Yadda za a yi polyhedron daga takarda. Polyhedrons daga takardun takarda

Abubuwan kaya ba kawai takardun wasiƙa da aikace-aikacen da aka sanya su a cikin nau'ikan samfurori. An samo samfurori masu girma na uku na uku (hoto na 1). Alal misali, za a iya gina takarda polyhedron. Bari muyi la'akari da wasu hanyoyi na aiwatar da shi, ta hanyar zane da hotuna.

Tarihin Figures

Kimiyyar ilmin lissafi na tsohuwar kimiyya ta samo asali a cikin nesa, a lokacin wadata na Romawa da Girka. Bayan haka ya zama al'ada don haɗawa da fasaha da fasaha. Sabili da haka, bisa ga koyarwar Plato (ɗaya daga cikin masu tunanin kirkanci na zamanin Girka), kowane polyhedra, wanda ya ƙunshi wasu lambobi daidai, alama ce guda ɗaya. Hotuna daga triangles - octahedron, icosahedron da tetrahedron - suna hade da iska, da ruwa da wuta kuma suna iya canzawa juna a saboda daidaito daga cikin fuskoki, kowannensu yana da nau'i uku. Ƙasa ta kuma nuna alamar murabba'i na murabba'i. Kuma dodecahedron, godiya ga sassanta na musamman na pentagon, yana da wani aikin da ya dace kuma yana da alamar jituwa da zaman lafiya.

An kuma san cewa ɗaya daga cikin masana lissafin Girka, Euclid, ya tabbatar da koyarwar "Principle" da keɓaɓɓe daga ƙwayoyin platonic da aka ambata da dukiyoyinsu "ya dace" a cikin wuri (photo 2). A polyhedron, wanda aka nuna daga takarda, an sanya shi ta hanyar nada hanyoyi guda ashirin da aka rufe tare. Wannan zane yana nuna alamar yadda za a yi adadi. Bari muyi la'akari dalla-dalla game da dukkan matakai na halittar wani icosahedron.

Yin dentagon

Gidan gine-ginen yana kunshe da magungunan isosceles masu daidaita. Ana iya sauƙaƙewa ta hanyar amfani da layin da aka nuna a Figure 2. Dauki takarda takarda. Sanya shi ashirin kamar girman da siffar triangles, saka su cikin layuka hudu. A wannan yanayin, kowanne fuska ɗaya zai kasance a gefe daya. Ana amfani da samfurin samfurin don yin aikin. Zai bambanta da samfurin basira ta wurin kasancewar alamomi don hadawa tare da dukkan layin waje. Yanke kayan aiki daga takarda, toshe shi tare da layin. Samar da polyhedron daga takarda, rufe matsanancin layuka tsakanin juna. A wannan yanayin, ana sanya nau'ikan da ke cikin kwakwalwa a cikin aya.

Musamman polyhedra

Dukkanin siffofin sun bambanta da juna ta hanyar daban-daban fuskoki da siffar su. Bugu da ƙari, wasu samfurori za a iya hada da takarda guda (kamar yadda aka kwatanta a cikin misalin masana'antun gumaka), wasu - kawai ta tattara daga ɗayan matuka. An yi la'akari da polyhedra na yau da kullum kamar yadda ya dace. Daga takarda da suke yi, suna bin tsarin mulkin daidaitacce - kasancewa a cikin samfurin siffofin gaba daya. Akwai manyan nau'o'i biyar na irin wannan adadi. Teburin yana bada bayani game da sunayensu, adadin da siffofin fuskoki:

Dabbobi masu yawa

Bisa ga nau'in jinsin da aka ba, ta yin amfani da fasaha da tunani, masu sana'a suna tsara nau'i daban-daban na takarda. Dandalin polyhedron zai iya bambanta da samfurori biyar da suka gabata, daga lokaci ɗaya daga fuskoki daban-daban a cikin fuskokin siffofi, misali daga murabba'i da ƙwayoyi. Don haka ana samun jikin jikin Archimedean. Kuma idan kun kalle ɗaya ko fiye da fuskoki, za ku sami adadi mai mahimmanci, kalli duka biyu daga waje da ciki. Don samar da samfurin lantarki, ana amfani da alamu na musamman, an cire su daga takarda mai yawa, takarda mai kyau. Suna yin polyhedron na musamman daga takarda. Shirye-shiryen irin waɗannan samfurori na samar da ƙarin ƙarin, ƙirar masu ɓata. Bari mu bincika hanyoyi yadda za mu gina siffar mai kyau ta amfani da misalin dodecahedron (hoto na 3).

Yadda za a yi daga takarda polyhedron da goma sha biyu a sama: hanyar farko

Irin wannan adadi kuma ake kira tauraron dodecahedron. Kowace daga ta vertices a karkashi ne a yau da kullum Pentagon. Saboda haka, suna yin irin wannan polyhedron na takarda a hanyoyi biyu. Shirye-shiryen masana'antu za su kasance daban-daban da juna. A cikin akwati na farko, wannan daki-daki ne guda (hoto na 4), sakamakon abin da samfurin ya gama. Baya ga manyan fuskoki, zane yana ƙunshe da sassan jiki don haɗawa, godiya ga wanda aka haɗa adadi. Don yin polyhedron a hanya ta biyu, dole ne a yi samfuri daban daban. Bari muyi la'akari da aikin aiki a cikin daki-daki.

Yadda za a yi polygon daga takarda: hanya ta biyu

Yi manyan shaci biyu (hoto na 5):

- Da farko. Rubuta sashi a kan takardar kuma raba shi a cikin sassa biyu. Ɗaya daga cikin mahimmancin ƙirar, ɗayan na biyu an share shi nan da nan don saukakawa. Raba sashi a cikin sassa guda biyar kuma iyakance dukkanin radii ta raguwa. Sakamakon haka, an haɗa nau'i guda biyar masu asali na asosceles. Zato kusa da tsakiya na tsakiya kusa da tsakiyar sashi daidai wannan semicircle, kawai a cikin madubi image. Sakamakon kashi yana kama da ma'aurata biyu lokacin da aka haɗe. Samar da irin waɗannan nau'ikan misalin guda shida kawai. Ana amfani da sashi na biyu, wanda za'a sanya shi cikin ciki.

- Na biyu. Wannan abin kwaikwayon shine tauraron biyar. Yi daidai wannan shafuka guda goma sha biyu. Ana yin polyhedron, kowane taurari tare da iyakar hawan sama an sanya shi a cikin sassa mai nau'i-nau'i kuma an kusantar da fuskoki.

Ana samo cikakkiyar tarin adadi ta hanyar shiga cikin harsuna guda biyu tare da wasu takardun takarda, suna motsa su cikin ciki. Samfurin gyaran samfurin, yana da matsala sosai don sanya su daban a cikin girman. Shirye-shiryen takarda polyhedra ba sauƙin karuwa ba. Don yin wannan, bai isa ba kawai don ba da izni ga dukkan iyakokin waje. Dole ne a auna girman kowane fuskoki. Sai kawai a wannan hanya yana yiwuwa a sami karamin ƙari na ainihin samfurin. Amfani da hanyar na biyu na yin polyhedron, yana da sauƙin yin wannan, tun da zai isa ya ƙara yawan ƙaddarar farko, bisa ga abin da aka buƙata lambar da aka buƙata na sassa daban-daban.