Regular polygon. Kuwanda mativi nguva polygon

Triangle, mativi, Hexagon - nhamba idzi vanozivikanwa anenge munhu wose. Asi pano kuti ndiyo nguva polygon, anoziva kwete vose. Asi zviri zvose zvakafanana geometric zvitarisiko. Kugara polygon unonzi ane vakaenzana pamakona pakati pachavo uye kurutivi. Izvi nhamba vazhinji, asi vose vane zvivako, uye anoshanda kwavari zvakafanana payakavakirwa.

Properties nguva dzose polygons

Chero nguva polygon, kana padare kana Zimbabwe Educational, inogona nokudhindwa denderedzwa. Izvi pfuma inokosha rinowanzoshandiswa pakuvaka nenhamba. Mukuwedzera, denderedzwa inogona nokudhindwa polygon uye. Kuwanda kuonana pfungwa akaenzana nokuwanda kumativi acho. Zvinokoshawo kuti denderedzwa nokudhindwa dzose polygon achava naye chimwe muzinda. Izvi geometric Nhamba inozviisa mumwe theorems. Chero pati zvakarurama N-gon chokuita nharaunda yacho denderedzwa kumativi R. Naizvozvo, rinogona rinowanikwa nokushandisa mutoo: a = 2R ∙ sin180 °. Kuburikidza nharaunda yacho denderedzwa anogona kuwanikwa kwete chete mapato asiwo mukomberedzo ane polygon.

How kuwana nhamba kumativi nguva polygon

Chero nguva N-gon rinoumbwa zvinoverengeka zvikamu akaenzana mumwe, iyo, kana zvabatanidzwa, kuumba namahwindo mutsetse. Panyaya iyi, vose pamakona vakaumba zvitarisiko zvakafanana ukoshi. Polygons akakamurwa nyore uye zvakaoma kunzwisisa. Boka rokutanga inosanganisira Triangle uye pachivara. Complex polygons vane hombe wandei kumativi. Ivo zvinosanganisira nyeredzi serin'i nhamba. In kunzwisisa nguva polygon mativi inowanikwa kuburikidza inscribing navo denderedzwa. Heino uchapupu. Wana nguva dzose polygon ane zvemasanga uwandu kumativi n. Tsanangura denderedzwa vakamupoteredza. Bvunza nharaunda R. Zvino fungidzira kuti vamwe wavakandipa N-gon. Kana pfungwa pamakona ayo okurutivi denderedzwa uye akaenzana mumwe, ipapo ruoko inogona kuwanikwa ne nzira: a = 2R ∙ sinα: 2.

Kuwana uwandu mativi yakanyorwa dzose Triangle

Equilateral netriangle - ndiyo nguva polygon. Formula anofanira kuiswa zvakafanana kuti yaiungana, uye N-gon. Triangle ichakurukurwa seanoshanda kana ine chete pamwe nokureba chikamu. The pamakona vakaenzana 60⁰. Kuvaka netriangle pamwe mativi zvakafanorongwa pakureba. Kuziva zvayo evaMedhia uye kukwirira, unogona kuwana kukosha kumativi acho. Nokuti ichi tinoshandisa nzira yokuwana mashoko nzira kuburikidza = X: cosα, apo X - evaMedhia kana kukwirira. Sezvo vose vanobatanidzwa, triangle vakaenzana, tinowana = b = c. Zvadaro chokwadi kune zvinotevera mashoko ane = b = d = X: cosα. Saizvozvowo, tinogona kuwana kukosha mapato muimba equilateral Triangle, asi achapiwa X kukwirira. Muchiitiko chino, zviri projected kuva zvakasimba pahwaro nenhamba. Saka, achiziva kukwirira X, kuwana divi ane isosceles netriangle kushandisa nzira A = B = X: cosα. Awana tsika imwe inogona dzaona kubva urefu zvitsigiro. We kushandisa theorem no kuti Achibvuma pfungwa yaPythagoras. Tinotsvaka pakadarowo hafu ukoshi c: 2 = √ (x: cosα) ^ 2 - (x 2) = √x ^ 2 (1 - Kosi ^ 2α): Kosi ^ 2α = X ∙ tgα. Zvadaro C = 2xtgα. Ndiyo nzira nyore unogona kuwana chero nhamba kumativi yakanyorwa polygon.

Kukarukureta pakati panhivi mativi nokudhindwa denderedzwa

Somumwe dzose polygon yakanyorwa sikweya ane vakaenzana mativi uye pamakona. Kwairi anoshandisa chete payakavakirwa souya netriangle. Change kurutivi mativi zvinogoneka kuburikidza kukosha diagonal. Funga nzira iyi zvizere. Zvinozivikanwa kuti diagonal bisects yorusvingo. Pakutanga kukosha kwayo kwakanga madhigirii 90. Saka, vaviri vari yakaumbwa mushure kugovera rectangular Triangle. pamakona avo nechepasi achava akaenzana madhigirii 45. Saizvozvowo, mumwe kurutivi mativi akaenzana, ndiko: a = b = C = D =, e e√2 ∙ cosα = 2, apo e - ndiro diagonal ane mativi kana nechimwe rakaumbwa pashure weboka ane rectangular Triangle. Izvi handizvo chete nzira yokuwana mativi akaenzana. Zvinyore mufananidzo mudenderedzwa. Kuziva nharaunda yacho denderedzwa R, tinowana chete mativi. We overenga nayo sezvinotevera a4 = R√2. The radii nguva dzose polygons rinowanikwa kubva nzira R = rimwe: 2tg (360 ^o: 2n), uko - divi pakureba.

How kuverenga mukomberedzo pamusoro N-gon

The mukomberedzo of N-gon pakuverengwa yayo yose kumativi. Zviri nyore kuverenga. Unofanira kuziva tsika mapato. Nokuti dzimwe mhando polygons, pane chinokosha Masvomhu. Vanobvumira here kuwana mukomberedzo ane mugove nokukurumidza. Zvinozivikanwa kuti chero nguva polygon ane zvakaenzana mativi. Naizvozvo, kuti overenga mukomberedzo kwayo, zvakatikwanira kuti vanoziva mumwe wavo. The yemaitiro achavaponesa nhamba mativi chimiro. Kazhinji, zvinoita sokunge ichi: R = ane, uko - ukoshi divi, uye N - Nhamba pamakona. Somuenzaniso, kuwana mukomberedzo munhu dzose Zimbabwe Educational ine divi 3 masendimita, unofanira muwande parutivi 8, kureva, P = 3 ∙ 8 = 24 masendimita Nokuti Hexagon ine divi 5 masendimita rinowanikwa sezvinotevera :. P = 5 ∙ 6 = 30 masendimita uye saizvozvo. mumwe polygon.

Kuwana mukomberedzo ane parallelogram, mativi uye nedhaimani

Zvichienderana sei mativi mazhinji anoita nguva polygon, overenga mukomberedzo kwayo. Izvi hwezvekukurukurirana zvikuru basa. Zvechokwadi, mukusiyana kune dzimwe zvidimbu, muchiitiko ichi hakudi kutarisa zvose muruoko rwake, zvakakwana chete. On the ichocho ndechokuti panguva mukomberedzo yacho quadrilateral, ndiko kuti, mativi uye nedhaimani. Pasinei vari manhamba akasiyana, kuti nzira iyo mumwe P = 4a, uko - divi. Heuno muenzaniso. Kana bato iri sikweya kana rhombus 6 cm tinowana mukomberedzo kunotevera: P = 4 ∙ 6 = 24 CM V parallelogram vari chete nevakomana mirayiridzo .. Naizvozvo, ayo mukomberedzo vari kushandisa imwe nzira. Saka, tinofanira kuziva urefu uye upamhi nemifananidzo. Tinobva kushandisa nzira P = (a + b) ∙ 2. parallelogram ane mativi ose akaenzana uye pamakona pakati pavo, rinonzi nedhaimani.

Kuwana mukomberedzo ane equilateral Triangle uye rectangular

Mukomberedzo rworudyi , triangle equilateral anogona kuwanikwa kubva nzira P = 3a, uko - divi pakureba. Kana isingazivikanwi, zvinogona kuwanika kuburikidza muMedhia akapiwa. In netriangle zvakanaka akaenzana ukoshi vari mativi maviri chete. Mujinga anogona kuwanikwa kuburikidza Pythagorean theorem no. Pashure vachaziva zvinokosheswa mapato ose matatu, isu ngaaverenge mukomberedzo. Rinogona kuwanikwa vachishandisa nzira R = munhu + b + c, uko, uye, b - vakaenzana kumativi, uye pamwe - pakadarowo. Yeuka kuti ari equilateral Triangle, ine = b = a, zvadaro + b = 2a, ipapo P = 2a + c. Somuenzaniso, kurutivi ane isosceles netriangle akaenzana 4 cm kuwana chawo uye mukomberedzo. Compute kukosha Pythagorean hypotenuse pamwe √a = ² + ² = √16 + 16 = √32 = 5,65 cm. Tava ngaaverenge mukomberedzo P = 2 ∙ 4 + 5.65 = 13.65 cm.

Sei kuwana pamakona ane dzose polygon

Kugara polygon unowanika hwedu zuva nezuva, somuenzaniso, zvatinosiita sikweya, Triangle, Zimbabwe Educational. Zvaizoratidza sokuti hapana nyore pane kuvaka chidimbu ichi pachako. Asi ndizvo pakutanga kuaona. Kuti kuvaka chero N-gon, zvinokosha kuziva kukosha kwayo pamakona. Asi sei chaunoona navo? Masayendisiti Kunyange kare vave vachiedza kuvaka dzose polygons. Wavaironga kukwanawo muvira denderedzwa. Zvino pamusoro rinoti kudikanwa pfungwa, unobva navo ngaatarire mitsetse. dambudziko racho ragadziriswa nokuda pakuvaka nyore zvitarisiko. Masvomhu uye theorems avapo. Somuenzaniso, Euclid mubasa rake yakakurumbira "Home" nokuti mhinduro matambudziko munyaya 3-, 4-, 5-, 6- uye 15-gons. Akawana nzira kuvaka uye kuwana pamakona. Ngationei kuti kuita izvozvo nokuti 15-gon. Chokutanga, unofanira kuverenga kuwanda kwayo nechomukati pamakona. Zvakakodzera kushandisa nzira S = 180⁰ (n-2). Saka, tiri kupiwa 15-gon, saka, nhamba N ndiyo 15. dzinomiririra known umboo uye kuwana nzira S = 180⁰ (15 - 2) = 180⁰ X 13 = 2340⁰. Tawana Verengai zvose nechomukati pamakona ane 15-mativi polygon. Zvino unofanira kuwana kukosha neimwe. pamakona All 15 kuti Masvomhu 2340⁰: 15 = 156⁰. Nokudaro, mumwe nomumwe womukati angled ndiyo 156⁰, zvino pamwechete nomubati uye kambasi anogona kuvaka yakarurama 15-gon. Asi chii pamusoro zvakawanda yakaoma N-gon? emakore masayendisiti vatamburira kugadzirisa dambudziko iri. It akawanikwa chete muzana remakore rechi18 kubudikidza Carl Fridrihom Gaussom. Akakwanisa kuvaka 65537 akaenzana. Kubvira ipapo dambudziko iri pamutemo zvaiona gadziriswa zvachose.

Kukarukureta of N-gon pakona mu radians

Chokwadi, pane nzira dzakawanda kuwana pamakona ose polygons. Kakawanda vari dzaona pamwero. Asi tinogona kuratidza navo radians. How kuzviita? Munobuda sezvinotevera. Chokutanga, tinoona kuwanda kumativi nguva polygon, uye ipapo bvisa kwazviri 2. Nokudaro, tinowana kukosha: N - 2. Muwande musiyano akawanikwa ari nhamba N ( "Pi" = 3.14). Zvino iwe chete kugovera kuti chigadzirwa nenhamba makona vari N-gon. Funga nezvomuenzaniso pakuverenga humboo zvakafanana pyatnadtsatiugolnika. Saka nhamba N akaenzana 15. Tine kushandisa nzira S = N (n - 2): n = 3,14 (15 - 2): 15 = 3,14 ∙ 13: 15 = 2.72. Izvi Ichokwadi, kwete chete nzira kuverenga pakona mu radians. Unogona kungoti vagovere kukura necheparutivi pamwero nenhamba 57,3. Pashure pezvose, madhigirii zhinji saka kwakafanana imwe radian.

Kukarukureta kuti pamakona mu grads

Mukuwedzera madhigirii uye radians, pamakona ane dzose polygon, unogona kuedza kuwana kukosha pamwero. Izvi zvinoitwa sezvinotevera. We bvisa kubva nhamba 2 pamakona, unonyatsoruramisa zvichiita musiyano nenhamba kumativi nguva polygon. Akawana mugumisiro zvikawanda ne 200. Pakazosvika nzira, chikwata ichi nokuyerwa pamakona sezvo grads, asiri kushandiswa.

Kukarukureta kuti kunze pamakona N-gon

Chero nguva polygon, mukuwedzera kune epamba, tinogona kuverenga zvakare chokunze wekona. Its kukosha kwakafanana mamwe nenhamba. Saka, kuwana zvokunze pakona imwe nguva polygon, unofanira kuziva kukosha munyika. Uyezve, tinoziva kuti kuwanda izvi zviviri pamakona nguva 180 inegumi. Naizvozvo, kukarukureta zvaitwa sezvinotevera: 180⁰ kubvisa yomukati wekona. Tinoona musiyano. Ichava kukosha rekona yakabatana nayo. Somuenzaniso, romukati pakona mativi ari madhigirii 90, ipapo pakaita achava 180⁰ - 90⁰ = 90⁰. Sezvatinogona kuona, zviri nyore kuwana. External angled atore ukoshi kubva + 180⁰ kusvikira ukuwo, -180⁰.