Yeepoligoni khaxa. Inkcazzo buyimilo khaxa. I idayagonali ye buyimilo khaxa

Ezi iimilo zejiyometri yonke indawo. Khaxa iimilo ezimacala maninzi zendalo, ezifana lobusi okanye eyenziweyo (umntu). La manani asetyenziswa ekuveliseni iintlobo ezahlukeneyo Ipeyinti kwimizobo, ukwakha, zobuhlalu, njl yeepoligoni khaxa babe yempahla amanqaku zabo kulala kwelinye icala umgca othe ngqo ugqithayo kuwo kwisibini of eziphezulu ezikufutshane lo mzobo zejometri. Kukho nezinye iingcaciso. Oku kubizwa polygon khaxa, nto leyo yahlulahlulwe enye enesiqingatha-moya ngokuphathelele kuwo nawuphi na umgca ngqo elinye macala.

yeepoligoni khaxa

Ekuhambeni we geometry samabanga zisoloko baphathwa yeepoligoni elula kakhulu. Ukuze siqonde iimpawu iimilo zejiyometri ufuna ukuqonda ubunjani bawo. Ukuqala ukuqonda ukuba evaliweyo yiyo nayiphi na umgca yakhe kwaseziphelweni ziyafana. Kwaye ke inani kwakhiwa kuyo, anokuba ezahlukahlukeneyo ukucupha. Polygon kuthiwa Somzobo onamacala amaninzi elula evaliweyo iiyunithi zabo ezikufutshane ungekho kulizwe kumgca enye ngqo. amakhonkco ayo neendawo ke, ngokulandelelana, emacaleni kunye kwiincopho mzobo zejometri. A Somzobo onamacala amaninzi elula kufuneka akufanele ahlangane ngokwayo.

eziphezulu ze polygon zibizwa ngokuba abamelwane, xa kunokwenzeka ukuba iziphelo elinye macala. A inani zejiyometri, eye n-th iqela eziphezulu, yaye ngenxa yoko i-n-th inani amaqela ebizwa ngokuba n-gon. Wona umgca yaphukile lowo umda okanye imiqolo yayo mzobo yemigca. moya Polygonal okanye yepholigoni caba ebizwa inxalenye yokugqibela nayiphi moya, umda wabo. amacala ezikufutshane lo mzobo zejometri ebizwa ziqwempu Somzobo onamacala amaninzi avela ukusuka enekona enye. Abayi kuba abamelwane ukuba zisekelwe eziphezulu ezahlukeneyo polygon.

Ezinye iinkcazelo yeepoligoni khaxa

Geometry samabanga aphantsi, kukho alingana eziliqela kwiinkcazo intsingiselo, ebonisa into ebizwa buyimilo khaxa. Ngaphezu koko, zonke ezi ngxelo ziyinyani ngokulinganayo. A polygon khaxa nguye oye:

• kwilungu ngalinye esithungelanayo naziphi na iingongoma ezimbini ngaphakathi kwayo, ubuxoki ngokupheleleyo kulo;

• kulala kuyo yonke idayagonali zayo;

• nawuphi na engile elingaphakathi umkhulu 180 °.

Polygon usoloko yahlula moya ibe ziinxalenye ezimbini. Omnye wabo - i umda (oko ngumluko isangqa), kunye nezinye - mda. Eyokuqala kuthiwa kummandla yangaphakathi, kwaye eyesibini - ummandla olungaphandle mzobo yemigca. Oku ekudibaneni kwe polygon (ngamanye amazwi - ingxenye iyonke) eziliqela isiqingatha-moya. Ngenxa yoko, esinye nganye iziphelo kwiindawo ziphantsi buyimilo fanele ngokupheleleyo kuye.

Iintlobo yeepoligoni khaxa

Inkcazo polygon khaxa ayibonisi ukuba zininzi iintlobo zazo. Yaye ngamnye kubo criteria ethile. Ngenxa yoko, iimilo khaxa, nto leyo ibe engile yangaphakathi 180 °, ekuthethwe khaxa kancinci. Lo mzobo lwezibalo khaxa oluthixo iincopho ezintathu, kuthiwa unxantathu, ezine - Ikwadrilatherali, ezintlanu - pentagon, njl ngalinye khaxa n-gons idibana nezi mfuno zilandelayo ibalulekileyo: .. N kufuneka ilingana no okanye inkulu ngaphezu 3. ngalinye oonxantathu yi khaxa. Lo mzobo zejometri kule hlobo apho zonke eziphezulu zimi isangqa, ebizwa kwisangqa sibhalwe. Wachaza polygon khaxa ubizwa ukuba zonke namacala aso ngeenxa kwisangqa ukuba umchukumise. eneepoligoni ezimbini zibizwa ngokulinganayo kuphela kwimeko xa usebenzisa okubekwe zinokudityaniswa. polygon Flat ebizwa moya polygonal (a inxenye moya) ukuba eli nani encinane zejometri.

yeepoligoni khaxa rhoqo

yeepoligoni rhoqo ebizwa iimilo zejiyometri kunye engile alinganayo macala. Ngaphakathi kwabo kukho ingongoma 0, nto leyo esigcina sikumgama ophantse ulingane ukusuka ngalinye eziphezulu yayo. Ibizwa ngokuba embindini mzobo zejometri. Lines ohlanganisa embindini kunye eziphezulu lo mzobo zejometri ekuthiwa apothem, nabo ukuqhagamshela ingongoma 0 kunye namaqela - radii.

uxande Lungisa - square. unxantathu alinganayo kuthiwa alinganayo. Kuba iimilo ezinjalo kukho ulawulo ilandelayo: yepholigoni engile nganye khaxa 180 ° * (n-2) / n,

apho n - inani eziphezulu lo mzobo khaxa yemigca.

Ummandla nayiphi yipolygon umiselwa ifomula:

S = p * h,

apho p ilingana isiqingatha udibaniso macala onke polygon, kunye h na apothem ubude.

Properties yeepoligoni khaxa

Khaxa Polygons iipropati ezithile. Ngoko ke, lo belo inxibelelanisa naziphi na iingongoma ezimbini umzobo zejometri, ngokuyimfuneko ibekwe kulo. ubungqina:

Masithi P - polygon khaxa. Thatha amanqaku ezimbini ngendlela engaqondakaliyo, umz, A no-B, ziphantsi P. ngu kwenkcazelo buyimilo khaxa, ezi ngongoma zisendaweni kwelinye icala kumgca othe ngqo equlathe naliphi na icala R. Ngenxa yoko, AB naye lo mhlaba kwaye iqulethwe R. A polygon khaxa njalo zingahlukaniswa oonxantathu eziliqela ngokupheleleyo zonke idayagonali, apho wayebambe esinye eziphezulu yayo.

Angles iimilo khaxa zejiyometri

Eliyi buyimilo khaxa - ezi engile ukuba zenziwe ngamaqela. iikona ngaphakathi kummandla ngaphakathi mzobo yemigca. I-angle eyenziwe emacaleni walo idibane kwindawo enekona, ebizwa ngokuba engile polygon khaxa. Iikona emelene zaso angaphakathi mzobo zejometri, ebizwa yangaphandle. ikona ngalinye buyimilo khaxa, amalungiselelo ngaphakathi kuyo, kuba:

180 ° - x

apho x - ixabiso ngaphandle ikona. Le yokubala elula ukwasebenza naluphi na uhlobo iimilo zejiyometri.

Ngokubanzi, emilenzeni ngaphandle ekhoyo zilandelayo mthetho: ngamnye khaxa yepholigoni engile elingana umahluko phakathi 180 ° kunye nexabiso engile elingaphakathi. Oku kunokuba amanani ukusuka -180 ° ukuya 180 °. Ngenxa yoko, xa angle bangaphakathi 120 °, ukuvela kuya kuba ixabiso ° 60.

Umdibaniso engile zepolygons khaxa

Umdibaniso engile ngaphakathi buyimilo khaxa lusekiwe yi ifomula:

180 ° * (n-2);

apho n - inani eziphezulu ze-n-gon.

Umdibaniso engile ye buyimilo khaxa sibalwa kakhulu nje. Cinga nayiphi imilo zejiyometri. Ukuze ubone inani engile kwi buyimilo khaxa kufuneka ukudibanisa enye eziphezulu zayo kwezinye eziphezulu. Ngenxa yesi senzo ujika (n-2) lo nxantathu. Yinto eyaziwayo ukuba udibaniso engile nawuphi kanxantathu isoloko 180 °. Ngenxa inani labo nayiphi polygon ilingana (n-2), udibaniso engile embindini mzobo ilingana 180 ° x (n-2).

Kwixabiso iikona polygon khaxa, oko kukuthi, naziphi engile ezikufutshane ezimbini zangaphakathi nezangaphandle kubo, kweli nani khaxa zejiyometri uya kusoloko kulingana 180 °. Ngenxa yesi sizathu, siya kumisela udibaniso zonke iikona zayo:

180 x n.

Umdibaniso i engile elingaphakathi 180 ° * (n-2). Ngako oko, udibaniso zonke iikona zangaphandle mzobo ebekwe yi ifomula:

180 ° * n-180 ° - (n-2) = 360 °.

Udibaniso engile kwangaphandle nawuphi na wepoligoni khaxa uya kusoloko kulingana 360 ° (kungakhathaliseki inani emacaleni aso).

kwikona Ngaphandle buyimilo khaxa abantu ngokubanzi zimelwe umahluko phakathi 180 ° kunye nexabiso engile elingaphakathi.

Ezinye iimpawu buyimilo khaxa

Ngaphandle kokuba iimpawu ezingundoqo ze data amanani zejiyometri, babe nezinye, ezithi zivele xa yokuzisingatha. Ngoko, naziphi na weepholigoni ukuze wohlukana khaxa ezininzi n-gons. Ukuze wenze oku, qhubeka ngalinye emacaleni salo, imilo zejiyometri ecaleni ezi imigca ethe ngqo. Sasazaa nayiphi polygon ibe ziinxalenye eziliqela khaxa kunokwenzeka ukuze phezulu nganye amaqhekeza ungqamane zonke eziphezulu yayo. Ukusuka isafobe zejometri kunokuba elula kakhulu ukuba oonxantathu lonke idayagonali ukusuka enekona enye. Ngenxa yoko, nayiphi yepholigoni, ekugqibeleni, lungohlulwa lube inani elithile zoonxantathu, leyo iluncedo kakhulu ekusombululeni imisebenzi eyahlukeneyo enxulumene izimo ezinjalo.

Umjikelezo polygon khaxa

Inxalenye yalo Somzobo onamacala amaninzi, amaqela yepholigoni emacala-ekuthiwa, ngokufuthi kuboniswe kunye neeleta zilandelayo: ab, BC, cd, de, EA. Le icala isafobe zejometri kunye eziphezulu a, b, c, d, e. Umdibaniso ubude macala buyimilo khaxa kuthiwa ikhaya layo.

La manani achazwe kwe polygon

Khaxa eneepoligoni ukuze bengena kuchazwe. Yenza isangqa tanjenti zonke emacaleni mzobo zejometri, kuthiwa ebhalwe kulo. Le polygon ngokuba ichazwe. Ngaphakathi kwelali okubhaliweyo polygon indawo yonqumlo bisectors-engile ngaphakathi imilo lwezibalo elinikiweyo. Ummandla polygon silingana:

S = p * r,

apho r - embindini wesangqa sibhalwe, yaye p - semiperimeter le polygon.

A isangqa equlathe eziphezulu polygon, esibizwa ngokuba ezichazwe kufuphi kuyo. Ngapha koko, eli nani khaxa zejiyometri kuthiwa sibhalwe. Iziko isangqa, elichazwa malunga buyimilo hlobo ebizwa ngokuba yi-ekudibaneni point midperpendiculars macala onke.

iimilo oxwesileyo khaxa zejiyometri

I idayagonali ye buyimilo khaxa - icandelo ukuba eziphezulu exhuma angabamelwane. Ngamnye kubo ngaphakathi eli nani yemigca. Inani idayagonali ye-n-gon umiselwe ngokomgaqo wokubala:

N = n (n - 3) / 2.

Inani idayagonali ye buyimilo khaxa lidlala indima ebalulekileyo geometry aphantsi. Inani triangles (K), nto leyo naphule zonke yepholigoni khaxa, ibalwa le ndlela ilandelayo:

K = n - 2.

Inani idayagonali ye buyimilo khaxa kusoloko kuxhomekeke kwinani eziphezulu.

Ulwahlulo of buyimilo khaxa

Kwezinye iimeko, ukusombulula imisebenzi geometry kuyimfuneko ukuba baphule yepholigoni khaxa zibe oonxantathu eziliqela kunye idayagonali non-ezidibanayo. Le ngxaki ingasombululwa ngokususa indlela ethile.

Ukuchaza ingxaki: ukubiza uhlobo lasekunene lothango ye khaxa n-gon zibe oonxantathu eziliqela idayagonali ukuba phambana kuphela xa eziphezulu ze ngokomzekeliso yemigca.

Isisombululo: Masithi ukuba P1, P2, P3, ..., PN - encotsheni n-gon. Inani Xn - inani zokwahlula yayo. Ngocoselelo cinga kubangela oxwesileyo mntu zejiyometri Pi PN. Xa naziphi na izahlulelo rhoqo P1 PN bobabo unxantathu ethile P1 Pi PN, apho 1

Makhe i = 2 liqela izahlulelo rhoqo, ngamaxesha equlethe oxwesileyo P2 PN. Inani izahlulelo ziqukiwe kuyo, lingana ne ukuya kwinani izahlulelo (n-1) -gon P2 P3 P4 ... PN. Ngamanye amazwi, ukuba uyalingana Xn-1.

Ukuba i = 3, yosinda izahlulelo iqela liya kusoloko i P3 P1 oxwesileyo kunye P3 PN. Inani izahlulelo elichanekileyo ziqulathwe iqela, uya kunye nenani izahlulelo (n-2) -gon P3, P4 ... PN idibana. Ngamanye amazwi, kuya kuba Xn-2.

Makathi i = 4, ngoko ke oonxantathu phakathi ulwahlulo oluchanekileyo ubotshiwe ukugcina unxantathu P1 PN P4, nto leyo eya adjoin le quadrangle P1 P2 P3 P4, (n-3) -gon P5 P4 ... PN. Inani izahlulelo elichanekileyo loo Ikwadrilatherali ilingana X4, kwaye inani izahlulelo (n-3) -gon lilingana Xn-3. Ngokusekelwe ngasentla, singatsho ukuba inani lilonke izahlulelo rhoqo ukuba ziqulathwe kweli qela lilingana Xn-3 X4. Amanye amaqela, apho i = 4, 5, 6, 7 ... kuya kuba 4 Xn-X5, Xn-5 X6, Xn-6 ... X7 zokwahlula rhoqo.

Makhe i = n-2, inani izahlulelo ezichanekileyo kwiqela elinikiweyo uza kuba ngaxeshanye inani izahlulelo kwiqela, apho i = 2 (ngamanye amagama, ilingana Xn-1).

Ekubeni X1 = X2 = 0, X3 = 1 X4 = 2, ..., inani izahlulelo ye polygon khaxa ngu:

Xn = Xn-1 + Xn-2 + Xn-3, Xn-X4 + X5 + 4 ... + X 5 + 4 Xn-Xn-X 4 + 3 + 2 Xn-Xn-1.

umzekelo:

X5 = X4 + X3 + X4 = 5

X6 = X4 + X5 + X4 + X5 = 14

X7 + X5 = X6 + X4 * X4 + X5 + X6 = 42

X7 = X8 + X6 + X4 * X5 + X4 * X5 + X6 + X7 = 132

Inani izahlulelo elichanekileyo ezidibanayo ngaphakathi enye oxwesileyo

Xa uhlola ngabanye, oko kuthathwa ukuba inani idayagonali ye n-gon khaxa ilingana udibaniso lwamaxabiso wonke izahlulelo le ndlela yetshathi (n-3).

Ubungqina yale vekeleke: Ndiba ukuba P1n = Xn * (n-3), ngoko nayiphi n-gon zingahlukaniswa (n-2) unxantathu. Kulo mzekelo omnye kubo zibe yimfumba (n-3) -chetyrehugolnik. Kwangaxeshanye, quadrangle ngamnye oxwesileyo. Ekubeni eli nani khaxa zejiyometri idayagonali ezimbini ingaqhuba iye phandle, nto leyo ethetha ukuba nayiphi na (n-3) -chetyrehugolnikah ukuze aqhube ezongezelelweyo oxwesileyo (n-3). Ngenxa yesi sizathu, sinokugqiba ukuba nanini na isahlulelo esifanelekileyo unalo ithuba (n-3) intlanganiso -diagonali iimfuno kwalo msebenzi.

Area yeepoligoni khaxa

Ngokufuthi, ekusombululeni iingxaki ezahlukeneyo geometry samabanga kukho imfuneko lijonge indawo buyimilo khaxa. Ucinge ukuba (Xi. Yi), i = 1,2,3 ... n imele ukulandelelana zilungelelanise zonke eziphezulu asebumelwaneni ye polygon, ukuba akukho self-ekudibana kuzo. Kulo mzekelo, indawo yayo ibalwa yi le ndlela ilandelayo:

_{S = ½ (Σ (X i} + X i + ₁₎ (Y _{i +} Y _i + _1)),

kuyo (X _1, Y _{1) = (X n +1, Y} n + _1).