Kweli nqaku uya kuba nako ukwazi ngamnye ukumelwa ezenza i izinto eziqinileyo zeplatonic, amanani abo ejometri ayingqayizivele kwaye ayifani nembali. Ke ngoko, siya kukubonelela ngolwazi olubalulekileyo nolunomdla malunga nezinto ezintlanu zepolygonal eziyinxalenye yeli qela lingaqhelekanga.
Ziziphi iiPlaton Solids?
Ziziqina eziqulethwe ngamacala amaninzi ngokomzobo, apho unokwazi khona injongo yazo kunye nokulingana abanako kubuso babo. Oko kukuthi, zonke izinto eziqinileyo zeplatonic zaziwa njengeepolygons eziqulathe zonke iindawo zazo ezinomgangatho oqhelekileyo, nto leyo ezenza zibonise umdla kakhulu. Ukongezelela, baneengile zabo zekhonkrithi ezilinganayo.
Kwelinye icala, kufuneka sikhankanye imvelaphi yeli gama linomdla kakhulu elibandakanya la manani ngakumbi, kuba "UPlato” Eso sithandi sobulumko esingumGrike samaxesha amandulo saba nethuba lokufundisisa eli qela lezinto eziqinileyo zikaplatonic ngaphambili. Ngenxa yesi sizathu, igama liguqulelwe ngokuhlonipha lo mlingiswa omkhulu, umfanekiso wembali kwinkalo yophando kunye nokufumanisa.
Ukongezelela, ezi zibonakaliso eziqinileyo ziye zaziwa kwimbali yoluntu ngamagama ahlukeneyo, ezibandakanya ngeendlela ezahlukeneyo zokusetyenziswa kunye nokudibanisa kwiinkalo zobomi, ukufunda kunye nokuziphendukela kwemvelo. Ngaloo ndlela, i-platonic solids ibe nohambo olunomdla kakhulu kunye nolubanzi, apho baye bakwazi ukudibanisa nemiba yezibalo, yokomoya, yesakhiwo kunye nobunye ubudlelwane obunomdla kakhulu.
Enkosi kula manani amangalisayo, namhlanje kukho izikhokelo ezahlukeneyo kwizihloko ezithile, eziye zanceda ukuseka imithetho yezibalo ebaluleke kakhulu efana nokwakhiwa kwamanani amaninzi, kuba baye basebenza njengempembelelo yendaleko kunye nophuhliso.
Izinto eziqinileyo zeplatonic ziyaziwa kwimixholo kunye neemeko ezahlukeneyo, ezibonelela ngoncedo ekuqondeni okuya nzulu kunesiqhelo okanye okuqhelekileyo, kuba zizinto ezibonisa ubukho bezinto ezinokuqulatha amacala alinganayo kwaye zibe luncedo ngokupheleleyo kubomi bemihla ngemihla. , kufuneka wazi nje ukuba ubazi njani.
Ngenxa yesi sizathu kwimbali kuye kwenzeka ukuba ukuqaphela iindawo ezibalulekileyo ezi ziqina, ezincitshiswe imiphetho zabo, amacala kunye neentlondi, olwazi alusoze lwahluka, kuphela ubukhulu babo okanye ukusetyenziswa kuya kuba ezahlukeneyo ezikhoyo kula manani akhethekileyo ukuba. musa ukuba akukho ukungalingani. Ukuba uyawathanda amanani, unokuba nomdla wokwazi ityhubhu ye-metron
Namhlanje, amanani ama-5 anokuthathwa njengezinto eziqinileyo zeplatonic ezidla ngokuxhaphake kakhulu kubomi bemihla ngemihla bomntu. Ukongeza, zidla ngokuba ziindlela zokuqala umntu afundiswa ngazo ukunika isiqalo sokuqonda, uphuhliso, ukuziphendukela kwemvelo okunempilo kunye nengqiqo epheleleyo.
Ngesi sizathu, kukho izifundo ezininzi eziye zaqhutywa ngokubhekiselele kwezi zinto ziqinileyo zeplatonic, ezinedatha yamandulo, kunye nekhoyo ngoku, apho ukusetyenziswa kunye noncedo lobukho bobu bungqina zisandiswayo, nto leyo eyenza umoya ube lula. kwizinto ezifunyenweyo, kuphando nakwiingxaki zenzululwazi.
Ukusukela kumaxesha amandulo ukuza kuthi ga ngoku, kunokuthiwa akukho nqobo zilinganayo kwamanye amanani aqulathe ukuqheleka okufanayo okanye umlinganiselo ongaqhelekanga njengalawo aqinileyo eplatonic. Ewe, akunakwenzeka ukwenza isiseko esitsha esifana nezi, kuba azikho izitudiyo ezinokuzakha, yiyo loo nto kukho izinto ezi-5 kuphela.
La ngawona manani aziwa kakhulu kwisijikelezi-langa somhlaba, athe anika ulwazi oluninzi kunye nokuhambelana kwezinto ezahlukeneyo ezifunyenweyo, kunye nophando lwezenzululwazi nezibalo ngakumbi. Izinto zayo zibalulekile ekuqondweni kwemixholo ekufuneka ixhaswe ngolu phawu lweplatonic.
Ii-vertices zabo zinoxanduva lokujoyina icala ngalinye leplatonic solids ukuze kwakhiwe ipolygon echanekileyo kunye ne-dimension, izenze zibe zezoqobo kwaye zibalasele xa kuthelekiswa namanye amanani akhoyo, enkosi kumathuba awo awodwa.
Ke, ezi zingqinisiso zeplatonic, eziye zafundwa ukususela kumaxesha amandulo, yeyona nto ikhuthazayo kwindalo yejometri enokubonwa kwihlabathi. Umzekelo woku inokuba yicubo” omelo oluluqilima oluye lwasebenza ekudaleni iibhokisi, idayisi, nezinye izinto ezisetyenziswa ngabantu rhoqo kubomi babo bemihla ngemihla.
Izinto eziqinileyo zeplatonic zizo eziye zafunyanwa kwaye zahlalutywa kwiimbono ezininzi kunye neenkulungwane ezahlukeneyo zizazinzulu ezingaqhelekanga, eziye zabeka phambili ukuseka inxalenye nganye, imilinganiselo kunye nabalinganiswa ababalulekileyo, ukuze bafezekise ukugqibelela. umfanekiso wayo kunye nolwakhiwo, lubashiya njengemiboniso yokuqala kunye neziseko ezahlukeneyo.
Ukongezelela, zezi ziqina eziye zabakho kuwo onke amaxesha obomi bomntu, zisebenza njengomzekelo ekusetyenzisweni kwe-polygonal yazo ngokugqibeleleyo kwiingxaki ezivela phambi kososayensi okanye kubomi bemihla ngemihla. Kwakhona, ngabo abaye benza imizamo kwimifanekiso eqingqiweyo yembali yoluntu, beshiya abaphandi abakhulu benolwazi olungenakulinganiswa nanto. Eminye imizobo ekwagqame ngokuba yi-symmetrical kakhulu iimandala ezinemibala
Nangona kunjalo, njengoko iminyaka yayihamba, ezi ziqina zeplatonic zanikwa olunye uhlobo lophawu kunye nesimboli. Ewe, izibonakaliso zejometri ezi-5 zithathwe njengezinto ezibaluleke kakhulu ebomini, oko kukuthi, zithathwe ngabo bantu bafuna uphawu lwaba.
Ngaloo ndlela kushiya umlilo, amanzi, umoya, umhlaba kunye ne-cosmos, njengezinto ezinokumelwa kunye ne-platonic solids. Oku kubangelwa ukugqibelela ukuba ezi zibalo zejometri, apho ezinye azizange zibandakanye.
Ke, izinto eziqinileyo zeplatonic zinohambo olunomdla kakhulu kubomi bomntu, nto leyo emangalisa kakhulu kwaye ibalulekile ukuyazi. Ukongeza, kunokuqondwa ukuba nganye kwezi zibonakaliso ze-5 zishiye ilifa elikhulu lakudala kunye elibalulekileyo, elisetyenziswa namhlanje ekuziphendukeleni komntu.
Historia
Njengoko besiqwalasela, la manani abizwa ngokuba "izinto eziqinileyo zeplatonic” zazisaziwa kumaxesha amandulo, zishiya uphando olubalulekileyo kunye nezinto ezifunyenweyo ngamnye kubo kwaye ngenxa yoku ziye zaziwa kwihlabathi langoku, apho ziye zaba luncedo olukhulu kunye nokusebenza kakuhle ukuxhasa uphuhliso lwabantu kubukrelekrele nokuqonda kwabo.
Kukho imibhalo esusela emva kwiminyaka emininzi, apho kuye kwenzeka ukwazi malunga nobukho be-5 yokumelwa okuqinileyo okukhoyo namhlanje. Nangona kunjalo, akuzange kwenzeke ukufumana ulwazi oluchanekileyo malunga nenkulungwane echanekileyo apho uphando oluchanekileyo lwezi zinto lwenziwa.
Nangona iye kwaziswa kwimisebenzi eyenziwa ngu “UPlato” ukuba nguye owaqala ukufunyanwa kwezi ziqina, yiyo loo nto zinelo gama. Ukongeza, ngolu lwazi lubalulekileyo kunokufunyaniswa ukuba le mizobo yejometri ikhona kwiminyaka yangaphambili yobukho bukaYesu Kristu emhlabeni.
Kubalulekile ukugxininisa ukuba ukususela ekubeni kukho izinto eziqinileyo zeplatonic, izazinzulu ezahlukeneyo kunye neefilosofi ziye zalawula ukufunda nganye yezi zinto ngobunzulu obukhulu. Ukuze ufumane idatha engakumbi, ukuze kwenziwe ngokusesikweni ulwazi olutsha kunye nokufunyanwa komntu kwiplanethi yomhlaba.
Ngesi sizathu, amagama ahlukeneyo anikwe ezi ziqina kwiminyaka. Noko ke, ukuthetha oko UPlato wayesisithandi sobulumko owayeka ukufunyanwa kwakhe kuqala, waza ekugqibeleni wabafanisa neziteketiso abanazo namhlanje.
Kukwabalulekile ukuqaqambisa oko UPlatoNgokutsho kwemibhalo yakhe, nguye owafumanisa kwaye waphuhlisa umfanekiso we-platonic solids, eshiya ilifa elibaluleke kakhulu. Nangona kunjalo, yayiyi "ithiyetetus” UmGrike owathi, ngokutsho kophando lwamandulo, waziwa njengesihlobo sefilosofi ekhankanywe ngasentla, owayenethuba, ingqondo kunye nesiseko sokubonisa ubukho bezinto ezi-5, ngendlela yezibalo.
Olu phando luthe lwavelisa izibalo eziyinyani kubume bazo kwaye ukulingana okukhoyo kubuso ngabunye abanabo kwaqinisekiswa, nto leyo ebonisa ukuba ngamanani amacala amaninzi.
Ndiyabulela ithiyetetus, kukuba kwakunokwenzeka ukwazi uhlobo lwemathematika ye-platonic solids, ebonisa ngamanani ngamnye wemilinganiselo, i-vertices kunye namacala abanawo. Ezingqiniswe njengeminxaninzi, oko kukuthi, ngesakhiwo esilinganayo ngokupheleleyo kubuso obunye abanabo. Ukongeza, nguye owathi enye imbonakalo yejografi efana nale ayinakwenziwa.
Leyo yayiyinto enomdla kakhulu efunyenweyo kwaye isaqhubeka ixhaswa namhlanje, kuba akukho mfanekiso wejometri oye wakwazi ukuqulatha iimpawu ezifanayo kunye ne-platonic solids, ngaloo ndlela ishiya i-5 ekhoyo yokumelwa njengeyodwa kwimbali yonke yoluntu.
Yiyo loo nto izinto eziqinileyo zeplatonic zibalulekile ekukhuleni kolwazi lomntu, oluye lwakhuthaza kakhulu izazinzulu nabaphandi emva kwala madoda abalaseleyo, athe agqama njengabo bahlonitshwa kakhulu nababalulekileyo ukucacisa imvelaphi yala masuntswana angama-polygonal.
Ukuzalisekiswa kwePlatonic Solids
Iimilo zejometri ezintlanu kweli qela elithile zilula kakhulu ukwenza. Nangona kunjalo, apha sikushiyela ividiyo ukuze uqonde ngcono ukuba lwenziwa njani ulwakhiwo lokwenyani lwezi polygons eziqhelekileyo.
Iimpawu ngokubanzi
Izinto eziqinileyo zeplatonic zaziwa ukusuka mandulo ukuza kuthi ga ngoku, njengokubonakaliswa kwepolygonal ngokupheleleyo. Oko kukuthi, onke amacala abenzayo balingana kakhulu kwaye baphumelele ngokuthe rhoqo, okubenza babe liqela lokuqala phakathi kwawo onke amanani ejometri akhoyo namhlanje.
Ngaloo ndlela, amalungu eli qela le-platonic solids achongwa ngokuboniswa kwe-5. Eyaziwayo namhlanje, ekubeni ingawona manani aphambili afakwe kwiimfundiso zokuqala zomntu, abe yinxalenye yokukhula kunye nophuhliso oluhle lwabantu. Ngoko ke, siya kukuxelela iimpawu eziphambili zomntu ngamnye ngezantsi.
itetrahedron
Enye yezinto eziqinileyo zokuqala zeplatonic ezatyhilwa kwimbali yayiyitetrahedron, umzobo wayo umelwe bubuso obu-4, imiphetho emi-6 kunye neendidi ezi-4. Idatha yabo ivumela ukuba sazi ukuba olu melo luyi-polygonal ngokupheleleyo, enye yemigaqo ekufuneka ibonakaliswe yeli qela elithile ihambelane nayo.
Ukongeza, ngumfanekiso oye wakwazi ukusebenza njengenkuthazo ekufezekiseni iiprojekthi ezahlukeneyo zokwakha. Ngokomzekelo, iphiramidi efunyenwe eYiputa ngumfanekiso omkhulu obonisa ukulingana okukhoyo phakathi kwecala ngalinye kunye nokunokubonwa ngokuchanekileyo ebomini bokwenene.
Kubalulekile ukugxininisa ukuba kwimbali yoluntu ukususela kumaxesha amandulo i-5 ye-platonic solids ithathwa njengento emele izinto ezi-5 ezilawula indalo kwiplanethi yomhlaba. Ngale ndlela i-tetrahedron ifanekisela umlilo, ngenxa yokufana kwayo nomfanekiso wayo ngokwalabo bantu.
Cube
I-cube iqulethe ubuso obu-6 obunomlinganiselo olinganayo kunye nokuqhelekileyo, ngenxa yesi sizathu ifakwe kweli qela le-platonic solids. Ukongezelela, inani lee-vertices elinalo lingadityaniswa kule ngcaciso, eyi-8. Emva koko, ngumfanekiso onamaphethelo angama-12, ngenxa yale datha kunokwenzeka ukwazi ubume obuchanekileyo beli candelo lejometri.
Lo mzobo unokuqatshelwa kuninzi lwezinto ezikhoyo eluntwini, ezincede uphuhliso olusebenzayo kunye nendaleko yomntu. Ewe, ityhubhu yindlela esebenzayo yokuyisebenzisa, nokuba kukumelwa okwenyani okanye kubalo lwemathematika.
Emva koko, i-cube ibe nenkcazo eyahlukileyo kwiinkolo zamandulo okanye iinkolelo apho lo mfanekiso ukhoyo, njengomqondiso womhlaba. Le yindlela engqinisiswa ngayo ukuguquguquka okunikwe kwizinto eziqinileyo zeplatonic kwiinkulungwane ezidlulileyo.
Octahedron
Olunye umboniso owaziwayo we-platonic solids yi-Octahedron, imilinganiselo yayo ikwaziwa ngokukwazi idatha yayo esisiseko, njengenani lamaphethelo (12) kunye neengqimba eziqulethwe kuzo, eziyi-6. inokunxulumanisa ukuzonwabisa kwamacala asi-8 enza lo mzobo ungaqhelekanga wejometri.
Ukongezelela, i-octahedron inokuqatshelwa njengesimboli se-air element, eyaziwayo kwiinkolelo zeminyaka edlulileyo, apho umzobo ngamnye unikwe into eyenza amacandelo aphambili obomi bomntu.
iDodekahedron
I-Dodekahedron iyaziwa ngamacala ayo ali-12 alinganayo, akhiwe ngamacangci angama-30 kunye neengqimba ezingama-20. Ukubonisa umfanekiso wepolygonal onomdla kakhulu, onokuthi wakhiwe ngeepentagon eziqhelekileyo ezaziwa kwihlabathi lejometri.
Le nto iqinileyo yeplatonic yayiyinxalenye yesimboli eyanikwa kumaxesha amandulo ngamaGrike, xa yayisaziwa njengokumelwa kwento ebaluleke kakhulu, kuba yachongwa njenge "Cosmos" le ijongwe kumfanekiso obalaseleyo enawo.
icosahedron
Enye yezinto eziqinileyo zeplatonic emehlweni omntu ibonakala intsonkothile, kuba inamacala angama-20 athi, xa edityanisiwe, enze umzobo wawo ongaqhelekanga aze avelise ukulingana ebusweni bawo ngamnye. Ngenxa yesi sizathu, liyinxalenye yeli qela libalulekileyo nelikhethekileyo.
Ukongezelela, ngumfanekiso onokuthi wenziwe ngonxantathu abaliqela, umahluko kukuba icala ngalinye linomlinganiselo ofanayo. Nangona kunjalo, umbono womfanekiso walo mboniso uqinileyo unokunikwa.
I-icosahedron ngulo mfanekiso unokuthi uchongwe nge-30 edges kunye ne-12 vertices, edibanisa ubuso obunye balo mzobo, omele i-polygon ngokulingana okupheleleyo. Kwakhona, yenye yezona zinto zinomtsalane kwaye mhlawumbi isetyenziswa kancinci, kodwa iba yinxalenye yokufunyaniswa okunokwenzeka.
Kumaxesha amandulo, ezinye iicawa zagqiba ekubeni zithathe umfanekiso ngamnye oqinileyo ukuze ubonise izinto ezibalulekileyo zobomi, zinika i-Icosahedron uphawu lwamanzi. Le yinyani eyaziwayo encinci kodwa ibaluleke kakhulu kwiinkulungwane ezidlulileyo. Okunye okufunyanisiweyo okunomdla ngokulinganayo kunokufunyanwa ngokusebenzisa i igama le-numerology
Iipropati zePlatonic Solids
I-platonic solids iqulethe iipropati ezahlukahlukeneyo, ezenza eli qela likhethekileyo kunye nejometri ibe yinto eguquguqukayo, ekubeni isetyenziswe kumasebe ahlukeneyo esayensi, imathematika kunye nesakhiwo. Ngenxa yesi sizathu, kuye kwenzeka ukuba kufundwe ngakumbi malunga nenkalo nganye yala manani, okwenza kucace ngamaxesha onke ukuba abaluleke kangakanani kwaye awodwa.
Thesis
Ngombulelo kwiithisisi eziqhutywe ekuhambeni kwexesha, kube nokwenzeka ukubonisa indlela ezihluke ngayo izinto eziqinileyo zeplatonic, ezinokumelwa kuphela ngoonxantathu abalinganayo, iipentagons okanye izikwere, ukuze kufumaneke umgaqo osisiseko: ukuhlaleka okuqinisekileyo kwindawo nganye. ubuso bayo.
Platonic Solids Equation
Kwintsimi yezibalo, kunokwenzeka ukwazi kwaye uqinisekise ubunyani bamacala alinganayo akwindawo nganye ye-5 ye-platonic solids, efunyenwe ngokudibanisa inani lobuso kunye nelo le-vertices yalo, ngale ndlela umphumo uya kuphosa. isixa semiphetho, apho i-2 kufuneka yongezwe kwaye ngaloo ndlela ifumane oko kufunwayo kumelo olufunekayo.