikhona, ngenxa yamathuba azo ahlukile.
Ngakho-ke, lezi zinto eziqinile ze-platonic, eziye zafundwa kusukela ezikhathini zasendulo, ziwugqozi olukhulu kakhulu lwendalo yejometri engabonwa emhlabeni. Isibonelo salokhu kungaba yi-cube” okumelela okuqinile okusebenzise ukwakha amabhokisi, amadayisi, nezinye izitsha abantu abavame ukuzisebenzisa ekuphileni kwabo kwansuku zonke.
Izinto eziqinile zikaplatonic yizo eziye zatholwa futhi zahlaziywa ngemibono eminingi nasemakhulwini eminyaka ahlukene ngososayensi abangavamile, abaye baba nokubaluleka kokusungula ingxenye ngayinye, izinyathelo kanye nezinhlamvu ezibalulekile, ukuze kuzuzwe ukuphelela isithombe nesakhiwo sawo, okushiya njengezethulo zangempela nezisekelo ezihlukene.
Ukwengeza, yilezi zinto eziqinile eziye zaba khona kuyo yonke inkathi yokuphila komuntu, zisebenza njengesibonelo ekusetshenzisweni kokuphelela kwazo kwe-polygonal ezinkingeni eziphakama ngaphambi kososayensi noma ekuphileni kwansuku zonke. Futhi, yibo abenza imizamo ezithombeni zomlando wesintu, beshiya abacwaningi abakhulu benolwazi olungenakuqhathaniswa. Ezinye izibalo ezigqamayo ngokuba ne-symmetrical kakhulu yilezi ama-mandala anemibala
Kodwa-ke, njengoba iminyaka yayihamba, lezi zinto eziqinile zikaplatonic zanikezwa olunye uhlobo lwenothi kanye nezimpawu. Yebo, izethulo ze-geometric ezi-5 zithathwe njengezici ezibalulekile ekuphileni, okungukuthi, zathathwa yilabo bantu ababefuna isibonakaliso salokhu.
Ngakho-ke kushiya umlilo, amanzi, umoya, umhlaba kanye necosmos, njengezakhi ezingase zimelelwa nokuqinile kwe-platonic. Lokhu kubangelwa ukuphelela ukuthi lezi zibalo zejometri ezinakho, ezinye zazo ezingahlanganisi.
Ngakho-ke, izinto eziqinile zikaplatonic zinohambo oluthakazelisa kakhulu empilweni yomuntu, oluhlaba umxhwele kakhulu futhi olubalulekile ukwazi. Ngaphezu kwalokho, kungaqondwa ukuthi ngayinye yalezi zithombe ezi-5 zishiye ifa elikhulu lasendulo nelibalulekile, elisetshenziswa namuhla ekuziphendukeleni komuntu.
historia
Njengoba kade sibuyekeza, lezi zibalo zibizwa ngokuthi "okuqinile kwe-platonic” zaziwa ezikhathini zasendulo, zishiya ucwaningo olubalulekile nokuvundululwe ngayinye yazo futhi ngenxa yalokhu seziyaziwa emhlabeni wanamuhla, lapho ziye zaba usizo olukhulu nempumelelo enkulu ukuze zihambisane nentuthuko yomuntu ekuhlakanipheni nasekuqondeni kwazo.
Kunemibhalo ehlehlela emuva eminyakeni eminingi, lapho bekukwazi khona ukwazi ngobukhona bezethulo ezi-5 eziqinile ezisekhona nanamuhla. Nokho, akukwazanga ukuthola ukwaziswa okunembile ngekhulu leminyaka lapho uphenyo olunembile lwalezi zici olwenziwa khona.
Nakuba kwaziswa emisebenzini eyenziwa ngu “Plato” ukuthi uyena owaqala ukutholakala kwalezi zinto eziqinile, yingakho zinalelo gama. Ngaphezu kwalokho, ngalolu lwazi olubalulekile kungatholakala ukuthi lezi zithombe zejometri zikhona kusukela eminyakeni edlule yokuba khona kukaJesu Kristu emhlabeni.
Kubalulekile ukugqamisa ukuthi selokhu kwaba khona izinto eziqinile zikaplatonic, ososayensi abahlukene nezazi zefilosofi bebephethe ukucwaninga ngayinye yalezi zakhi ngokujula okukhulu. Ukuze uthole idatha eyengeziwe, ukuze kwenziwe ngokusemthethweni ulwazi olusha nokutholakala komuntu emhlabeni.
Ngalesi sizathu, amagama ahlukene anikezwe lezi zinto eziqinile eminyakeni edlule. Nokho, ukusho lokho Plato wayeyisazi sefilosofi owashiya okokuqala ekutholeni kwakhe, wagcina ebakhomba ngezibizo abanazo namuhla.
Kubalulekile futhi ukukugqamisa lokho Plato, ngokwemibhalo yakhe, nguye owathola futhi wathuthukisa umfanekiso wezinto eziqinile zikaplatonic, eshiya ifa elibaluleke kakhulu. Nokho, kwaba "ithiyetetus” umGreki, ngokocwaningo lwasendulo, owaziwa njengesihlobo sesazi sefilosofi okukhulunywe ngaso ngenhla, esinethuba, ubuhlakani nesisekelo sokukhombisa ubukhona bezakhi ezi-5, ngendlela yezibalo.
Uthe uphenyo luveze izibalo eziyiqiniso mayelana nokubunjwa kwazo kanye nokulingana okukhona ebusweni obunye ezinabo kwaqinisekiswa, okukhombisa ukuthi zingama-polygonal ngokuphelele.
Siyabonga ithiyetetus, ukuthi kwakungenzeka ukwazi uhlobo lwezibalo lwe-platonic solids, ukukhombisa ngezinombolo ubukhulu, ama-vertices kanye nezinhlangothi ezinazo. Eziqinisekiswa njengamapholigoni, okungukuthi, anesakhiwo esilingana ngokuphelele ebusweni ngabunye abanabo. Ngaphezu kwalokho, nguyena owathi akunakwenziwa okunye ukumelelwa kwezindawo ezifana nalezi.
Lokho kwaba ukutholakala okuthakazelisa kakhulu futhi okusaqhubeka nokusekelwa namuhla, njengoba kungekho omunye umfanekiso wejometri okwazile ukuqukatha izici ezifanayo neziqinile ze-platonic, ngaleyo ndlela kushiye izethulo ezi-5 ezikhona njengeziwukuphela kwazo emlandweni wonke wesintu.
Yingakho izinto eziqinile zikaplatonic zibalulekile ekukhuleni kolwazi lomuntu, okube wugqozi olukhulu kososayensi nabacwaningi ngemuva kwalaba bantu abakhulu, abagqame njengabantu abahlonishwa kakhulu nababalulekile ukuchaza umsuka walezi zakhi ze-polygonal.
Ukugcwaliseka kwe-Platonic Solids
Izimo ezinhlanu zejiyomethri kuleli qembu elithile kulula kakhulu ukwenza. Nokho, lapha sikushiyela ividiyo ukuze uqonde kangcono ukuthi ukwakheka kwangempela kwalawa mapholigoni avamile kwenziwa kanjani.
Izici ezijwayelekile
Izinto eziqinile ze-platonic zaziwa kusukela ezikhathini zasendulo kuze kube manje, njengezethulo ze-polygonal ngokuphelele. Ngamanye amazwi, zonke izinhlangothi ezizenza zilingana kakhulu futhi zivame ukuphumelela, okuzenza iqembu langempela phakathi kwazo zonke izibalo zejiyomethri ezikhona namuhla.
Ngakho-ke, amalungu aleli qembu lama-platonic solids akhonjwa ngezethulo ezi-5. Okuyaziwa namuhla, njengoba kuyizibalo eziyinhloko ezifakwe ezimfundisweni zokuqala zomuntu, zibe yingxenye yokukhula nokuthuthuka okuhle kwabantu. Ngakho-ke, sizokutshela izici eziyinhloko zomunye wabo ngezansi.
i-tetrahedron
Enye yezinto eziqinile ze-platonic ezavezwa emlandweni kwakuyi-tetrahedron, umfanekiso wayo umelelwe ubuso obu-4, imiphetho engu-6 kanye nama-vertices angu-4. Idatha yabo isivumela ukuthi sazi ukuthi lokhu kuvezwa ku-polygonal ngokuphelele, okungenye yezimiso okumele izethulo zaleli qembu elithile zihambisane nazo.
Ngaphezu kwalokho, yisibalo esikwazile ukusebenza njengogqozi ekugcwalisekeni kwemiklamo ehlukahlukene yezakhiwo. Isibonelo, umbhoshongo otholakala eGibhithe ungumfanekiso omkhulu obonisa ukulingana okukhona phakathi kwezinhlangothi zawo ngalunye futhi okungabonwa ngokunembe kakhudlwana ekuphileni kwangempela.
Kubalulekile ukugcizelela ukuthi emlandweni wesintu kusukela ezikhathini zasendulo izinto eziqinile ze-platonic ezi-5 zathathwa njengokumelela izakhi ezi-5 ezilawula imvelo emhlabeni. Ngale ndlela i-tetrahedron ifanekisela umlilo, ngenxa yokufana kwayo emfanekisweni wayo ngokwalabo bantu.
The Cube
I-cube iqukethe ubuso obuyi-6 obunobukhulu obulinganayo kanye nokujwayelekile, ngenxa yalesi sizathu ifakwe kuleli qembu le-platonic solids. Ngaphezu kwalokho, inani lama-vertices elinalo lingangezwa kulolu lwazi, oluyi-8. Ngakolunye uhlangothi, isibalo esinemiphetho engu-12, ngenxa yale datha kungenzeka ukwazi ukuma okuqondile kwalesi sici sejometri.
Lesi sibalo singabonakala futhi ezintweni eziningi ezikhona esintwini, ezisize ukuthuthukiswa okusebenzayo nokuziphendukela kwemvelo komuntu. Nokho, ikhyubhu iyindlela engokoqobo yokuyisebenzisa, kungaba ukumelwa kwangempela noma izibalo zezibalo.
Ngokulandelayo, i-cube ibe nesethulo esihlukile ezinkolweni noma ezinkolelweni zasendulo lapho lesi sibalo sikhona, njengophawu lomhlaba. Yile ndlela okuqinisekiswa ngayo ukuguquguquka okunikezwe izinto eziqinile zikaplatonic emakhulwini eminyaka adlule.
I-Octahedron
Esinye sezethulo ezaziwa kakhulu zezinto eziqinile ze-platonic i-Octahedron, ubukhulu bayo bungaziwa ngokwazi idatha yayo eyisisekelo, njengenombolo yemiphetho (12) kanye nama-vertices ewaqukethe, angu-6. Ngalokhu, i- ingahlobanisa ukuzilibazisa kwezinhlangothi eziyi-8 ezakha lesi sibalo esingajwayelekile sejometri.
Ngaphezu kwalokho, i-octahedron ingaqashelwa njengophawu lwesici somoya, esiye saziwa ezinkolelweni zeminyaka edlule, lapho isibalo ngasinye sanikezwa isici esakha izingxenye eziyinhloko zokuphila komuntu.
I-Dodekahedron
I-Dodekahedron yaziwa ngezinhlangothi zayo ezilinganayo eziyi-12, ezakhiwe ngamachopho angama-30 kanye nama-vertices angama-20. Ibonisa isithombe se-polygonal esithakazelisa kakhulu, esingashiwo ukuthi sakhiwe ngama-pentagon avamile aziwa emhlabeni we-geometry.
Lokhu okuqinile kwe-platonic nakho kwakuyingxenye ye-symbogy eyanikezwa ezikhathini zasendulo amaGreki, lapho yaziwa njengokumelela kwento engavamile kakhulu, njengoba yaziwa ngokuthi "i-Cosmos" lokhu kuqondiswe kumuntu obabazekayo enayo.
icosahedron
Enye yezinto eziqinile ze-platonic ezibonakala ziyinkimbinkimbi emehlweni omuntu, njengoba iqukethe izinhlangothi ezingu-20 okuthi, uma zihlangene, zakhe isibalo sazo esingavamile futhi zikhiqize ukulingana ebusweni bazo ngalunye. Ngenxa yalesi sizathu, iyingxenye yaleli qembu elibalulekile neliyingqayizivele.
Ngaphezu kwalokho, isibalo esingasho ukuthi sakhiwe ngonxantathu abaningana, umehluko wukuthi uhlangothi ngalunye lunesilinganiso esifanayo. Kodwa-ke, umbono wesithombe salokhu kumelela okuqinile unganikezwa.
I-icosahedron yileso sithombe esingakhonjwa ngeziphetho ezingu-30 kanye nama-vertices angu-12, ahlanganisa ubuso obunye balo mfanekiso, omele ipholigoni enokulingana okuphelele. Futhi, ingenye yezinto ezihlaba umxhwele kakhulu futhi mhlawumbe esetshenziswa kancane, kodwa iba yingxenye yokutholwa okungenzeka.
Ezikhathini zasendulo, ezinye izinkolo zanquma ukuthatha isithombe ngasinye esiqinile ukuze simelele izici ezibalulekile zokuphila, zinikeze i-Icosahedron uphawu lwamanzi. Leli yiqiniso elincane elaziwayo kodwa kwabaluleka kakhulu emakhulwini eminyaka adlule. Okunye okutholwe ezithakazelisayo ngokulinganayo kungatholwa ngokusebenzisa i igama lenumerology
Izakhiwo ze-Platonic Solids
Izinto eziqinile ze-platonic zihlanganisa izakhiwo ezihlukahlukene, okwenza leli qembu elikhethekile kanye nejometri ibe yinto ehlukahlukene, njengoba isetshenziswe emagatsheni ahlukene esayensi, izibalo kanye nesakhiwo. Ngenxa yalesi sizathu, kube nokwenzeka ukufunda kabanzi mayelana nengxenye ngayinye yalezi zibalo, okwenza kucace ngaso sonke isikhathi ukuthi zibaluleke kangakanani futhi zihlukile kangakanani.
Umqondo
Ngenxa yemibono eyenziwe ngokuhamba kwesikhathi, kube nokwenzeka ukukhombisa ukuthi izinto eziqinile ze-platonic zihluke kangakanani, ezingamelelwa kuphela ngonxantathu abalinganayo, ama-pentagon noma izikwele, ukuze kutholwe umgomo oyisisekelo: ukujwayela okungenakuphikiswa endaweni ngayinye. ubuso bayo.
I-Platonic Solids Equation
Emkhakheni wezibalo, kungenzeka ukwazi nokuqinisekisa iqiniso lezinhlangothi ezilinganayo ezisezindaweni eziqinile ze-platonic ezi-5, ezitholakala ngokungeza inombolo yobuso naleyo yama-vertices ayo, ngale ndlela umphumela uzophonsa. inani lemiphetho, lapho i-2 kufanele yengezwe futhi ngaleyo ndlela ithole lokho okufunwayo ekumeleleni okudingekayo.