Zonse polygon. Chiwerengero cha mbali ya polygon zonse

Triangle, lalikulu, hexagon - Chiwerengerochi zimadziwika chifukwa pafupifupi aliyense. Koma apa kuti ndi polygon zonse, sadziwa aliyense. Koma izo ziri chimodzimodzi onse akalumikidzidwa zojambula. A polygon zonse amatchedwa amene ali kumathandiza kupeza ngodya zabwino ofanana pakati pa iwo ndi mbali. Chiwerengerochi zambiri, koma iwo ali ndi katundu yemweyo, ndipo akugwira ntchito kwa iwo chilinganizo chomwecho.

Katundu wa polygons zonse

Aliyense polygon zonse, kaya lalikulu kapena octagon, akhoza alembedwa bwalo. Mundawu zofunika kawirikawiri amagwiritsidwa ntchito yomanga kanjedza. Komanso, bwalo akhoza alembedwa polygon ndi. chiwerengero cha mfundo kukhudzana ndi wofanana ndi chiwerengero cha m'mbali mwake. N'kofunikanso kuti bwalo alembedwa mu polygon nthaŵi zonse naye malo wamba. Chiwerengerochi zojambula imvera theorems wina. chipani chilichonse zolondola N-gon chikugwirizana ndi utali wozungulira bwalo mozungulira icho R. Choncho, kuchita masamu pogwiritsa ntchito mfundo zotsatirazi: a = 2R ∙ ° sin180. Kudzera mwa utali wozungulira bwalo angapezeke magulu komanso kukafika kutsogolo kwa polygon a.

Kodi kupeza chiwerengero cha mbali ya polygon zonse

Aliyense zonse N-gon ndi angapo a zigawo ofanana ndi mnzake, imene zimagwira kupanga mzere chatsekedwa. Mu nkhani iyi, wamitundu kumathandiza kupeza ngodya zabwino anapanga ndi phindu chomwecho. Polygons anawagawa yosavuta zovuta. Gulu loyamba zikuphatikizapo makona ndi lalikulu. polygons zovuta ndi nambala yaikulu ya mbali. Iwo monga nyenyezi woboola pakati chithunzi. Mu zovuta mbali zonse polygon amapezeka ndi inscribing iwo bwalo. Apa pali umboni. Lembani polygon zonse ndi chiwerengero umasinthasintha mbali N. Fotokozani mozungulila iye. Funsani utali wozungulira R. Tiyerekezenso kuti ena anapatsidwa N-gon. Ngati nsonga ya m'makona ake kugona pa bwalo ndi wofanana ndi mzake, ndiye dzanja angapezeke mfundo: a = 2R ∙ sinα: 2.

Kupeza chiwerengero cha mbali ya alembedwa makona zonse

Equilateral makona - ndi polygon zonse. Chilinganizo tidzakwatulidwa ntchito zofanana ndi a lalikulu, ndi N-gon. Triangle tidzakambirana chomveka ngati ali yemweyo pamodzi kutalika kwa mbali. The kumathandiza kupeza ngodya zabwino ndi ofanana 60⁰. Kumanga kansalu ndi mbali ya anakonzeratu kutalika a. Kudziwa apakatikati ake ndi kutalika, mungapeze mtengo wa m'mbali mwake. Pakuti ichi tinena ntchito njira kupeza njira kupyolera = ×: cosα, kumene × - apakatikati kapena msinkhu. Popeza onsewo onse ngofanana makona, ife kupeza = B = c. Ngati zili choncho zotsatirazi mawu = B = m'ma = ×: cosα. Mofananamo, ife tikhoza kupeza phindu la zipani mu makona equilateral, koma kudzapatsidwa × msinkhu. Pankhaniyi, izo muno zivute zitani pamaziko a manambalawo. Choncho kudziwa kutalika kwa ×, kupeza mbali ya makona isosceles ntchito chilinganizo A = B = ×: cosα. Pambuyo kupeza mfundo za akhoza kuchita masamu ndi kutalika kwa m'munsi lapansi. Ife ntchito Lingaliro Lovomerezeka la Pythagoras. Timayesetsa m'munsi theka mtengo m'ma: 2 = √ (×: cosα) ^ 2 - (× 2) = √x ^ 2 (1 - Ko ^ 2α): Ko ^ 2α = × ∙ tgα. Ndiye m'ma = 2xtgα. Ndiyo njira yosavuta mungapeze chiwerengero cha mbali ya polygon alembedwa.

Mawerengedwe a m'mbali mwa lalikulu alembedwa bwalo

Ngati wina aliyense polygon zonse alembedwa lalikulu ali mbali ofanana ndi kumathandiza kupeza ngodya zabwino. Kuti lidalembedwa chilinganizo mofanana makona a. Kuwerengetsa mbali ya lalikulu kupyolera mtengo wa opendekera. Taganizirani njira imeneyi mwatsatanetsatane. Amadziwika kuti opendekera bisects njingayo. Poyamba mtengo wake unali madigiri 90. Choncho, awiri anapanga pambuyo kugawa makona anayi. kumathandiza kupeza ngodya zabwino awo pa maziko adzakhala wofanana ndi madigiri 45. Choncho, mbali lalikulu ndi wofanana, ndiko: a = B = m'ma = D = mauthenga e√2 ∙ cosα = 2, pamene mauthenga - ndi opendekera wa apakati kapena m'munsi anapanga pambuyo Chigawo cha kansalu anayi. Iyi ndi njira chabe ya kupeza mbali ya lalikulu ayi. Kukhomereza chithunzi bwalo. Kudziwa utali wozungulira bwalo R, ife tikupeza malangizo a mbali zinayi zofanana. Ife kuwerengetsa izo motere A4 = R√2. The radii wa polygons nthawi zonse masamu ndi chilinganizo R = ndi: 2tg (360 ^O: 2n), kumene - mbali kutalika.

Kodi kuwerengera kukafika kutsogolo kwa N-gon

Kukafika kutsogolo kwa N-gon ndi Uwerenge mbali zake zonse. N'zosavuta kuwerengetsa. Muyenera kudziwa mfundo za zipani zonse. A mitundu ina polygons, pali mitunduyi wapadera. Iwo amalola kupeza kukafika kutsogolo kwa kwambiri msanga. Amadziwika kuti aliyense polygon zonse ali mbali ofanana. Choncho, pofuna kudziwa wozungulira ake, suffices kudziwa mmodzi wa iwo. Ndondomeko kudzadalira chiwerengero cha mbali ya mawonekedwe a. Ambiri, izo zikuwoneka ngati izi: R =, komwe ndi - phindu mbali, ndi N - chiwerengero cha kumathandiza kupeza ngodya zabwino. Mwachitsanzo, kupeza kukafika kutsogolo kwa octagon zonse ndi mbali ya 3 cm, muyenera kuchulukitsa izo ndi 8, ndiko kuti, P = 3 ∙ 8 = 24 masentimita kwa hexagon ndi mbali ya 5 cm kuchita masamu motere :. P = 5 ∙ 6 = 30 cm ndi chifukwa. lililonse polygon.

Kupeza kukafika kutsogolo kwa parallelogram ndi, lalikulu ndi diamondi

Malinga ndi mmene mbali ambiri amachita polygon zonse, kuwerengera wozungulira ake. Izi facilitates kwambiri ntchitoyo. Zoonadi, mosiyana ndi zidutswa zina, Pankhaniyi sizikusoweka kuyang'ana zonse m'manja mwake, moti wa munthu. Mfundo imene ili pa kukafika kutsogolo kwa quadrilateral, ndicho, lalikulu ndi diamondi. Ngakhale kuti ali kanjedza osiyana, chilinganizo chimene wina P = 4a, kumene - mbali. Pano pali chitsanzo. Ngati chipani ndi lalikulu kapena rhombus 6 cm, ife tikupeza wozungulira motere: P = 4 ∙ 6 = 24 masentimita V parallelogram okha zosiyana malangizo .. Choncho, wozungulira ake pogwiritsa ntchito njira ina. Choncho, tiyenera kudziwa kutalika ndipo m'lifupi chithunzi a. Ndiye ife ntchito chilinganizo P = (a + b) ∙ 2. parallelogram amene kumbali zonse ofanana ndi kumathandiza kupeza ngodya zabwino pakati pawo, chotchedwa diamondi.

Kupeza kukafika kutsogolo kwa chinthu cha makona equilateral ndi amakona anayi

Wozungulira bwino equilateral makona angapezeke pa chilinganizo P = 3a, kumene - mbali kutalika. Ngati ndi losadziwika, angapezeke kudzera apakatikati pa. Mu kansalu bwino ndi wofanana ndi mtengo Walira chabe. M'munsi angapezeke mwa Lingaliro Lovomerezeka Pythagorean. Pambuyo adzadziwa mfundo za zipani zonse zitatu, ife kuwerengera wozungulira. Angapezeke ntchito chilinganizo R = munthu + b + m'ma, komwe ndi B - mbali ofanana ndipo ndi - m'munsi ndi. Kumbukirani kuti chinthu cha makona equilateral, ndi = B =, ndiye munthu + B = 2a, ndiye P = 2a + c. Mwachitsanzo, mbali ya chinthu cha makona isosceles ndi wofanana ndi masentimita 4, kupeza maziko ake ndi wozungulira. Kugwira ntchito zowerengetsa phindu Pythagorean hypotenuse ndi √a = ² + ² = √16 + 16 = √32 = 5,65 cm. Ife tsopano kuwerengera wozungulira P = 2 ∙ 4 + 5,65 = 13,65 cm.

Kodi kupeza kumathandiza kupeza ngodya zabwino kwa polygon zonse

A polygon zonse opezeka mu miyoyo athu tsiku lirilonse, mwachitsanzo, mwachizolowezi lalikulu, makona, octagon. Zingatanthauze kuti palibe mosavuta kuposa kumanga kachidutswa nokha. Koma zimenezo ziri pa koyamba. Pofuna kulimbikitsa aliyense N-gon, m'pofunika kudziwa kufunika kumathandiza kupeza ngodya zake. Koma kodi kuwapeza? Asayansi ngakhale wakale ndakhala ndikuyesa kumanga polygons zonse. Iwo anapeza kuti agwirizane iwo mu bwalo. Ndiyeno linanena kufunika mfundo, kulumikiza ndi mizere yowongoka. akayanjana yomanga mosiyanasiyana yosavuta. Mitunduyi ndi theorems zimapezeka. Mwachitsanzo, Euclid mu ntchito yake yotchuka "Home" njira yothetsera mavuto nawo 3-, 4-, 5-, 6- ndi 15 gons. Iye anapeza njira kumanga ndi kupeza kumathandiza kupeza ngodya zabwino ndi. Tiyeni tiwone momwe angachitire izo kwa 15-gon. Choyamba, muyenera kuwerengera ndalama za kumathandiza kupeza ngodya zabwino zam'mimba. M'pofunika ntchito chilinganizo S = 180⁰ (n-2). Choncho, timapatsidwa 15 gon, motero chiwerengero N ndi 15. akazipatsa deta kudziwika ndi kupeza chilinganizo S = 180⁰ (15 - 2) = 180⁰ × 13 = 2340⁰. Tidapeza Uwerenge kumathandiza kupeza ngodya zabwino mkati mwa munthu polygon 15 amaganiza. Tsopano muyenera kupeza phindu ya aliyense wa iwo. Onse kumathandiza kupeza ngodya 15 kuwerengetsera 2340⁰: 15 = 156⁰. Choncho, aliyense ngodya mkati ndi 156⁰, tsopano ndi mkulu ndi kampasi angathe kumanga olondola 15-gon. Koma nanga bwanji zovuta kwambiri N-gon? zaka zambiri asayansi akhala akulimbana ndi vutoli. Anapeza kokha m'zaka 18 ndi Carl Fridrihom Gaussom. Iye anali wokhoza kupanga 65537 lalikulu. Kuyambira pamenepo vutoli mwalamulo maganizo kwathunthu kuthetsedwa.

Mawerengedwe a mbali N-gon mu radians

Kumene, pali njira zingapo chopeza kumathandiza kupeza ngodya zabwino za polygons. Nthawi zambiri iwo mopitirira mu madigiri. Koma tingathe kusonyeza iwo mu radians. Kodi kuchita izo? Chitani motere. Choyamba, ife tikupeza chiwerengero cha mbali ya polygon zonse, kenako kuchotsera therefrom 2. Choncho, timachotsa mtengo: N - 2. kuchulukitsa kusiyana opezeka ndi nambala N ( "PI" = 3.14). Tsopano inu kugawanitsa kuti mankhwala ndi nambala ya ngodya mu N-gon. Taganizirani chitsanzo cha kuwerengetsa deta ya pyatnadtsatiugolnika chomwecho. Choncho, chiwerengero N ndi wofanana 15. Ife ntchito chilinganizo S = N (n - 2): N = 3,14 (15 - 2): 15 = 3,14 ∙ 13: 15 = 2.72. Izi, ndithudi, si njira yokhayo kuwerengera mbali mu radians. Inu akhoza kungoyankha kugawa kukula kwa makona amakhala ndi nambala 57,3. Ndipotu, madigirii ochuluka ndi lofanana radian wina.

Mawerengedwe a kumathandiza kupeza ngodya zabwino mu grads

Kuwonjezera madigiri ndi radians, angelo a polygon zonse, mungathe kuyesa kupeza phindu mu madigiri. Izi zachitika motere. Ife kuchotsera kwa chiwerengero 2 kumathandiza kupeza ngodya zabwino, kugawa kusiyana chifukwa ndi chiwerengero cha mbali ya polygon zonse. Anapeza chifukwa ndi kuchulukitsa ndi 200. Mwa njira, ichi unit wa muyeso wa kumathandiza kupeza ngodya zabwino monga grads, nkomwe ntchito.

Mawerengedwe a kumathandiza kupeza ngodya zabwino kunja N-gon

Aliyense polygon zonse, kuwonjezera zoweta, tingathe kuwerengera komanso ngodya akunja. Mtengo wake mofanana kanjedza ena. Choncho, kupeza ngodya kunja kwa polygon zonse, muyenera kudziwa ubwino mkati. Komanso tiyenera kudziwa kuti Uwerenge kumathandiza kupeza ngodya zabwino awiriwa nthawi zonse madigiri 180. Choncho, mawerengedwe zachitika motere: 180⁰ opanda ngodya lamkati. Ife tikupeza kusiyana. Zidzakhala mtengo wa ngodya pafupi izo. Mwachitsanzo, ngodya mkati a lalikulu ndi madigiri 90, ndiye maonekedwe adzakhala 180⁰ - 90⁰ = 90⁰. Monga tikuonera, n'zosavuta kupeza. njingayo kunja zingatenge mtengo kuchokera + 180⁰ kuti, motero, -180⁰.