Ezimacala maninzi. Iintlobo ezimacala kunye neempawu zazo

Ezimacala ayiyi kuba nkulu kuphela indawo ephambili geometry, kodwa kwenzeka kubomi bemihla ngemihla wonke umntu. Singasathethi yokufakelwa izinto ezinxulumene ngendlela ezahlukeneyo weepholigoni, ukuqalela kwi bhokisi kunye nesiphelo izinto yokwakha indalo zenzeka ziikristale kwi form of a cube (ityuwa), iintlobo (crystal), iphiramidi (scheelite), octahedra (diamond), njl . d.

Ingcamango emacala, kwiintlobo geometry we polyhedrons

isayensi Geometry iquka icandelo stereometry ojongene iimpawu kunye neempawu ezikhulu milo. Geometric amacala umzimba akhiwa isithuba-ntathu lingqongwe moya (iinkalo) zaziwa ngokuba "polytopes". Iintlobo ezimacala enze ngaphezu kokuba ngabameli kweshumi inani ezahlukeneyo ukuma ubuso.

Kunjalo, bonke ezimacala kufuneka iipropati eziqhelekileyo:

1. Bonke babe amacandelo amathathu elipheleleyo: ubuso (umphezulu polygonal), umphezulu (i-engile eqalisiweyo imiba emhlabeni compound), emphethweni (icala okanye usike iimilo kwasekwa kwisiphambuka ubuso ezimbini).
2. edge polygon nganye inxibelelanisa le ezimbini, yaye ubuso ezimbini kuphela ukuba ngokunxulumene nenye ezikufutshane.
3. Kwexeshana kuthetha ukuba umzimba sizilungise ngokupheleleyo kwelinye kuphela icala moya apho ilala enye ubuso. Lo mthetho usebenza kuzo ubuso onke emacala. Ezi iimilo zejiyometri kwikota geometry eqinileyo ebizwa ezimacala khaxa. Ngaphandle ke ezimacala stellate apho zivela imizimba rhoqo polygonal yemigca.

Ezimacala lungohlulwa lube:

1. Iintlobo ezimacala khaxa, eyenziwa mahlelo alandelayo: eqhelekileyo okanye Classic (kwimilo, iphiramidi, ibhokisi), ekunene (ekwabizwa ngokuba eziqinileyo zikaPlato), nangokuya (igama yesibini - eziqinileyo Archimedean).
2. polyhedrons Non-khaxa (stellate).

Prism kunye neempawu zayo

Geometry njenge geometry candelo ufunda iimpawu zeemilo-ntathu, iintlobo ezimacala (prism phakathi kwabo). Prism wabiza umzimba zejometri ethe efunekayo ubuso ezimbini twatse (ekwabizwa ngokuba iziseko) ulele moya parallel, n-th ka icala elijonge ngohlobo parallelograms. Ngenxa yoko, le iprism kananjalo iintlobo eziliqela, kuquka iintlobo enjalo ezimacala, ezifana:

1. Parallelepiped - lamiswa xa isiseko na parallelogram - buyimilo kunye ngambini-engile amabini aphikisanayo alinganayo ngambini kuzo macala malunga ziyakuvumela.
2. Kwimilo nkqo ukuya kwiziphelo zesiseko.
3. Le bemilo uthambekele luphawulwa angle ngqo (ngaphandle kwe-90) phakathi ubuso noseko.
4. Eyiyo ebonakala iziseko bemilo ngohlobo yipolygon zinamacala alinganayo lateral.

Eyona engundoqo iimpawu prizim:

• iziseko ziyakuvumela.
• Zonke kungqameko bemilo ayalingana kwaye ingqamene omnye komnye.
• Bonke ubuso emibi imilo ye parallelogram.

iphiramidi

Iphiramidi wabiza umzimba zejometri ukuba iqulathe isiseko kunye omnye n-th le ubuso ezingoonxantathu adibanayo kwindawo enye - phezulu. Kufuneka kuqatshelwe ukuba ukuba ubuso icala iphiramidi zimelwe oonxantathu kufuneka, ngoko ke esisiseko kufana buyimilo elingunxantathu okanye Ikwadrilatherali kwaye pentagonal, njalo njalo infinitum intengiso. Kulo mzekelo, igama iphiramidi lihambisana yepholigoni esisekweni. Umzekelo, ukuba isiseko yi iphiramidi unxantathu - iphiramidi olunxantathu, Ikwadrilatherali - quadrangular, etc ...

Iiphiramidi - it konusopodobnye ezimacala maninzi. Iintlobo ezimacala eli qela, ukongeza koku kungentla, nazo zibandakanya ezi bameli balandelayo:

1. iphiramidi rhoqo isiseko se yipolygon, ukuphakama kwayo kulindeleke ukuba embindini kwisangqa ebhaliwe isiseko okanye nezisekelwe ngeenxa zonke.
2. A iphiramidi yoxande senziwa xa omnye kungqameko ecaleni phambana isiseko kwindawo esinekona sasekunene. Kwimeko enjalo, esi ngohlangothi kananjalo ngokuba ukuphakama iphiramidi.

Properties Pyramid:

• Kwimeko apho lonke icala imiphetho iiphiramidi ziyakuvumela (ukuphakama efanayo), bonke ziyadibana isiseko kwi engile mnye, nasesangqeni esisiseko bazobe isangqa kunye kwiziko coinciding kunye ezayo le enekona le iphiramidi.
• Ukuba esisekweni bephiramidi yipolygon, zonke ezinemiphetho osecaleni ezi ziyakuvumela, yaye Ubuso isosceles oonxantathu.

Rhoqo Ipolihedron: iintlobo neempawu ezimacala

Xa stereometrical ziyathandwa umzimba zejometri kunye alingana ngokupheleleyo ezinye iinkalo nganye eziphezulu ze oludityaniswe inani elifanayo iimbambo. La maqumrhu ibizwa ngokuba eziqinileyo zikaPlato, okanye ezimacala rhoqo. Iintlobo ezimacala kunye propati, kukho kuphela amanani amahlanu:

1. Tetrahedron.
2. Hexahedron.
3. Octahedron.
4. Dodecahedron.
5. Icosahedron.

Igama ezimacala lakhe rhoqo kufuneka sobulumko yamandulo yamaGrike uPlato wachaza ezi imizimba zejometri emsebenzini wabo ukuqhagamshela kwabo izakhi yendalo: umhlaba, amanzi, umlilo, umoya. nani Fifth kunikezelwa ezifanayo kunye nokwakheka kwendawo yonke. Ngokutsho kwakhe, iintlekele zemvelo athom bafana iintlobo ezimacala rhoqo. Ngenxa osemqoka bayo bendalo - macala, ezi iimilo zejiyometri umdla omkhulu hayi nje kuphela ngenxa zezibalo yamandulo kunye zobulumko, kodwa ngenxa nabayili bezakhiwo, ngabapeyinti kunye abakroli lonke ixesha. Ubukho kweentlobo-5 kuphela ngokupheleleyo macala ezimacala ingqalelo bebone into ebalulekileyo, bade bawongwa uxhulumaniso yaphezulu.

Hexahedron kunye neempawu zayo

Xa uhlobo ezihlangwini hexahedron uPlato kucingelwa ukufana kunye nobume atom zomhlaba. Kakade ke, ngoku, wawancamisa ngokupheleleyo lo mbono, kodwa, nakuba kunjalo, oku kuphazamisana imizobo modernity ukutsala iingqondo amanani ezaziwayo-kakuhle ezingenamandla ze kubuhle bayo.

Geometry, a hexahedron, yena xa Cube uthathwa ityala eyodwa bhokisi, nto leyo, i uhlobo prism. Ngako oko, le iipropati ezinxulumene iipropati cube prism kuphela umahluko ukuba bonke beskrini kunye neekona cube iyalingana. Kule mihlaba ilandelayo:

1. Zonke Iikona enamacala ezi ziyakuvumela kwaye ilala moya ngaxeshanye ngokuphathelele omnye komnye.
2. Bonke ubuso - izikwere ziyakuvumela (ukuba amagaqa 6), naziphi na leyo kuthathwa njengesiseko.
3. Zonke angles ayalingana intergranal 90.
4. Ukusuka enekona ngalinye inani elilinganayo iimbambo, oko kukuthi 3.
5. Le cube has ezisithoba amazembe yolingano-macala, apho bonke yendlela yokwenza imigca iwela kwindawo ekudibaneni kwe-idayagonali le hexahedron, nezaziwa njengeziko wolingano-macala.

tetrahedron

Tetrahedron - a tetrahedron elintlangothi alinganayo kwimilo zoonxantathu, enekona nganye yazo kwindawo ekuhlangana ezinemiphetho ezintathu.

Iimpawu tetrahedron rhoqo:

1. Zonke ebusweni tetrahedron - a unxantathu alinganayo, nto leyo ithetha ukuba bonke ubuso ye tetrahedron ezi ziyakuvumela.
2. Ekubeni isiseko oyintsobi rhoqo zejiyometri, oko kukuthi, iye amacala alingane, ubuso tetrahedron kwaye idibane kwinkalo enye, ngamanye zonke engile bayalingana.
3. angles Isixa Planar kwi nganye eziphezulu ilingana 180, ekubeni bonke engile bayalingana, nayiphi engile a tetrahedron rhoqo 60.
4. Ngalinye eziphezulu eqikelelwayo ekudibaneni ingongoma eziphakamileyo malungana (orthocenter) ubuso.

Octahedron kunye neempawu zayo

Ichaza iintlobo ezimacala rhoqo, kufanele kuphawulwe ukuba into njengomntu octahedron, leyo ngokwenkangeleko zimelwe njengoko iziseko ezibini ethe Ikwadrilatherali of iiphiramidi rhoqo.

Iimpawu octahedron:

1. kanye igama lequmrhu zejometri ixelela inani ubuso bayo. Octahedron akhiwa 8 oonxantathu ziyakuvumela alinganayo, nganye lilingana nenani ubuso eziphezulu convergent, oko kukuthi 4.
2. Ekubeni zonke Ubuso octahedron ayalingana kunye ezimbombeni zaso intergranal, nganye ngu 60, kwaye angles udibaniso Planar nayiphi na eziphezulu ndlela 240.

dodecahedron

Ukuba simele sicinge ukuba zonke ubuso umzimba zejometri i pentagon rhoqo, ufumana dodecahedron - umzobo yepolygons 12.

Properties dodecahedron:

1. Xa enekona nganye yendlela yokwenza imigca iwela ecaleni kumacala amathathu.
2. Bonke ubuso bayalingana yaye ubude elifanayo iimbambo, kunye indawo ngokulinganayo.
3. Xa dodecahedron 15 namazembe moya yolingano-macala, kunye nayiphi na enye kuzo udlula phakathi ubuso phezulu emphethweni esahlukileyo.

icosahedron

Enye into enika umdla kwe dodecahedron, inani icosahedron imele umzimba zejometri-ntathu 20 enamacala alinganayo. Phakathi iimpawu icosahedron ekunene zezi zilandelayo:

1. Zonke Ubuso icosahedron - isosceles oonxantathu.
2. Xa enekona ngalinye Ipolihedron idibane ubuso ezintlanu, yaye isixa-engile ezikufuphi nayo ezincotsheni 300.
3. Icosahedron iyafana kunye dodecahedron, 15 namazembe moya macala edlula iingongoma embindini ngapha nangapha.

yeepoligoni nangokuya

Koko eziqinileyo zikaPlato, polyhedrons iqela khaxa ikwaquka eziqinileyo Archimedean, ezo polyhedrons thumbanails rhoqo. Iintlobo ezimacala kweli qela le mihlaba ilandelayo:

1. umzimba Geometric bubuso pairwise elilinganayo iintlobo, umzekelo, tetrahedron thumbanails iyafana nje tetrahedron rhoqo, ubuso 8, kodwa umzimba kwimeko-4 ubuso Archimedean ezi yonxantathu ezimise 4 - ezinamacala amahlanu.
2. Zonke angles ezi ziyakuvumela ukuba enekona enye.

stellate ezimacala

iintlobo Abameli neobomnyh imizimba zejometri - polyhedrons stellate, ibobaa yendlela yokwenza omnye komnye. Bangakwazi lisekwa kokudityaniswa izidumbu ezimbini rhoqo-ntathu okanye ngenxa nokuqhubeka ubuso babo.

Ngenxa yoko, ezifana eyaziwayo stellate ezimacala njengokuba: imilo stellate of an octahedron, dodecahedron, icosahedron, cuboctahedral, icosidodecahedron.