Amanqaku kwiringi: Ukuhamba okusebenzisanayo kwengxaki yezibalo edumileyo

Amanqaku kwiRingi: UkuHamba okuSebenzayo kweNgxaki edumileyo yeMathematika

IMathematika isoloko ibonwa njengommandla weesimboli ezingabonakaliyo kunye neefomula ezingangeneki. Ukanti, ezinye zezona ngxaki zibangela umdla zibangelwa ziimeko ezilula ezikhohlisayo. Ingxaki "yamanqaku kwiringi" ngumzekelo ogqibeleleyo-iphazili eqala ngesiseko esisisiseko kwaye ityhileke kuphononongo olutyebileyo lwejometri, ukuphuculwa, kunye nokucinga okucwangcisiweyo. Ngokuhamba kule ngxaki sisebenzisanayo, sinokutyhila iipatheni ezisebenza ngaphaya kwephepha, ngakumbi kwindlela esimisa ngayo iinkqubo ezintsonkothileyo. E-Mewayz, sibona oku njengothelekiso olunamandla lwendlela yemodyuli esiyintshatsheli: ukudibanisa izinto ezidityanisiweyo ukuyila yonke into edibeneyo nesebenzayo.

Ukuseta: Isangqa kunye nokuxhawula isandla

Khawube nomfanekiso wesangqa. Ngoku, beka inani lamanqaku malunga nesangqa sawo, zibekwe ngokulinganayo. Ingxaki iqala xa sidibanisa la manqaku omnye komnye ngemigca ethe tye, okanye iichords. Umceli mngeni uthe ngqo: kumanqaku ka-'n' kwisangqa, zingaphi iichowudi onokuzizoba ukuze kungabikho chowudi zintathu zinqumlanayo kwindawo enye ngaphakathi kwesangqa? Oku akukho malunga nemikrolo engacwangciswanga; imalunga nokufumana elona nani liphezulu loqhakamshelwano olungaphambanisiyo. Olu lungiselelo lubonisa ingxaki yeshishini eqhelekileyo: uneseti yezixhobo (amanqaku) kwaye kufuneka umisele unxibelelwano olusebenzayo phakathi kwabo (iichords) ngaphandle kokudala ungquzulwano oluphazamisayo (iindlela zokuhlangana).

Ukwenza iMaphu yoQhagamshelwano: Ukusuka kumanqaku ama-3 ukuya kwipateni

Masizakhele isisombululo sethu. Qala ngelona nani lincinci lamanqaku avumela iichords: amanqaku ama-3. Ukuzidibanisa zonke kudala unxantathu, kodwa njengoko sizoba iichords *ngaphakathi* kwisangqa, ngamanqaku ama-3, ungazoba amacala amathathu kanxantathu kuphela, kwaye akukho nanye kwezi diagonals inqumla ngaphakathi kwesangqa. Ngoko ke, ku-n=3, elona nani liphezulu leechords ezingaphambanisi sisi-3.

Ngoku, yongeza inqaku lesine. Ubunzima buyanda. Ungadibanisa amanqaku ngeendlela ezininzi, kodwa ukwandisa inani leechords ezingaphambanisiyo, kufuneka ucinge ngobuchule. Undoqo kukuqonda ukuba nanini na ukongeza inqaku elitsha, unokulidibanisa namanye amanqaku ngendlela eyahlula amanqaku akhoyo abe ngamaqela macala omabini echord entsha.

• n=3: Iichords ezi-3 (unxantathu).
• n=4: Ungazoba iichords ezi-4 ezinganqumliyo? Makhe sijonge. Ukuba uzama ukuzoba lonke uqhagamshelo olunokwenzeka, iichords ziyakunqumlana. Eyona nto iphezulu yi-4, yenza i-quadrilateral kunye ne-diagonal yayo emibini edibeneyo, kodwa linda-indlela yokuhlangana iphula umthetho wethu! Ubuninzi obuchanekileyo be-n = 4 bufezekiswa ngokuzoba kuphela iichords ezenza umda we-convex quadrilateral, emacala angama-4, kodwa akukho diagonal yangaphakathi. Ngokwenyani, makhe sicacise: ubuninzi obuchanekileyo be-n=4 yi-2 yediagonal engaphambanisiyo. Kulapho ipateni ifumana umdla.

Le nkqubo yoqhagamshelo olongezelekayo yiyo kanye iqonga elifana neMewayz eliququzelela iinkqubo zoshishino. Endaweni yokuzama ukudibanisa yonke into ngexesha elinye kwaye udale isiphithiphithi esibambeneyo, uyakha ukudityaniswa ngokufanelekileyo nangokulandelelana, uqinisekisa uzinzo nokucaca.

Isityhilelo: Amanani eCatalan kunye neModyuli yokuCinga

Njengoko uqhubeka le ndlela yokuhamba kunye ne-5, 6, kunye namanqaku amaninzi, ulandelelwano olumangalisayo luvela: 1, 2, 5, 14 ... Lawa ngamanani eCatalan, ulandelelwano oludumileyo kwii-combinatorics. Inani leendlela zokuzoba iichords ezingadibaniyo phakathi kwamanqaku u-n linikwe ngu (n-2) inombolo yesiCatalan. Esi sisombululo sihle sibonisa indlela ingxaki ethintelweyo enokuvelisa ngayo ipateni entle kunye neyendalo yonke.

"Ukuvela kwamanani eCatalan ukusuka kwisithintelo esilula sejometri lububungqina besakhiwo esifihlakeleyo esiphantsi kweenkqubo ezibonakala zinzima."

La ngamandla esakhelo semodyuli. Ngokuthobela isiseko semigaqo-njengokuqinisekisa unxibelelwano olungaphambanisiyo-unokwakha iisistim ezintsonkothileyo neziyomeleleyo ukusuka kumacandelo alula, anokuphinda asetyenziswe. I-Mewayz iyilwe ngokwalo mgaqo. I-OS yethu yemodyuli yeshishini ikuvumela ukuba uqhagamshele ii -apps zakho ezizithandayo kunye nemithombo yedatha (amanqaku) kwindawo ecwangcisiweyo, engenazingxabano (i-non-intersecting chords), ekuvumela ukuba ukwandise ukusebenza kakuhle ngaphandle kwesiphithiphithi seenkqubo ezingahambelaniyo.

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Ngaphaya kweSangqa: I-Business Takeaway

Ingxaki "yamanqaku kwiringi" ingaphezulu komdla wezibalo; sisifundo kuqhagamshelwano olucwangcisiweyo. Kwishishini, awongezi nje amanqaku ngokungenamkhethe; udibanisa izixhobo, idatha, kunye namaqela ngobuchule. Injongo kukwenza umnatha apho ulwazi luhamba kakuhle ngaphandle kweebhotile okanye iingxabano-inkqubo apho yonke into inkulu kunesixa samalungu ayo. Nokuba ulungisa ikhonkco lokubonelela, ukwakha inkqubo yesoftware, okanye uyila ukuhamba komsebenzi weprojekthi, umgaqo uhlala ufana: uqhagamshelo olukrelekrele ngundoqo. Ngokwamkela indlela yemodyuli, exhaswa ngamaqonga afana ne-Mewayz, ungaguqula isangqa samathuba ube sisimfoni elungelelaniswe kakuhle yemveliso.

Imibuzo Ebuzwa Rhoqo

Amanqaku kwiRingi: UkuHamba ngokuSebenzayo kweNgxaki edumileyo yeMathematika

IMathematika isoloko ibonwa njengommandla weesimboli ezingabonakaliyo kunye neefomula ezingangeneki. Ukanti, ezinye zezona ngxaki zibangela umdla zibangelwa ziimeko ezilula ezikhohlisayo. Ingxaki "yamanqaku kwiringi" ngumzekelo ogqibeleleyo-iphazili eqala ngesiseko esisisiseko kwaye ityhileke kuphononongo olutyebileyo lwejometri, ukuphuculwa, kunye nokucinga okucwangcisiweyo. Ngokuhamba kule ngxaki sisebenzisanayo, sinokutyhila iipatheni ezisebenza ngaphaya kwephepha, ngakumbi kwindlela esimisa ngayo iinkqubo ezintsonkothileyo. E-Mewayz, sibona oku njengothelekiso olunamandla lwendlela yemodyuli esiyintshatsheli: ukudibanisa izinto ezidityanisiweyo ukuyila yonke into edibeneyo nesebenzayo.

Ukuseta: Isangqa kunye nokuxhawula isandla

Khawube nomfanekiso wesangqa. Ngoku, beka inani lamanqaku malunga nesangqa sawo, zibekwe ngokulinganayo. Ingxaki iqala xa sidibanisa la manqaku omnye komnye ngemigca ethe tye, okanye iichords. Umceli mngeni uthe ngqo: kumanqaku ka-'n' kwisangqa, zingaphi iichowudi onokuzizoba ukuze kungabikho chowudi zintathu zinqumlanayo kwindawo enye ngaphakathi kwesangqa? Oku akukho malunga nemikrolo engacwangciswanga; imalunga nokufumana elona nani liphezulu loqhakamshelwano olungaphambanisiyo. Olu lungiselelo lubonisa ingxaki yeshishini eqhelekileyo: uneseti yezixhobo (amanqaku) kwaye kufuneka umisele unxibelelwano olusebenzayo phakathi kwabo (iichords) ngaphandle kokudala ungquzulwano oluphazamisayo (iindlela zokuhlangana).

Ukwenza iMaphu yoQhagamshelwano: Ukusuka kumanqaku ama-3 ukuya kwipateni

Masizakhele isisombululo sethu. Qala ngelona nani lincinci lamanqaku avumela iichords: amanqaku ama-3. Ukuzidibanisa zonke kudala unxantathu, kodwa njengoko sizoba iichords *ngaphakathi* kwisangqa, ngamanqaku ama-3, ungazoba amacala amathathu kanxantathu kuphela, kwaye akukho nanye kwezi diagonals inqumla ngaphakathi kwesangqa. Ngoko ke, ku-n=3, elona nani liphezulu leechords ezingaphambanisi sisi-3.

Isityhilelo: Amanani eCatalan kunye neModyuli yokuCinga

Njengoko uqhubeka le ndlela yokuhamba kunye ne-5, 6, kunye namanqaku amaninzi, ulandelelwano olumangalisayo luvela: 1, 2, 5, 14 ... Lawa ngamanani eCatalan, ulandelelwano oludumileyo kwii-combinatorics. Inani leendlela zokuzoba iichords ezingadibaniyo phakathi kwamanqaku u-n linikwe ngu (n-2) inombolo yesiCatalan. Esi sisombululo sihle sibonisa indlela ingxaki ethintelweyo enokuvelisa ngayo ipateni entle kunye neyendalo yonke.

Ngaphaya kweSangqa: I-Business Takeaway

Ingxaki "yamanqaku kwiringi" ingaphezulu komdla wezibalo; sisifundo kuqhagamshelwano olucwangcisiweyo. Kwishishini, awongezi nje amanqaku ngokungenamkhethe; udibanisa izixhobo, idatha, kunye namaqela ngobuchule. Injongo kukwenza umnatha apho ulwazi luhamba kakuhle ngaphandle kweebhotile okanye iingxabano-inkqubo apho yonke into inkulu kunesixa samalungu ayo. Nokuba ulungisa ikhonkco lokubonelela, ukwakha inkqubo yesoftware, okanye uyila ukuhamba komsebenzi weprojekthi, umgaqo uhlala ufana: uqhagamshelo olukrelekrele ngundoqo. Ngokwamkela indlela yemodyuli, exhaswa ngamaqonga afana ne-Mewayz, ungaguqula isangqa samathuba ube sisimfoni elungelelaniswe kakuhle yemveliso.