Matarau. Types o matarau me ratou āhuatanga

Matarau kore noho noa i te wahi nui i roto i te āhuahanga, engari puta ano hoki i roto i te ora ia rā o te tangata katoa. E kore e ki te whakahua i te horihori tūemi e pā ana i roto i te whānuitanga o ngā taparau, timata mai i te māti, me te mutu huānga hoahoanga i roto i te āhua puta hoki tioata i te puka o te kupiki (tote), poro (karaihe), koeko (scheelite), octahedra (taimana), me ētahi atu . d.

Ko te ariā o te matarau, i roto i ngā momo āhuahanga o polyhedrons

Geometry pūtaiao Kei roto wāhanga stereometry e mahi ki te āhuatanga, me ngā āhuatanga o nuinga āhua. Āhuahanga taha tinana e hanga e i roto i te wāhi e toru-ahu rohe e rererangi (āhuatanga) e mohiotia ana ko "polytopes". Ngā momo o te matarau he neke atu i te māngai tatini o te tau rerekē me te āhua o mata.

Otiia, matarau katoa i āhuatanga noa:

1. E ratou katoa e toru ngā wāhanga wāhi: te mata (mata Tapamaha), te tihi (te koki i hanga i roto i te pūhui āhuatanga whenua), he mata (taha tapahia āhua i hanga i te komititanga o rua mata ranei).
2. Ia mata tapamaha hono te rua, a e rua anake kanohi e te hunga i roto i te pā ana ki tahi i te tahi e pātata.
3. tikanga ana te matakoma e te tino whakaritea te tinana i tetahi anake taha o te rererangi i runga i nei kei tetahi o nga mata. E pā ana te ture ki mata katoa o te matarau. Enei āhua āhuahanga i roto i te wā āhuahanga totoka i huaina matarau koropuku. Okotahi he stellate matarau e kua ahu mai i tinana āhuahanga Tapamaha auau.

Ka taea te wehea matarau ki:

1. Ngā momo o matarau ohu nei, arā, o te akomanga e whai ake nei: tikanga matarohia ranei (he poro, he koeko, he pouaka), tika (i huaina ano hoki totoka Platonic), pē '(te ingoa tuarua - totoka Archimedean).
2. polyhedrons Non-ohu nei (stellate).

Prism me ona āhuatanga

Geometry rite te āhuahanga wehenga e tuatapapa i te āhuatanga o ngā āhua e toru-ahu, momo o matarau (poro i roto ia ratou). ka karanga a Prism tinana āhuahanga kua hiahiatia e rua hoki nga mata ōrite (i huaina ano hoki turanga) e takoto ana i roto i rererangi whakarara, me n-th o te taha anga i roto i te puka o parallelograms. I roto i tahuri, i te poro hoki he maha ngā momo, tae atu taua momo o matarau, pērā i:

1. Parallelepiped - i hanga, no te te turanga ko te tapawhā whakarara - he taparau ki takirua o rua hoariri koki rite, me te rua o ona taha e rite pū takirua.
2. Ko hāngai ki te taha o te turanga poro.
3. Te poro i tahuri āhuatanga e koki autaki (i tua atu i 90) i waenganui i mata me te turanga.
4. Tika āhuatanga turanga poro i roto i te puka o te taparau auau ki taha lateral rite.

Ko te āhuatanga matua o te poro:

• turanga rite pū.
• He rite a whakarara ki ia atu nga taha katoa o te poro.
• kanohi taha katoa i te āhua o te tapawhā whakarara.

koeko

ka karanga a Tara tinana āhuahanga e Kei roto i te turanga, me tetahi o te n-th o nga kanohi tapatoru e hono ana i te wāhi kotahi - te tihi. Me kï reira e te mea e hiahiatia ana i te mata taha o e faahoho'ahia e tapatoru te tara te, ka taea e te turanga rite te taparau tapatoru ranei tapawhā me te pentagonal, a na runga i pānuitanga infinitum. I roto i tenei take, ko te ingoa o te koeko hāngai ki te taparau i te turanga. Hei tauira, ki te ko te turanga, he tara tapatoru - he koeko tapatoru, tapawhā - tapawha, aha ...

Koeko - konusopodobnye reira matarau. Ngā momo o matarau o tenei rōpū, i roto i te tua ki te runga ake, ano ngā te māngai e whai ake nei:

1. koeko te wā he pūtake o te taparau auau, ka matapae tona tiketike e ki te pokapū o te porowhita tuhituhia i roto i te turanga ranei circumscribed a tawhio reira.
2. i hanga te koeko tapawhā te ina whakawhiti tetahi o nga taha taha te turanga i te koki matau. I roto i te take taua, tenei mata pono i huaina ano hoki teitei tara.

Āhuatanga Tara:

• I roto i te take i reira ngā tapa te taha katoa koeko rite pū (i te taua tiketike), īnaki ratou katoa ki te turanga i tetahi koki, me huri noa te turanga e taea te utu i te porohita ki te pokapū coinciding ki te ngä o te akitu o te tara.
• Ki te ko te turanga o te tara i te taparau auau, he rite pū tapa lateral katoa, me nga mata, he waerite tapatoru.

matarau i ia te wā: momo me ngā āhuatanga o te matarau

I roto i te stereometrical noho i te wahi motuhake i te tinana āhuahanga ki te rite rawa ki tetahi ki tetahi āhuatanga te akitu o nei hono te ki te taua maha o rara. E huaina ēnei tinana totoka Platonic, ranei matarau auau. Ngā momo o te matarau ki taua āhuatanga, i reira e rima whika anake:

1. Matawhārite.
2. Papatupu.
3. Matawaru.
4. Tekau mā rua.
5. Matarau tekau.

E hiahiatia ana tona ingoa matarau auau ki te philosopho Kariki tawhito whakaahuatia Platon enei tinana āhuahanga i roto i to ratou mahi, a ki te hono a ratou ki nga mea timatanga o te natura: whenua, he wai, te ahi, te hau. whakawhiwhia ahua rima ritenga ki te hanganga o te ao. E ai ki a ia, māori fakatamaki ngota rite nga momo o matarau auau. Ngā mihi ki tona āhuatanga tino mīharo - hangarite, enei āhua āhuahanga o te moni nui e kore anake mo nga mathematicians tawhito me philosopho, engari ano hoki mo te kaihoahoa, kaipeita me kaiwhakairo o te wā katoa. Ko te aroaro o 5 anake momo ki matarau hangarite tino whakaaro he kitea taketake, whakawhiwhia ara ratou hononga ki te hanahana.

Papatupu me ona āhuatanga

I roto i te puka o-riiwhi papatupu riro Platon faitatau ki te hanganga o ngā ngota te whenua. O te akoranga, inaianei tino ta tenei whakapae, e, Heoi, e kore e pokanoa ki nga drawings me hurihuri ki te kukume i te hinengaro o ngā tau o tona rerehua pai-mohiotia.

I roto i te āhuahanga, whakaaro he papatupu, Cube o ia te he take motuhake o te pouaka, e, i roto i te tahuri, ko te ahua o te poro. Nä, e pā ana te āhuatanga ki ngā āhuatanga kupiki poro ki anake te rerekētanga e he rite tapa katoa me koki o te kupiki. Mai i tenei te āhuatanga e whai ake nei:

1. He āhua rite tapa katoa o te kupiki me takoto i roto i rererangi whakarara ki te faatura ki tahi i te tahi.
2. kanohi katoa - tapawhā rite pū (o te orapa o 6), tetahi o e taea te tangohia rite te pūtake.
3. He rite intergranal 90 koki katoa.
4. Mai ia akitu he maha rite o rara, ara 3.
5. E iwa te kupiki toki o hangarite, e whakawhiti katoa i te mata o te pūtahitanga o te hauroki o te papatupu, tuku ki rite te pokapū o te hangarite.

matawhārite

Matawhārite - he matawhārite ki tapa rite i roto i te āhua o tapatoru, ia akitu o e ko te wāhi komititanga o toru tapa.

Ko te āhuatanga o te matawhārite auau:

1. nga mata katoa o te matawhārite - he tapatoru rite, e te tikanga e he rite pū nga mata katoa o te matawhārite.
2. Mai te mea te ahua āhuahanga auau te turanga, e ko, kua reira rite taha, nga mata o te matawhārite me ūngutungutu i te taua koki, i.e. e rite koki katoa.
3. koki nui planar i ia o nga akitū he rite ki te 180, mai he rite koki katoa, tetahi koki o te matawhārite auau 60.
4. Ia o nga akitū kaupapa mata pūtahitanga o nga wahi tiketike o te ritenga atu (orthocenter) mata.

Matawaru me ona āhuatanga

Whakaahua momo o matarau auau, kia tuhia te reira e ahanoa hei matawaru, e taea te ngā māngai rite rua Katahi turanga tapawhā o koeko auau.

Ko te āhuatanga o te matawaru:

1. Ko te ingoa rawa o te tinana āhuahanga parau te maha o ona mata. Matawaru titoa o 8 tapatoru rite rite pū, ia o nei he rite ki te maha o mata akitū convergent, ara 4.
2. Mai e rite kanohi katoa o te matawaru me intergranal ona koki, ia o nei ko 60, me te moni o te planar koki ko te kupu 240 tetahi o akitū.

tekau mā rua

Ki te whakaaro tatou e te mata katoa o te tinana āhuahanga ko te auau taparima, whiwhi koe i te tekau mā rua - he ahua o 12 taparau.

Āhuatanga papatupu:

1. I ia akitu whakawhiti haere e toru taha.
2. He rite kanohi katoa, me te whai i te roa taua o rara, me wāhi rite.
3. I te tekau mā rua 15 titaha, me rererangi o hangarite, me tetahi tetahi o ratou e tika ana i te waenganui o te mata runga me te mata te ritenga.

matarau tekau

E rite ngā atu i tekau mā rua, e tohu ana matarau tekau ahua te toru-ahu tinana āhuahanga 20 ki taha rite. I roto i te āhuatanga matarau tekau matau ko te whai ake:

1. kanohi katoa o te matarau tekau - waerite tapatoru.
2. I ia akitu o te matarau ūngutungutu rima mata, me te moni o te koki pātata ko 300 tihi.
3. Ko te taua rite me papatupu, 15 titaha, me rererangi o hangarite haere i roto i te ngā waenga o taha ritenga matarau tekau.

taparau pē '

I tua atu totoka platonic, polyhedrons rōpū ohu nei hoki ngā totoka Archimedean, e he rāpopototia polyhedrons auau. Momo o te matarau i roto i tenei rōpū i te āhuatanga e whai ake nei:

1. tinana Geometric He pairwise mata rite o te maha ngā momo, hei tauira, ko te taua rite te matawhārite auau, 8 mata matawhārite rāpopototia, engari i roto i te tinana take 4 mata Archimedean he tapatoru ahuahu me 4 - hexagonal.
2. He āhua rite koki katoa ki te kotahi akitu.

matarau stellate

Māngai momo neobomnyh tinana āhuahanga - polyhedrons stellate, te mata e whakawhiti ki ia atu. Ka taea te hanga e ratou i te hanumi o e rua tinana e toru-ahu auau rite ki te hua o te haere tonu o ratou mata ranei.

Ko te kupu, taua matarau stellate mōhiotia rite: āhua stellate o te matawaru, tekau mā rua, matarau tekau, cuboctahedral, icosidodecahedron.