Mau iieeaii. Ka helu o nāʻaoʻaoʻelua o kekahi mau iieeaii

Triangle, heʻahā like, hexagon - i ike mau i na kii no ka aneane a pau. Akā, iʻaneʻi i ka mea he regular iieeaii, ike ole a pau. Akā, ka mea, 'o nā mea a pau i ka ia geometric kinona. A regular iieeaii ua kapaia ka mea e loaʻa like pana pua ma waena o lakou iho, a me kaʻaoʻao. Mau oeeo? He nui loa, akā, ka mea a pau i ka mea ia waiwai, a ua pili no ia i ka ia haʻilula.

Waiwai o mau polygons

Kekahi regular iieeaii, ina heʻahā like paha octagon, hiki ke kakauia ma ke kaiapili. Kēia kumu waiwai ua pinepine hoʻohana 'ia i loko o ka hana o ka huahelu. Eia hou, i ka p ÷ ai hiki ke kākauʻia i loko o ka iieeaii a. I ka helu o ka hui 'kumu i mea like me ka helu o kona aoao. Ua mea i nui i ke kaiapili kākauʻia i loko o ka papa iieeaii e i me ia i kekahi, he pono ole waena. Mau geometric oeeo? I malalo iho i kekahi theorems. Ko kekahi 'aoʻao pololei N-gon ua pili i ka ke kahahńnai o ka p ÷ ai a puni ia R. Nolaila, ka mea hiki ke ho omaulia hoʻohana' ana i nā kēia haʻilula: i = 2R ∙ sin180 °. Ma ke kahahńnai o ka p ÷ ai hiki ke loaʻa ole wale na aoao elua, aka, i ke anapuni o ka iieeaii.

Pehea e imi i ka helu o ka aoao o kekahi mau iieeaii

Kekahi regular N-gon ua haku o ka helu ana o Hoʻohana like i kekahi i kekahi, a, i ka wa hui, hana i ka paʻa laina. Ma keia hihia, a pau i ka pana pua i hana kinona i ka ia cia. Polygons i maheleia i noonoo ole a me ka eiiieaena. Ka mua pūʻulu ka loaʻa o ka triangle, a me ka hale ma. Complex polygons i ka nui helu o nāʻaoʻaoʻelua. Ka mea i loaʻa i ka hoku-hoʻokino huahelu. Ma eiiieaena regular iieeaii aoao ua loaʻa ma kakauia ia i loko o ka kaiapili. Eia ka ka maopopo. E kaha i ka papa iieeaii me ka ākeʻakeʻa kumu helu o nāʻaoʻao n. Kākau pili i ka pōʻai a puni ona. E noi i kekahi ke kahahńnai o R. Now manao wale ia kekahi hāʻawiʻia N-gon. Inā i ka wahi o kona mau kihi moe ma luna o ka hoa kanaka, a me ka ewaewa ole i kekahi i kekahi, a laila, hiki ke loaʻa i ka lima ma ka haʻilula: i = 2R ∙ sinα: 2.

Loaa i ka helu o ka aoao o ke kākau mau triangle

Equilateral triangle - mea he mau iieeaii. Haʻilula e e hoopili i ka ia me ia o ka huinahalike, a me ka N-gon. Triangle e e noonoo i pololei ia ina ka mea, i ka ia a me ka lōʻihi o ka mahele. Ka pana pua e like 60⁰. Kükulu i kekahi triangle me ka aoao o ka hoʻoholo ma mua loa o ka. Ike ana i kona Media, a kiekie, e hiki ke 'imi i ka waiwai o kona aoao. No keia, ua hana i kekahi ano o ka loaa i ka haʻilula ma ka = m: cosα, kahi m - Media a me ke kiekie. No nā aoao e like triangle, ua loaa i ka = b. = C. A laila, eʻoiaʻiʻo i ka mea kēia mau māmala'ōlelo i = b. = C. = M: cosα. Like, ua hiki ke loaʻa i ka waiwai o ka 'aoʻao i loko o ka equilateral triangle, akā, e hāʻawiʻia mai e m kiʻekiʻe. Ma keia hihia, ka mea, uaʻana o ke kai e ikaika ma ka kumu o na huahelu. No laila, e ike ana i ke kiekie o ka m, huli i kekahiʻaoʻao o ka isosceles triangle ka hoʻohana 'ana i ka haʻilula A = B = m: cosα. Ma hope o loaa na aiee o ka hiki ke ho omaulia mai o ka loa o ka waihona ipu. Mākou pili i ka theorem o Pythagoras. E imi i ka waihona ipu hapa cia l: 2 = √ (m: cosα) ^ 2 - (m 2) = √x '2 (1 - cos ^ 2α): cos ^ 2α = m ∙ tgα. A laila, e = 2xtgα. A o ka poe noonoo ole ala e hiki ke 'imi i kekahi helu o ka aoao o ka mea kākauʻia iieeaii.

I ka ho omaulia ana o na aoao o ka hale kākauʻia i loko o ka kaiapili

Like kekahi'ē aʻe regular iieeaii kākauʻia heʻahā like, ua like aoao a me ka pana pua. No ka mea, hoʻohana i ka hookahi haʻilula me ia o ka triangle. E huli i kaʻaoʻao o ka huinahalike mea hiki ma ka waiwai o ka mea diagonal. E hoomanao i keia hana ma hou au mamuli. Ua ua ike ia ka diagonal bisects huina. Initially kona waiwai i 90 degere. Ke'ī mai,ʻo nā mea i hanaʻia ma hope o ka mahele ana i ka huinahń triangle. Lākou mau pana pua ma ka waihona ipu nō e like me 45 degere. Alaila, kēlāʻaoʻao o ka huinahalike mea like, i mea: he = b. = C. = B = E e√2 ∙ cosα = 2, kahi e - o ka diagonal o ka huinahalike paha kekahi kumu i hanaʻia ma hope o ke ku e ana o kekahi mau huinahń triangle. Kēia mea,ʻaʻole ka mea wale ala o loaa i ka aoao o ka hale. Kakauia i ka huahelu i loko o ka kaiapili. Ike i ka ke kahahńnai o ka p ÷ ai R, ua loaʻa i ka olelo o ka huinahalike. Mākou e huli ia me penei a4 = R√2. Ke Radii o regular polygons he pōpilikia mai ka haʻilula R = i: 2tg (360 ^{o ke:} 2n), kahi i -ʻaoʻao lōʻihi.

Pehea e hoʻomaulia i ka anapuni o ka N-gon

Ke anapuni o ka N-gon o ka huina o ka a pau kona aoao. He oluolu e hoʻomaulia. Oe Pono eʻike i nā aiee o nā 'aoʻao. No kekahi mau 'ano o nā polygons, he mea kūikawā nā papakuhikuhi. Ka mea, ae 'oe e huli i ke anapuni o ka hailona wikiwiki. Ua ua ike ia kekahi mau iieeaii mea like aoao. No laila, ma ka mea e hoʻomaulia i kona anapuni, ka mea, ke kala i ka ike i ka liʻiliʻi loa i kekahi o ia mau mea. Ka haʻilula e hilinaʻi ma ka helu o ka aoao o ke kinona. Ma mau, ka mea nana e like keia: R = ka, ma ka - waiwaiʻaoʻao, a me N - helu o ka pana pua. No ka laʻana, e imi i ke anapuni o ka papa octagon me kaʻaoʻao o ka 3 knm, e pono e hoonui ia ma ka 8,ʻo ia hoʻi, P = 3 ∙ 8 = 24 knm No ka hexagon me kaʻaoʻao o ka 5 knm he pōpilikia like penei :. P = 5 ∙ 6 = 30 knm, a no laila, no ka. kēlā me kēia iieeaii.

Loaa i ke anapuni o ka parallelogram,ʻahā like a me ka daimana

Ke kaumaha ma muli ehia na aoao e hana ana i ka regular iieeaii, ho omaulia kona anapuni. He nui kōkua ai i nā ka hana. No, ma Akä naÿe i ka'ē aʻe liilii, ma keia hihia, aole ia e pono ai i ka nānā aku i nā mea a pau i kona lima, lawa o ka hoʻokahi. Ma ka ia rula mea ma ke anapuni o ka quadrilateral, i mea,ʻahā like a me ka daimana. I loko nō o ka mea i ka mea, e okoa huahelu, i ka haʻilula no i kekahi P = 4a, kahi o ka -ʻaoʻao. Eia he laʻana. Inā kekahi aoao o ke kuea a me ka rhombus 6 knm, ua loaʻa anapuni penei: P = 4 ∙ 6 = 24 knm V parallelogram mea wale nō e ku pono anaʻaoʻao .. Nolaila, kona anapuni e ka hoʻohana 'ana i kekahi hana. No laila, ua pono e ike i ka loa a me ka laula o ka aka. A laila, pili mākou i ka haʻilula P = (i + b) ∙ 2. parallelogram kona mau aoao a pau like, a me ka pana pua ma waena o ia mau mea, i kapa daimana.

Loaa i ke anapuni o ka equilateral triangle a me ka mau huinahń loa

Anapuni pono equilateral triangle hiki ke loaʻa mai o ka haʻilula P = 3a, kahi i -ʻaoʻao lōʻihi. Inā ka mea, i ike ole ia, ka mea hiki ke loaʻa ma ka Media. Ma ka'ākau triangle mea like i ka waiwai e pono nāʻaoʻaoʻelua. Ke kumu hiki ke loaʻa ma ka Pythagorean theorem. A ma hope iho, eʻike i nā aiee o nā aoao ekolu, ua ho omaulia ana i ke anapuni. Ua hiki ke loaʻa hoʻohana 'ana i ka haʻilula R = i + e + pela aku, ma kahi o ka a + e - like aoao, a me - he kumu. Hoole i loko o ka equilateral triangle, he = E = i, laila, he + a b = 2a, laila, P = 2a + c. No ka laʻana, i kaʻaoʻao o ka isosceles triangle mea like i 4 knm, loaʻa kona kumu a me ka anapuni. Compute i ka waiwai Pythagorean hypotenuse me ka √a = ² + ² = √16 + 16 = √32 = 5,65 knm. Mākou e ho omaulia i ke anapuni P = 2 ∙ 4 + 5,65 = 13,65 knm.

Pehea e loaʻa i ka pana pua o kekahi mau iieeaii

A regular iieeaii ua loaʻa i loko o ko makou mau ola kēlā lā, no ka mea hoike, ka mea mau huinahalike, triangle, octagon. Ua makemake mea ia, aohe mea i hiki pono ma mua, e kūkulu i kēia paukū e pili pū oe ia oe iho. Akā, i ka pono ma mua kilohi. I mea e kūkulu i kekahi N-gon, ia mea e pono ke ike i ka waiwai o kona pana pua. Akā, pehea e oe i loaʻa iā lākou? E like kahikoʻepekema i ua ho'āʻo ana e kūkulu mau polygons. Lakou kii, e pono ia i loko o ka p ÷ ai. A laila, ma luna o ka mea memo o ka nele i ka wahi, ai pili aku ia me ka pololei laina. ka pilikia i wehe pilikia no ka hana o ka poe noonoo ole kinona. Nā papakuhikuhi a me theorems i loaa. No ka laʻana, ka mea Euclid ma kona kaulana hana "Home" no ka pāʻoihana o ka pilikia 'ole i loko o ka 3-, 4-, 5-, 6- a me ka 15-gons. He loaʻa aoao, e kūkulu, a loaʻa i ka pana pua. E ka ike pehea e hana ia no ka 15-gon. Mua, e pono e hoʻomaulia i ka huina o kona Kalaiaina pana pua. He mea pono e hoʻohana i ka haʻilula S = 180⁰ (N-2). No laila, ua hāʻawiʻia mākou i kekahi 15-gon, ma keia hope aku, i ka helu N o 15. hookomoia ka ikeʻikepili, a loaa iho la i ka haʻilula S = 180⁰ (15 - 2) = 180⁰ m 13 = 2340⁰. We loaʻa i ka huina o ka a pau Kalaiaina pana pua o ka 15-kapakahi iieeaii. Ano, e pono e kiʻi i ka waiwai o kela mea keia mea o lakou. All pana pua 15 e hoʻomaulia 2340⁰: 15 = 156⁰. Nolaila, kēlā na huina o 156⁰, e me ke alii, a me ka puni ke? Ieoaeunoai i ka pololei 15-gon. Akā, i ka mea e pili ana i oi luna 'n-gon? He nui na kenekuliaʻepekema i aumeume ana e hoʻoponopono i kēia pilikia. Ua Ua loaʻa wale nō i loko o ka 18th kenekulia ma Carl Fridrihom Gaussom. He ua hiki ke kūkulu i 65537-ahalike. No laila, o ka pilikia ua kauoha aku manaoia loa Wehewehe i nā hāʻina.

I ka ho omaulia ana o ka N-gon huina ma radians

O ka holo ana, loaʻa nō kekahi mau 'ano o ka loaa i ka pana pua o polygons. Loa pinepine ka mea, i mau hōʻailona i loko o degere. Akā, ua hiki ka hoike ia ma radians. Pehea e hana ia? Ke hoomau aku penei. Mua, ua loaʻa mai i ka helu o ka aoao o ka regular iieeaii, a laila, unuhi mea 2. Nolaila, e hele mākou i ka waiwai: N - 2. E hoonui i ke koena unuhi loaʻa ma ka helu N ( "pi" = 3.14). Ano oe wale e puunaue i ka huina hoonui ma ka helu o nā kihi o ka N-gon. i ka hana o ka helu ana i ka 'ikepili o ka ia pyatnadtsatiugolnika noonoo. Penei, ka helu N mea like i ka 15. E pili ka haʻilula S = N (N - 2): N = 3,14 (15 - 2): 15 = 3,14 ∙ 13: 15 = 2.72. Keia, o ka papa, i ka mea wale ala, e hoʻomaulia i ka huina i loko o radians. Oe hiki wale puʻunaue i ka nui o ka huina i degere ma ka helu 57,3. Ma hope o nā mea a pau, no laila, he nui nā degere he mea like me kekahi radian.

I ka ho omaulia ana o pana pua i loko o grads

Ma waho aʻeo ia degere, a radians, pana pua o ka regular iieeaii, e hiki ke ho'āʻo e imi i ka waiwai i loko o degere. Kēia Ua hana like penei. E unuhi mai i ka huina helu 2 pana pua, māheleʻana i ka kūpono likeʻole ma ka helu o nāʻaoʻao o ka mau iieeaii. Loaʻa ka hopena ua hoonuiia ka 200. Ma ke ala, keia pa alima o ka ana o ka pana pua i grads, Ane hiki i hoʻohana.

I ka ho omaulia o ka paia waho pana pua N-gon

Kekahi regular iieeaii, i hou i wahi lulu, ua hiki ke ho omaulia i ka pā kihi. Kona waiwai o ka mea ia e like me ia no ka mea'ē aʻe huahelu. No laila, e loaʻa kekahi mawaho huina o ka regular iieeaii, e pono i ka waiwai o na. Eia, ua ike no ia i ka huina o kēia mau pana pua, he mau 180. No laila, i ka ho omaulia ua hana like penei: 180⁰ hua o ka pahale kihi. Mākou i loaʻa i ka likeʻole. Ka mea, e ia i ka waiwai o ka huina e pili ia ia. No ka laʻana, i ka loko kihi o ka hale, he 90 degere, alaila, i keʻano, e e 180⁰ - 90⁰ = 90⁰. Me mākou ke ike, ia mea maʻalahi ka loaʻa. Mawaho huina e lawe i ka waiwai mai ka + 180⁰ i, pakahi, -180⁰.