I-polyhedra evamile emvelweni

Yini eyokwenzeka uma kukhona uhlobo olulodwa kuphela lwesibalo emhlabeni, isibonelo, ifomu efana ne-rectangle? Ezinye izinto ngeke zishintshe nakancane: izivalo, izinqola zempahla, izinkundla zebhola - zonke zibukeka zifanayo. Kodwa kuthiwani mayelana nokuphatha umnyango? Bekungaba okungajwayelekile. Futhi amasondo ezinqola? Lokho bekungeke kwenzeke. Futhi ibhola? Kunzima ukucabanga. Ngenhlanhla, izwe ligcwele izinhlobo eziningi ezahlukene. Ingabe kukhona i- polyhedra evamile emvelweni? Yebo, futhi kukhona eziningi zazo.

Iyini i-polygon?

Ukuze isibalo sibe yi-polygon, izimo ezithile ziyadingeka. Okokuqala, kuzomele kube nezinhlangothi eziningi nama-angles. Ngaphezu kwalokho, kufanele kube ifomu elivaliwe. I-polygon evamile iyinombolo nazo zonke izinhlangothi ezilinganayo nama-angles. Ngakho-ke, ngokungalungile bangakwazi ukukhubazeka kancane.

Izinhlobo zama-polygoni avamile

Iyini inombolo encane yezinhlangothi ukuthi i-polygon ejwayelekile ingaba nayo? Omunye umugqa awukwazi ukuba nezinhlangothi eziningi. Izinhlangothi zombili nazo azikwazi ukuhlangana futhi zakha ifomu elivaliwe. Futhi izinhlangothi ezintathu zingakwazi-ngakho kuvela unxantathu. Futhi njengoba sikhuluma ngama-polygons avamile, lapho izinhlangothi zonke nama-angles zilingana, sisho unxantathu olinganayo.

Uma ungeza olunye uhlangothi, uthola isikwele. Ingabe umugqa, lapho izinhlangothi ezingalingani khona, ube yi-polygon ejwayelekile? Cha, lesi sibalo sizobizwa ngokuthi i-rectangle. Uma ungeza uhlangothi lwesihlanu, uthola i-pentagon. Ngakho-ke, kukhona ama-hexagon, ama-heptagons, ama-octagons nokunye okungahambisani nesikhangiso.

I-geometry eqalayo

Ama-Polygons azinhlobo ezahlukene: ukuvuleka, kuvaliwe nokuzihlanganisa. E-geometry esisekelo, i-polygon iyinombolo yendiza ehlanganiswe ngethunge oluphelele lwezingxenye zesikhombimsebenzisi ngendlela evulekile ye-polyline noma i-contour. Lezi zingxenye ziyizingxenyeni noma izinhlangothi zalo, futhi amaphuzu lapho ukuhlangana okubili kuphakama khona. Ingxenye yangaphakathi ye-polygon ngezinye izikhathi ibizwa ngokuthi umzimba wayo.

Polyhedra emvelo kanye nokuphila komuntu

Ngenkathi amaphethini e-pentagonal eningi emafomu amaningi aphilayo, umhlaba we-amaminerali ukhetha ukulinganisa okuphindwe kabili, kathathu, kwesigatshana nesithupha. I-hexagon yindlela enesibindi, ehlinzeka ngokusebenza kahle kwesakhiwo. Kuyinto evamile kakhulu emkhakheni wama-molecule kanye nama-crystals, lapho amafomu e-pentagonal asondela khona akwenzeki. I-steroids, i-cholesterol, i-benzene, amavithamini C no-D, i-aspirin, ushukela, i-graphite yonke imidwebo ye-symmetry eyisithupha. Kuphi i-polyhedra efanele emvelweni? Isakhiwo esivelele kakhulu se-hexagonal sakhiwa izinyosi, ama-sawps kanye nama-hornet.

Ama-molecule ayisithupha amanzi ayingxenye yesikhumba ngasinye seqhwa. Ngakho kuvela i-snowflake. Ingxenyeni yendiza ihlanganisa ilungiselelo elihlanganisiwe elinama-hexagonal. Iyini i-polyhedra efanele emvelweni? Ziyi-crystal zamanzi nedayimane, amakholomu ase-basalt, amangqamuzana e-epithelial esweni, amanye amaseli esitshalo nokuningi okuningi. Ngakho-ke, i-polyhedra eyenziwe ngemvelo, kokubili ephilayo futhi engewona ophilayo, ikhona empilweni yomuntu ngenani elikhulu futhi ehlukahlukene.

Yini enquma ukuthandwa kwama-hexagon?

Ama-snowflakes, ama-molecule aphilayo, amakristalu e-quartz kanye nama-basalts e-columnar yizingxube. Isizathu salokhu yi-symmetry engokwemvelo. Isibonelo esithinta kakhulu yi-honeycomb, isakhiwo se-hexagonal esinciphisa ukukhubazeka kwendawo, ngoba yonke indawo iyadliwa kakhulu. Kungani uhlukanisa ngamaseli afanayo? Izinyosi zidala i-polyhedra evamile emvelo ukuze zizisebenzise ngezidingo zazo, kufaka phakathi ukugcina uju nokubeka amaqanda. Kungani imvelo ikhetha ama-hexagon? Impendulo yalo mbuzo inganikezwa ngamathematika ayisisekelo.

• Triangles. Thatha izintambo ezingu-428 ze-equilateral ngehlangothini olungaba ngu-7.35 mm. Ubude bawo buyi-3 * 7.35 mm * 428/2 = 47.2 cm.
• Rectangles. Sithatha izikwele ezingu-428 ngecala eliba ngu-4.84 mm, ubude bawo buyi-4 * 4.84 m * 428/2 = 41.4 cm.
• Ama-hexagon. Futhi ekugcineni, thatha amahektha angu-428 ohlangothini lwe-3 mm, ubude bawo buyi-6 * 3 mm * 428/2 = 38.5 cm.

Ukunqoba kwe-hexagons kuyabonakala. Yile fomu esiza ukunciphisa isikhala futhi ikuvumela ukuba ufake izibalo eziningi ngangokunokwenzeka endaweni encane. Amaseli lapho izinyosi zigcina khona i-amber nectar ziyizinto ezimangalisayo zobunjiniyela obucacile, amaqoqo amaningi we-prismoid ane-cross-section ephelele. Izindonga ze-Wax zenziwe ngobukhulu obukhulu kakhulu, amangqamuzana ahloswe ngokucophelela ukuze avimbele ukulahlekelwa uju olunamahloni, futhi isakhiwo sonke sihambelana ngokuhambisana nensimu yamandla omhlaba. Okumangalisa ukuthi izinyosi zisebenza ngesikhathi esisodwa, zihlanganisa imizamo yazo.

Kungani ama-hexagon? Lena geometry elula

Uma ufuna ukuqoqa ndawonye ngesimo esifanayo namasayizi wesayizi, ukuze bagcwalise yonke indiza, izibalo ezintathu ezijwayelekile (ezinamacala onke kanye nama-angles afanayo) zizosebenza: izilinganiso ze-equilatateral, izikwele nezinsimbi ze-hexagon. Kulezi, amangqamuzana angama-hexagonal adinga ukulinganisa okungaphelele kwendonga uma kuqhathaniswa namathantathu noma izikwele zendawo efanayo.

Ngakho-ke, ukhetho lwezinyosi ngezinyosi lunengqondo. Ngasekuqaleni kwekhulu leshumi nesishiyagalolunye, isazi sesazi uCharles Darwin sathi ama-honeycombs angama-hexagonal "angcono kakhulu ekusindiseni abasebenzi ne-wax." Wayekholelwa ukuthi ukukhethwa kwemvelo kwanikeza izinyosi ukudala lezi zindlu zama-wax, ezaba nenzuzo yokunikeza amandla nesikhathi esingaphansi kokudala ezinye izinhlobo.

Izibonelo ze-polyhedra emvelweni

Amehlo ezinambuzane zigcwele i-hexagonal, lapho ingxenye ngayinye ikhona lensi exhunyiwe esitokisini eside esincane se-retina. Izakhi ezakhiwa ngamaqoqo amangqamuzana ephilayo zivame ukuba nezimo ezilawulwa yimithetho efanayo ne-bubbles kwisisombululo sensipho. Isakhiwo esincane kakhulu esibhekene nesiso singesinye sezibonelo ezinhle kakhulu. Isiqephu ngasinye sineqoqo lamaseli amane atholakalayo anomumo ofanayo neqoqo lama-bubbles amane avamile.

Yini enquma le mithetho yesepha amafilimu nokuma kwamabhule? Imvelo ibhekene nakakhulu nokulondoloza kunezinyosi. Ama-bubbles nesepha amafilimu akhiwa ngamanzi (nge-addition soap), futhi ukuphakama kwamanzi kuphakamisa ubuso be-liquid ngendlela yokuthi kunikezwe indawo encane kunazo zonke. Yingakho amaconsi angama-spherical (ngaphezulu noma angaphansi) uma ewa: le sphere ine-surface encane kunoma yimuphi omunye umumo onomsindo ofanayo. Emshini we-wax, amaconsi amanzi ahanjiswa abe ubuhla obuncane ngenxa yesizathu esifanayo.

Lokhu kuphazamiseka komzimba kuchaza amaphethini we-bubble rafts ne-foam. I-Foam izobukeka isakhiwo esinesisindo esincane kunazo zonke, okuzoqinisekisa ukuthi indawo encane yodonga. Nakuba i-geometry ye-saphili amafilimu ebizwa ngokuthi ukusebenzisana kwamandla kagesi, ayisitsheli ukuthi isimo se-foam sizosiphi. I-foam ejwayelekile iqukethe amangqamuzana e-polyhedral ehlukeneko nobukhulu obuhlukahlukene. Uma ubheka ngokucophelela, i-polyhedra efanele emvelweni ayilungile. Amaphethelo abo ajwayelekile ngokuqondile.

Lungisa amabhulogi

Ake sithi ungenza iphunga "elihle", lapho wonke amabhubhu anesayizi ofanayo. Uyini ukuma okuphelele kweseli, okwenza indawo yonke yebhande lobu bubble ibe mncane ngangokunokwenzeka. Lokhu kuye kwaxoxwa iminyaka eminingi, futhi isikhathi eside kwacatshangwa ukuthi ukuma kwesilwane esihle kunama-polyhedron ayi-14 enezinhlangothi ezinezinhlangothi ezinezinhlangothi ezine.

Ngo-1993, kwakhiwe isakhiwo esincane esakhiwe, esakhiwa iqembu eliphindaphinda lamafomu ayisishiyagalombili ahlukene. Le ndlela eyinkimbinkimbi eyengeziwe yayisetshenziselwa ukugqugquzela umklamo we-foamy wenkundla yokubhukuda phakathi neMidlalo yama-Olimpiki ka-2008 eBeijing.

Imithetho yokwakheka kwamaseli ku-foam iphinde ilawulwe amaphethini athile afunwa emasethini aphilayo. Akuyona nje iso lezinhlanzi ezihlanganisiwe elibonisa ukupakisha okufanayo kwe-hexagonal yezici njengebhola eliphambene. Amangqamuzana akhanyayo ngaphakathi kwamalensi ngayinye nawo ajoyina emaqenjini abukeka njengamabhola ensipho.

Izwe lama polyhedra emvelweni

Amaseli ezinhlobonhlobo ezihlukahlukene zezinto eziphilayo, kusukela ezitshalweni kuya ezigodini, aqukethe izitho zangasese nezinhlaka ezincane kakhulu. Akekho owaziyo ukuthi bangubani, kodwa zande kangangokuthi kuhle ukucabanga ukuthi banomsebenzi obalulekile. Mhlawumbe bahlukanisa inqubo eyodwa yezinto eziphilayo, begwema ukuphazanyiswa.

Noma mhlawumbe lokhu kuyindlela ephumelelayo yokwakha indiza enkulu yokusebenza, ngoba izinqubo eziningi zezinto eziphilayo zenzeka ezinqenqemeni, lapho izakhi ze-enzyme namanye ama-molecule asebenzayo angeneka khona. Noma yikuphi umsebenzi we-polyhedra emvelo, ungakhathazeki ukudala iziyalezo eziyinkimbinkimbi zofuzo, ngoba imithetho ye-physics izokukwenza.

Ezinye izimvemvane zineziphahla ezinamaphiko eziqukethe i-labyrinth ekhethiwe yento ehlala njalo okuthiwa i-chitin. Umthelela wamagagasi okukhanya okuphuma emagqumeni ajwayelekile kanye nezinye izakhiwo ezingaphezulu kwephiko liholela ekutheni amanye ama-wavelengths (okungukuthi, eminye imibala) ayanyamalala, kanti abanye baqinisa omunye nomunye. Ngakho, isakhiwo se-polygonal sinikeza izindlela ezinhle kakhulu zokukhiqiza umbala wesilwane.

Ukuze wenze amanethiwekhi anqunywe amaminerali anzima, ezinye izinto ezibonakalayo zakha uhlobo lwezinambuzane eziguquguqukayo eziguquguqukayo, bese zikhanyela izinto eziqinile ngaphakathi komunye wamanethiwekhi wokuxhumana. I-honeycomb isakhiwo sezitshalo ezincane ezingenawo ngaphakathi emineni e-chitinous yegundane elwandle elingavamile eyaziwa njengegundane lolwandle liguqulela lezi zakhiwo ezinjengezinwele zibe yizintambo zemvelo ezikwazi ukuqondisa ukukhanya, ziguqule kusuka ezibomvu zibe ziluhlaza okwesibhakabhaka kuye ngokuqondisa kokukhanyisa. Lokhu kuhlotshaniswa kungasiza ekuvimbeleni izidumbu.

Imvelo ibonakala kakhulu

Umhlaba wezitshalo nezilwane ugcwele izibonelo ze-polyhedra eziphilayo eziphilayo, kanye nezwe elingapheli lamatshe namaminerali. Kusukela ekubonweni okuziphendukela kwemvelo, isakhiwo se-hexagonal ngumholi ekukhuliseni amandla okusetshenziswa kwamandla. Ngaphezu kwezinzuzo ezibonakalayo (ukugcina isikhala), ama-polyhedral grids ahlinzeka ngobuningi bombuso, ngakho-ke, inani lomakhelwane landa, elinomphumela omuhle kulo lonke isakhiwo. Umphumela wokuphela kwalokhu ukuthi ulwazi landa ngokushesha kakhulu. Kungani i-hexagonal kanye ne-stellate polyhedra engavamile emvelo injalo? Mhlawumbe, ngakho-ke kuyadingeka. Umoya uyazi kangcono, uyazi kangcono.