Khonvekse dikhutlontsi. Tlhaloso ya khutlontsi khonvekse. The diagonals tsa khutlontsi khonvekse

dibopeho tsena tsena tsa thutatekanyo kaofela re potolohileng. Khonvekse dikhutlontsi ba tlhaho, tse kang khekhe ea linotši kapa maiketsetso (monna entsoeng). lipalo tsena li sebelisoa ho hlahisa mefuta e fapaneng ya coatings ka bonono, mehaho, mekhabiso e, joalo-joalo dikhutlontsi khonvekse na le thepa ea hore lintlha tsa bona leshano ka lehlakoreng le leng la mola o otlolohileng le fetelang ka para ea divertise haufi tsa palo tsa thutatekanyo. Ho na le litlhaloso tse ling. Ho bitsoa khutlontsi khonvekse, e leng e lokisetsa e le 'ngoe halofo sefofane mabapi le mola ofe kapa ka kotloloho e nang e' ngoe ea mahlakore a eona.

dikhutlontsi khonvekse

Ha ba ntse ba le geometry mathomo ba kamehla tšoaroa dikhutlontsi e bonolo ka ho fetisisa. Ho utloisisa thepa ya dibopeho tsena tsa thutatekanyo u lokela ho utloisisa lintho tsa tlhaho tsa bona. Ho qala ho utloisisa hore koetsoeng ke mola ofe kapa ofe bao lipheletsong aa tšoana. Le palo thehoa ke e, ho ka ba le mefuta e fapaneng ya diphetolo. Khutlontsi o bitsoa ka tsela e itekanetseng koetsoeng polyline bao haufi diyuniti ha ba teng ka mola e mong otlolohile. maqhama lona le nodes ba, ka ho latellana, mahlakoreng le litlhōrō tsa palo tsa thutatekanyo. A polyline e bonolo ha ea lokela intersect boeona.

divertise tsa khutlontsi li bitsoa baahelani, haeba ba ba lipheletsong tsa e mong oa mahlakoreng a sona. A palo thutatekanyo, e nang le n g-th, palo ea divertise, 'me ka hona ho n g-th, nomoro ya mekga e bitsoa n g-em o sai gon. Ka boeona e robehileng moleng e leng moeli kapa ea moeli ea palo thutatekanyo. Polygonal sefofane kapa a bataletseng khutlontsi bitsoa karolong e qetellang ea sefofane leha e le efe, e fokolang bona. Haufi mahlakoreng tsa palo thutatekanyo bitsoa likarolo polyline tsoang ho tswa vertex tšoanang. Ba ke ke ba ba baahelani ba ha ba li thehiloe divertise e fapaneng ya khutlontsi ena.

Litlhaloso tse ling tsa dikhutlontsi khonvekse

Ka le geometry mathomo, ho na le tse 'maloa lekanang ka litlhaloso moelelo, e leng se bontšang seo e bitsoa khutlontsi khonvekse. Ho feta moo, lipolelo tsena tsohle ke ka tsela e tsoanang ba 'nete. A khutlontsi khonvekse ke eena ea nang le:

• e mong karolo e le hore connects lintlha leha e le efe tse peli tse ka har'a oona, larileng ka ka ho feletseng ka lona;

• ho eona leshano diagonals eohle ea eona;

• efe kapa efe angle hare ha le leholo ho 180 °.

Khutlontsi kamehla e arola ka sefofane likarolo tse peli. E mong oa bona - ho lekanyetsoa feela (ho ka kenyeleditsweng ka lesakaneng a), le tse ling tse - se nang moeli. Pele o bitsoa sebaka ka hare, 'me ea bobeli - sebaka ka ntle la palo thutatekanyo. Sena ke mateanong a litsela tsa khutlontsi le (ka mantsoe a mang - ho motsoako palo yohle) 'maloa halofo lifofane. Kahoo, e mong le e karolo le lipheletsong ka lintlha tseo ho matleng a khutlontsi ka ho feletseng e leng oa hae.

Mefuta e sa tsoaneng ya dikhutlontsi khonvekse

Tlhaloso khonvekse khutlontsi ha bontša hore ho na le mefuta e mengata ea tsona. Le e mong le ba bona ba na le ka litekanyetso tse itseng. Kahoo, dikhutlontsi khonvekse, e na le hlaha ka lehlakoreng le ka hare la 180 °, a bua ka hanyenyane khonvekse. The khonvekse thutatekanyo palo e litlhōrō tse tharo, e bitsoa triangolo, e mene - sekhutlonne, tse hlano - khutlotlhano, joalo-joalo ka mong ea khonvekse n g-gons kopana e latelang ditlhoko tsa bohlokoa: .. N lokela ho lekana le kapa moholo ho feta 3. Kaofela ha dikhutlotharo ke khonvekse. The thutatekanyo mokhabo-mofuta ona oo divertise kaofela ba teng ka selika-likoe, bitsoa lesakaneng ngotsoe. O ile a hlalosa khonvekse khutlontsi o bitsoa ha mahlakore a eona ho potoloha le selika-likoe sa ame hae. dikhutlontsi tse peli li bitsoa lekanang feela tabeng ea ha ba sebelisa koahele ka ho kopantswe. Flat khutlontsi bitsoa polygonal sefofane (a sefofane kabelo) hore ena e fokolang tsa thutatekanyo palo.

Kamehla dikhutlontsi khonvekse

dikhutlontsi kamehla bitsoa dibopeho tsena tsa thutatekanyo le dikhutlo e lekanang le mahlakoreng. Ka hare ho na le ntlha 0, e leng sebaka se tšoanang le e mong le la divertise lona. E bitsoa e le setsi sa palo tsa thutatekanyo. Mela o tlohang setsi le divertise ya palo thutatekanyo bitsoa apothem, 'me ba e hokela ntlha 0 le mekga e - radii.

Nepahetse khutlonne - lisekoere. Matlhakore aa lekanang triangolo o bitsoa matlhakore aa lekanang. Bakeng sa dibopeho tsena joalo ho na le puso e latelang: e mong le e khonvekse khutlontsi angle ke 180 ° * (n g-2) / n g,

moo n g - palo ea divertise ba khonvekse thutatekanyo palo.

Sebakeng khutlontsi efe kapa efe ea kamehla e laolwang ke moralo wa:

S = leq * H,

moo leq o lekana le chelete eo ba ka etsang halofo ea ka mahlakoreng 'ohle ba khutlontsi,' me H ke bolelele apothem.

Properties khonvekse dikhutlontsi

Khonvekse dikhutlontsi na thepa itseng. Kahoo, karolo eo e amahanya lintlha leha e le efe tse peli tsa mokhabo thutatekanyo, hakaalo teng ho eona. bopaki:

Ha re nke hore P - the khonvekse khutlontsi. Nka lintlha tse peli tse hatellang, mohlala, A le B, e leng ho matleng a P. By tlhaloso jwale ya khutlontsi khonvekse, lintlha tsena li fumaneha ka lehlakoreng le leng la otlolohileng hore e na le tataiso efe kapa efe R. Ka lebaka leo, AB boetse e na le thepa ena le ho e leng ka R. A khutlontsi khonvekse kamehla ka 'na ka aroloa ka dikhutlotharo' maloa ka ho feletseng diagonals tsohle, eo e neng e tšoaretsoe mong oa divertise lona.

Dikhutloteng khonvekse dibopeho tsena tsa thutatekanyo

The dikhutloteng tsa khutlontsi khonvekse - ke dikhutloteng tse thehoa ka mekga e. likhutlong ka hare a ka sebakeng seo ka hare tsa palo thutatekanyo. The hlaha ka lehlakoreng le hore Ho thehoa ke mahlakore a eona eo converge ka vertex e bitsoang angle tsa khutlontsi khonvekse. Likhutlong haufi ho likhutlong hare tsa palo tsa thutatekanyo, e bitsoang ka ntle. E mong le e k'honeng ea ka khutlontsi khonvekse, o ile a lokisetsa ka har'a eona, ke ena:

180 ° - x,

moo x, - boleng kantle sekhutlo. Ena moralo e bonolo e sebetsang ho mofuta ofe kapa ofe ya dibopeho tsa thutatekanyo joalo.

Ka kakaretso, bakeng sa likhutlong kantle yo latelang puso ea: e mong le e khonvekse khutlontsi angle lekanang le phapang pakeng tsa 180 ° le boleng ba le hlaha ka lehlakoreng le ka hare. E ka ba le melao ea boitšoaro ho tloha -180 ° ho 180 °. Ka lebaka leo, ha hlaha ka lehlakoreng le ka hare e 120 °, ponahalo e tla ba le boleng ba 60 °.

Balang tsa dikhutlo tsa dikhutlontsi khonvekse

Balang tsa dikhutloteng hare-hare ho ka khutlontsi khonvekse Ho thehoa ke moralo wa:

180 ° * (n g-2),

moo n g - palo ea divertise ea n g-em o sai gon.

Balang tsa dikhutloteng tsa khutlontsi khonvekse e balwa haholo feela ho. Nahana ka leha e le efe joalo thutatekanyo sebopeho. Ho fumana hore na chelete ea dikhutloteng ka khutlontsi khonvekse lokela ho hokela e mong oa divertise lona ho divertise tse ling. Ka lebaka la bohato bona bo fellang kateng le (n-2) triangolo ena. E o tsejoa hore Balang tsa dikhutlo tsa triangolo efe kapa efe e kamehla 180 °. Hobane palo ea tsona e khutlontsi efe kapa efe lekana le (n-2), chelete ea dikhutloteng hare-hare ho motho enoa a lekana le 180 °: x (n g-2).

Tšoana le khonvekse khutlontsi likhutlong, e leng, leha e le efe tse peli tse haufi ka hare le kantle dikhutloteng ho bona, ena khonvekse thutatekanyo palo tla lula ho lekana le 180 °. Motheong ona, re ka fumana hore na chelete ea likhutlong tsohle tsa eona:

180: x n g.

Balang tsa dikhutloteng hare-hare ke 180 ° * (n g-2). Ka lebaka leo, o bala likhutlong tsohle tsa ka ntle tsa palo o behiloeng ke moralo wa:

180 ° * n g-180 ° - (n g-2) = 360 °.

Bala dikhutloteng le Link tsa khutlontsi efe kapa efe khonvekse tla lula ho lekana le 360 ° (ho sa tsotellehe hore palo ea mahlakore a eona).

Kantle k'honeng ea ka khutlontsi khonvekse ka kakaretso emeloang ke phapang pakeng tsa ° 180 le boleng ba le hlaha ka lehlakoreng le ka hare.

thepa tse ling tsa ka khutlontsi khonvekse

Ntle ho thepa ea motheo ya data lipalo tsa thutatekanyo, ba boetse ba na le tse ling tse, e leng se etsahalang ha ho sebetsana le tsona. Kahoo, e 'ngoe ea dikhutlontsi ka aroha multiple khonvekse n g-gons. Ho etsa sena, u tsoele pele ho e mong le e tsa mahlakore a eona le ho e khaola ka sebopeho thutatekanyo hammoho mela tsena otlolohile. Arola khutlontsi efe kapa efe ka likarolo tse 'maloa khonvekse ka etsahala le ho e le hore ka holimo ka mong likotoana le tsamaisane le kaofela divertise lona. From mokhabo jeometeri ka ho ba bonolo haholo ho etsa dikhutlotharo ka diagonals tsohle ho tloha vertex ngoe. Kahoo, khutlontsi efe kapa efe, qetellong, ka aroloa le palo e itseng ea kgutlotharo, e leng molemo haholo ho rarolla mesebetsi e sa tšoaneng tse amanang le tsa dibopeho tse joalo tsa thutatekanyo.

Pherimitha ya khutlontsi khonvekse

The likarolo tsa polyline e, khutlontsi thoeng mekga, hangata a bontša ka mangolo a latelang: ho ka ab, BC, Cd, de Khao, pele.. lehlakoreng lena la mokhabo jeometeri le divertise A, B, se c, le d, e. Balang ba bolelele ba mahlakoreng a khutlontsi khonvekse o bitsoa pherimitha lona.

The sedikiso khutlontsi ho

Khonvekse dikhutlontsi ka kena 'me o ile a hlalosa. Circle tangent ho mahlakoreng 'ohle a palo tsa thutatekanyo, bitsoa ngotsoe ka ho sona. khutlontsi ena o bitsoa a hlalosa. E le setsi lesakaneng eo e ngotsoe khutlontsi ke ntlha ea motsoako ya bisectors tsa dikhutloteng ka hare ho e itseng sebopeho thutatekanyo. Sebakeng khutlontsi le o lekana le:

S = leq dagelever *,

moo a r - the radius ea selika-likoe sa ngotsoe, le leq - semiperimeter khutlontsi ena.

selika-likoe se nang le khutlontsi divertise, bitsoang hlalosoa e haufi le eona. Ho feta moo, ena khonvekse thutatekanyo palo bitsoang ngotsoe. E le setsi lesakaneng, e leng e hlalosoa e mabapi le jwalo khutlontsi ke seo ho thoeng ke motsoako ntlha midperpendiculars mahlakoreng 'ohle.

Diagonale khonvekse dibopeho tsena tsa thutatekanyo

The diagonals tsa khonvekse khutlontsi - karolo hore connects sa boahelani divertise. E mong le e ba bona ba e ka hare palo ena thutatekanyo. Palo ea diagonals ea n g-em o sai gon e behiloeng ka ho ea ka moralo o balletsweng e:

N = n g (n g - 3) / 2.

palo ea diagonals tsa khutlontsi khonvekse phetha karolo ea bohlokoa ka ho le geometry mathomo. Palo ea kgutlotharo (K), e ka 'na ea senya e mong le khutlontsi khonvekse, balwa ka ho ya ka moralo o latelang:

K = n g - 2.

palo ea diagonals tsa khutlontsi khonvekse ke kamehla itšetleha ka palo ea divertise.

Dia a khutlontsi khonvekse

Maemong a mang, ho rarolla le geometry mesebetsi hlokahala hore roba khutlontsi khonvekse ka dikhutlotharo 'maloa le diagonals bao e seng intersecting. bothata bona ka a rarolla ka ho tlosa ea ka moralo o itseng.

Hlalosang bothata: bitsa mofuta tokelo ea dia a khonvekse n g-em o sai gon ka dikhutlotharo 'maloa ke diagonals hore intersect feela ka divertise ya mokhabo thutatekanyo.

Tharollo: Nka hore P1, P2, P3, ..., Pn - tlhōrōng ea n g-em o sai gon. Number Xn - palo ea, partitions lona. Hlahloba ka hloko ho sephetho le diagonale thutatekanyo palo Pi Pn. Ka leha e le efe, partitions kamehla P1 Pn ke ea itseng triangolo P1 Pi Pn, eo ho eona 1

A re ke re kea = 2 ke sehlopha sa, partitions kamehla, kamehla nang diagonale P2 Pn. Palo ea, partitions hore li akarelletsa ho eona, tse lekanang ka palo ea, partitions (n g-1) -gon P2 P3 P4 ... Pn. Ka mantsoe a mang, ho ke ke ba lekanang Xn-1.

Ha kea = 3, joale e ntan'o ba, partitions tse ling sehlopha se tla lula ba le ka diagonale P3 P1 le P3 Pn. palo ea, partitions nepahetse hore ba leng sehlopheng sa, e tla tsamaisane le palo ea, partitions (n g-2) -gon P3, P4 ... Pn. Ka mantsoe a mang, e tla ba Xn-2.

A kea = 4, joale e ntan'o ba kgutlotharo har'a dia nepahetse e tlangwa ho na le triangolo P1 Pn P4, e leng tla adjoin le quadrangle P1 P2 P3 P4, (n g-3) -gon P5 P4 ... Pn. palo ea, partitions nepahetse sekhutlonne joalo lekana X4, 'me palo ea, partitions (n g-3) -gon lekana Xn-3. E Thehiloe ho se boletsoeng ka holimo, re ka bolela hore palo ea, partitions kamehla tse leng sehlopheng sena lekana Xn-3 X4. lihlopha tse ling, eo ho eona kea = 4, 5, 6, 7 ... e tla ba le 4 Xn-X5, Xn-5 x6 ko phai, Xn-6 ... X7, partitions kamehla.

A re ke re kea = n g-2, palo ea, partitions nepahetse ka sehlopha fanoeng tla tsamaisane le palo ea, partitions sehlopheng, eo ho eona kea = 2 (ka mantsoe a mang, lekana le Xn-1).

Kaha X1 = x2 = 0, X3 = 1 le X4 = 2, ..., palo ea, partitions tsa khutlontsi khonvekse ke:

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

mohlala:

X5 = X4 + X3 + X4 = 5

X6 ko phai = X4 + X5 + X4 + X5 = 14

X7 + X5 = x6 ko phai + X4 * X4 + X5 + x6 ko phai = 42

X7 = X8 + x6 ko phai + X4 * X5 + X4 * X5 + x6 ko phai + X7 = 132

Palo ea, partitions nepahetse intersecting ka hare ho e mong diagonale

Ha ho hlahloba Maemong a motho ka mong, ho ka ba nka hore palo ea diagonals ba khonvekse n g-em o sai gon o lekana le sehlahisoa sa, partitions tsohle tsa paterone ena chate (n g-3).

Bopaki ba khopolo ena: nahana hore P1n = Xn * (n g-3), ka nako eo leha e le efe-n-em o sai gon ka arotsoe ka (n g-2) ke triangolo. Tabeng ena e 'ngoe ea tsona ka stacked (n g-3) -chetyrehugolnik. Ka nako e tšoanang, e mong le e quadrangle ke diagonale. Kaha sena khonvekse thutatekanyo palo diagonals tse peli ka ho phethahatsoa, e leng ho bolelang hore ka efe kapa efe (n g-3) -chetyrehugolnikah a ka tsamaisa eketsehileng diagonale (n g-3). Motheong ena, re ka etsa qeto ea hore ho dia efe kapa efe e nepahetseng na le monyetla oa ho (n g-3) -diagonali sebokeng se seng se hlokoang ke mosebetsi ona.

Area khonvekse dikhutlontsi

Hangata, ho rarolla mathata a fapa-fapaneng tsa lipalo, geometry mathomo ho nang le tlhokahalo ho fumana hore na sebaka seo a khutlontsi khonvekse. Nahana hore (Xi. Yi), kea = 1,2,3 ... n g e emela ka tatelano ea okamelang oa tsa boahelani divertise kaofela khutlontsi ea, ba se nang ho intša mateanong a litsela. Tabeng ena, sebakeng sa lona se balwa ka ho ya ka moralo o latelang:

_{S = ½ (Σ (X kea} + X kea + ₁₎ (Y _{kea +} Y _kea + _1)),

moo (X _1, Y _{1) = (X-n +1, Y} n g + _1).