Geesoolayaashu Convex. Qeexid geesoole convex. The diagonals geesoole convex

Kuwani waa qaababka joomateri oo dhan nagu wareegsan. geesoolayaashu Convex waa dabiiciga ah, sida awlallada malabka ama aan dabiici ahayn (nin sameeyey). tirooyinka waxaa loo isticmaalaa in soo saara noocyada kala duwan ee blaastiigga farshaxanka, naqshadaha, isku sharraxdid, iwm geesoolayaashu Convex leeyihiin hantida in dhibcood ay been ka on hal dhinac oo ah xariiq toosan in maraa labada ciyaaryahan ee geesaha xiga ee tiradaasi joomatari. Waxaa jira sharaxyo kale. Waxaa loo yaqaan geesoolayaasha ku convex, oo waxaa loo qabanqaabiyaa in hal bar-diyaarad si ixtiraam leh in kasta oo line toos ah oo ay ku jiraan mid ka mid ah dhinac.

geesoolayaashu convex

In koorsada of geometry hoose waxaa mar kasta loola dhaqmo geesoolayaashu aad u fudud. Si loo fahmo sifooyinka qaababka joomateri ee aad u baahan tahay si ay u fahmaan oo ay dabeecadda. Si aad u bilaabaan si ay u fahmaan in ay u xiran yahay line kasta oo darafyadiisa oo waa isku mid. Oo tiradaasi u uumay by, waxay yeelan karaan noocyo kala duwan oo gaadmada ah. Geesooleyaasha waxaa lagu magacaabaa polyline xiran fudud kuwaas oo halbeeg ku xiga aan ku taalla mid ka mid ah line toos ah. Its links iyo qanjidhada yihiin, siday u kala horreeyaan, dhinacyada oo dushooda tiradaasi joomatari. polyline A fudud waa in ayan marnaba jareyso.

geesaha of geesoolayaasha waxaa loo yaqaan jaarka, haddii ay dhacdo ay yihiin darafyadiisa oo mid ka mid ah dhinac. tiradaasi A joomateri, taas oo uu leeyahay tiro n-aad ee geesaha ah, iyo halkan tirada n-aad ee dhinacyada ugu baaqay n-gon ah. Laftiisa line jabay waa soohdinta ama dusha of tiradaasi joomateri. Diyaarad Polygonal ama geesoolayaasha guri yeedhay qaybtii ugu danbaysay ee diyaarad kasta oo, ay xadidan. dhinac ku xiga ee tiradaasi joomateri yeedhay qaybaha polyline asal ahaan ka soo vertex isku. Iyagu ma ay noqon doonaan deriska haddii ay ku salaysan yihiin geesaha kala duwan ee geesoolayaasha ah.

sharaxyo kale ee geesoolayaashu convex

In geometry hoose, waxaa jira dhowr wax u dhigma in sharaxyo macnaha, taasoo muujinaysa waxa la yiraahdo geesoolayaasha a convex. Waxaa intaa dheer, statements oo dhan si siman run. geesoolayaasha A convex waa mid ka mid ah in uu leeyahay:

• gabal kasta oo isku xirta laba barood oo kasta waxaa gudahood, been gebi ahaanba waxa ku jira;

• dhexdeeda jiifsan dhan diagonals daayee;

• xagal gudaha kasta oo aan ka badan 180 ° weyn.

Geesooleyaasha had iyo jeer kala qaybinaya diyaarada laba qaybood. Mid ka mid ah iyaga ka mid ah - ay ku koobnayn (waxaa lagu soo lifaaqay karaa goobo a), iyo kale - aan xad lahayn. ugu horeeyay waxaa lagu magacaabaa gobolka ugu hooseeyey, oo kii labaadna wuxuu ahaa - meesha sare ee tiradaasi joomateri. Tani waa isgoyska of geesoolayaasha ah (si kale loo dhigo - qayb wadarta) dhowr bar-diyaaradood. Sayidka, qeybta kasta isagoo darafyadiisa at dhibcood oo ka tirsan geesoolayaasha a gebi ahaanba iska leh isaga.

Noocyo of geesoolayaashu convex

Qeexid geesoolayaasha convex ma tilmaamaya in ay jiraan noocyo badan oo iyaga ka mid ah. Oo mid kasta oo iyaga ka mid ah waxay leedahay shuruudo gaar ah. Sayidka, ka geesoolayaashu convex, kaas oo ay leeyihiin xagal gudaha ee 180 °, gudbiyo yar convex. Tirada convex joomateri in uu leeyahay saddex danbow, waxaa loo yaqaan xagal, afar - afargeesle, shan - geeska, iwm kasta oo ka mid ah convex n-gons kulmay soo socda looga baahan yahay oo muhiim ah: .. N waa in uu ahaado siman yahay ama uu ka weyn yahay 3. Mid kasta oo ka saddexagal waa convex. Tirada joomateri ee noocan ah, taas oo geesaha oo dhan ku yaalaan on goobada, loo yaqaan goobada Isasaaray. Ku tilmaamay geesoolayaasha convex waxaa lagu magacaabaa haddii dhinacyada oo dhan ay ku wareegsan goobada inaad iyada taabato. Laba geesoolayaashu waxaa lagu magacaabaa siman kaliya ee kiiska marka la isticmaalayo dahaadhaa ah lagu dari karaa. geesoolayaasha Flat yeedhay diyaarad polygonal (qaybtii diyaarad a) in this tirada joomatari kooban.

geesoolayaashu joogtada ah convex

geesoolayaashu joogto ah u yeedhay qaababka joomateri ee la xaglo iyo dhinac loo siman yahay. iyaga Inside jiro hal dhibic 0, taas oo ah masaafo la mid ah ka soo kasta oo geesaha ay. Waxaa lagu magacaabaa xarunta of tiradaasi joomatari. Lines xira xarunta la geesaha of tiradaasi joomateri yeedhay apothem, iyo kuwa ku xirmaan barta 0 iyada oo labada dhinac - Fatuuq.

leydi saxda ah - square. xagalka isle waxaa lagu magacaabaa isle. Waayo, qaababka sida jiro xukunka soo socda: kasta xagal geesoolayaasha convex waa 180 ° * (n-2) / n,

halkaas oo n - tirada geesaha of tiradaasi convex joomateri.

degaanka ee geesoolayaasha caadiga ah waxaa lagu go'aamiyaa formula ah:

S = p * h,

halkaas oo p waxa ay le egtahay wadarta dhammaan dhinacyada geesoolayaasha badhkiis, iyo h waa apothem oo dhererkiisu.

Guryaha geesoolayaashu convex

geesoolayaashu Convex leeyihiin guryaha qaarkood. Sayidka, qeybta xiriirisa laba dhibcood ka mid ah tiradaasi joomateri, qasab ku yaalla waxa ku jira. caddayn:

Ka soo qaad in P - geesoolayaasha ku convex. Qaado laba dhibcood loo aabo yeelin, tus, A iyo B, kaas oo ka tirsan P. By qeexidda hadda geesoole convex, dhibcood kuwan waxaa ku yaal hal dhinac oo khadka si toos ah in ka kooban yahay jihada kasta R. awgeed, AB kale oo uu leeyahay hantida iyo waxa uu ka koobanyahay R. A geesoolayaasha convex had iyo jeer laga yaabaa in lagu kala qaybiyey dhowr saddexagal gabi ahaanba diagonals oo dhan, kaas oo lagu qabtay mid ka mid ah geesaha ay.

Xaglaha qaababka joomateri convex

Xaglo geesoolayaasha a convex - waa xaglo in loo sameeyay ay labada dhinac. rukun Inside yihiin aagga gudaha tiradaasi joomateri. xagal ah in la aasaasay by dhinac oo isugu at vertex ah, yaqaana xagal ee geesoolayaasha ku convex. Corners ku xiga in labada geesood gudaha ee tiradaasi joomatari, loo yaqaan dibadda. geeska kasta oo ka geesoolayaasha a convex, diyaarin waxaa gudaha, waa:

180 ° - x

halkaas oo x - qiimaha baxsan geeska. formula fudud waa mid ku habboon in nooc kasta oo ka mid ah qaababka joomateri ee sida.

Guud ahaan, labada geesood ka baxsan jira ka dib markii xukunka: kasta xagal geesoolayaasha convex loo siman yahay farqiga u dhexeeya 180 ° iyo qiimaha xagal gudaha. Wuxuu yeelan karaa qiimaha laga bilaabo -180 ° 180 °. Sidaas awgeed, marka xagal hoose waa 120 °, muuqaalka yeelan doontaa qiimaha a of 60 °.

wadarta xaglo geesoolayaashu convex

Wadarta xaglaha oo ka mid ah gudaha geesoole convex waxaa lagu taagaa formula ah:

180 ° * (n-2),

halkaas oo n - tirada geesaha of n-gon ah.

Wadarta xaglaha geesoolayaasha of a convex waxaa loo xisaabiyaa arrin fudud. Tixgeli qaab kasta sida joomateri. Si loo go'aamiyo wadarta xaglaha geesoolayaasha convex u baahan tahay in lagu xiro mid ka mid ah geesaha ay geesaha kale. Sidaas darteed ficilkan jirsado (n-2) ee saddexagalka. Waxaa la og yahay in wadarta xaglo xagal kasta oo had iyo jeer waa 180 °. Maxaa yeelay tiradoodu geesoolayaasha kasta oo u dhiganta (n-2), wadarta xaglo gudaha ee tiradaasi u dhigmaa 180 ° x (n-2).

Inta geesood geesoolayaasha convex, kuwaas oo, laba xaglaha isku qabsan kasta oo gudaha iyo dibadda iyaga, in this tirada joomateri convex mar walba noqon doonaa si siman u 180 °. Iyadoo ku saleysan, waxaynu go'aamin karnaa in wadarta labada geesood oo dhan:

180 n x.

Wadarta xaglaha oo ka mid ah gudaha waa 180 ° * (n-2). Iyadoo la raacayo, wadarta dhan geesood sare ee tiradaasi dhigay by formula ah:

180 ° * n-180 ° - (n-2) = 360 °.

Sum of xaglo dibadda ee geesoolayaasha kasta convex mar walba noqon doonaa si siman u 360 ° (iyadoon loo eegayn tirada dhinacyadeeda).

geeska ka baxsan geesoolayaasha a convex guud ahaan wakiil ka faraqa u dhexeeya 180 ° iyo qiimaha xagal gudaha.

guryaha kale ee geesoolayaasha a convex

Ka sokow sifooyinka aasaasiga ah ee xogta tirokoobyada joomateri, waxay sidoo kale leeyihiin oo kale, oo waxay dhacdaa marka iyaga taabato. Sidaas darteed, mid ka mid ah geesoolayaashu loo kala qeybin karaa convex badan n-gons. Si arrintan loo sameeyo, sii wadaan in ay mid kasta oo dhinac ka gooyay qaabka joomateri ay weheliyaan kuwaas khadadka toosan. Kala jabeen geesoolayaasha kasta oo dhowr qaybood convex waxaa suurtagal ah iyo si sare ee mid kasta oo burburiyey ku beeganto oo dhan geesaha ay. From tiradaasi joomatari noqon kartaa mid aad u fudud in la sameeyo saddexagal dhex diagonals dhan oo ka yimid mid ka mid vertex. Sayidka, geesoolayaasha kasta, ugu dambeyntii, waxa loo qaybin karaa tiro cayiman oo saddexagal, taas oo aad u faa'iido badan ee hawlaha kala duwan ee la xiriira muuqaalada joomatari oo kale.

wareega ee geesoolayaasha ku convex

The qeybaha kala duwan ee polyline ah, dhinacyada geesoolayaasha lagu magacaabo, inta badan tilmaamay la waraaqaha soo socda: ab, bc, cd, de, EA. Tani dhinac oo tiradaasi joomatari la geesaha a, b, c, d, e. wadarta dheer oo ka mid ah dhinacyada geesoolayaasha a convex waxaa loo yaqaan ay wareega.

goobada ee geesoolayaasha ah

geesoolayaashu Convex laga yaabaa in lagu soo galay oo ku tilmaamay. Taabte Circle dhammaan dhinacyada tiradaasi joomateri, loo yaqaan Isasaaray Naxariis u galay. geesoolayaasha Tan waxaa lagu magacaabaa tilmaamay. goobada dhexe oo lagu qoro geesoolayaasha waa dhibic ka mid ah isgoyska of bisectors xaglaha gudahood qaab siiyey joomateri. degaanka ee geesoolayaasha waa loo siman yahay si ay:

S = p r *,

halkaas oo r - gacan ku goobada Isasaaray Naxariis, iyo p - semiperimeter geesoolayaasha this.

goobaabin A oo ka kooban geesaha geesoolayaasha ah, lagu magacaabo ku tilmaamay, waxay u dhow. Intaas waxaa sii dheer, taas tiradaasi joomateri convex la yiraahdo Isasaaray. xarunta goobada, kaas oo lagu qeexay ku saabsan geesoolayaasha noocan oo kale ah waa wax-u barta isgoyska a midperpendiculars dhinacyada oo dhan.

qaababka joomateri convex dadab

The diagonals geesoole convex - qeybta ah isku xira geesaha aan deriska ah. Mid kasta oo iyaga ka mid ah waa gudaha tiradaasi joomateri. Tirada diagonals ah n-gon ayaa lagu wadaa sida ay caanaha,

N = n (n - 3) / 2.

Tirada diagonals geesoole convex kaalin muhiim ah in geometry hoose. Tirada saddexagal (K), kaas oo laga yaabaa in jebin geesoolayaasha kasta convex, xisaabiyaa by formula soo socda:

K = n - 2.

Tirada diagonals geesoole convex mar walba ku xidhan tahay tirada geesaha.

Barzakh geesoole convex

Xaaladaha qaarkood, si ay u xalliyaan hawlaha joomatariga lagama maarmaan ah in ay jebiyaan geesoolayaasha a convex dhowr saddexagal leh diagonals non-intersecting. dhibaatadan loo xalin karo iyadoo la fogeynayo formula gaar ah.

Qeexida dhibaatada: wac nooca saxda ah ee Risaalo of convex a n-gon dhowr saddexagal by diagonals in jareyso kaliya ee geesaha of tiradaasi joomateri.

Solution: Ka soo qaad in P1, P2, P3, ..., Pn - sare ee n-gon ah. Number Xn - tirada qoruhu ay. Si taxaddar leh u fiirsada keentay tiradaasi joomateri dadab Pi Pn. In mid ka mid ah maqaal qoruhu si joogto ah P1 Pn iska leh xagal gaar ah P1 Pi Pn, taas oo 1

Ha i = 2 waa koox ka mid ah maqaal qoruhu si joogto ah, had iyo jeer ka kooban dadab P2 Pn. Tirada qoruhu ku jira waxa ku jira, si siman u tirada qoruhu (n-1) -gon P2 P3 P4 ... Pn. In si kale loo dhigo, waa loo siman yahay si Xn-1.

Haddii i = 3, markaas ayaa maqaal qoruhu kale kooxda had iyo jeer ku jiri doona a dadab P3 P1 iyo P3 Pn. Tirada qoruhu sax in ku jira kooxda, beeganto doonaa tirada qoruhu (n-2) -gon P3, P4 ... Pn. In si kale loo dhigo, waxa ay noqon doontaa Xn-2.

Ha i = 4, markaas saddexagal dhexdooda Risaalo saxda ah waxay ku xidhan tahay in ay ka kooban yihiin saddex xagalka ah P1 Pn P4, taas oo dhaarsan doonaa afar geesle ah P1 P2 P3 P4, (n-3) -gon P5 P4 ... Pn. Tirada qoruhu sax afargeesle sida uyeelaysaan kuwo X4, iyo tirada qoruhu (n-3) -gon uyeelaysaan kuwo Xn-3. Iyada oo ku saleysan ku qorani, waxaan dhihi karaa in tirada guud ee maqaal qoruhu si joogto ah kuwaas oo ku jira group wuxu u dhigmaa Xn-3 X4. Kooxaha kale, taas oo i = 4, 5, 6, 7 ... jiri doona 4 Xn-X5, Xn-5 X6, Xn-6 ... X7 qoruhu si joogto ah.

Ha i = n-2, tirada qoruhu saxda ah ee koox la siiyo iyadoo tirada qoruhu in kooxda, taas oo i = 2 (si kale loo dhigo, uyeelaysaan kuwo Xn-1) beeganto doonaa.

Tan iyo X1 = X2 = 0, X3 = 1 iyo X4 = 2, ..., tirada qoruhu ee geesoolayaasha convex waa:

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

tusaale ahaan:

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

Tirada qoruhu sax intersecting mid dadab gudahood

Marka hubinta kiisas gaar ah, waxa la malaysan karo in tirada diagonals of n-gon convex waa loo siman yahay si wax soo saarka oo dhan qoruhu of hannaanka shaxda this (n-3).

Caddeynta of this malo: u malaynayaa in P1n = Xn * (n-3), ka dibna wax kasta oo n-gon waxaa loo qaybin karaa (n-2) waa saddex-xagalka ah. Xaaladdan oo kale mid ka mid ah in la Mire Waqaf oo karo (n-3) -chetyrehugolnik. Isla mar ahaantaana, afar geesle kasta waa dadab. Tan iyo markii this tirada joomateri convex laba diagonals la fulin karo, taas oo macnaheedu yahay in wax kasta oo (n-3) -chetyrehugolnikah samayn karaan dheeraad ah dadab (n-3). Iyadoo ku saleysan, waxaannu ku tirinnaa karaa in qoqobkii wax sax ah uu leeyahay fursad uu ku (n-3) Kulanka -diagonali shuruudaha hawshan.

Aagga geesoolayaashu convex

Inta badan, xalinta dhibaatooyinka kala duwan ee geometry hoose waxaa loo baahan yahay si loo ogaado meesha of geesoolayaasha a convex. U qaadan in (Xi Yi.), I = 1,2,3 ... n ka dhigan tahay isku xigxiga oo ka mid ah wadataa dhammaan geesaha deriska la ah ee geesoolayaasha ah, aan lahayn is-isgoysyada. Xaaladdan oo kale, meelaha loo xisaabiyaa by formula soo socda:

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

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