Yintoni ecacileyo kwaye yintoni na?

Njengoko kwaziwa kwi-geometry, "ngokuchanekileyo" kuthetha into engagqibekanga kwaye ijika. Ukhokelo oluchanekileyo, kwindlela enqumlayo, ingxoxo ecacileyo ikwabizwa ngokuba yilizwi elifanayo. Le ngqiqo, eqinisweni, isetyenziswe kwezinye iindawo zobomi, kubandakanywa neencwadi kunye nokuqhagamshelana okuqhelekileyo kwabantu phakathi kwabo.

Into ebizwa ngokuba yiyo ngqo

Ukuze siqonde intsingiselo yegama elithi "ngqo", makhe sikhumbule indlela esisebenzisa ngayo kwintetho eqhelekileyo. Emva koko siya kuhamba ngento nganye ngokuhlukileyo. Ngoko, ukuhlaziywa okulula kunokuthiwa ngamagama alandelayo ngala magama:

• Indlela echanekileyo;
• Ingxoxo ngqo;
• Kwinqanaba elifanelekileyo;
• Ukuxhomekeka ngokuthe ngqo;
• Umgca ochanekileyo;
• Xabiso ngqo;
• Intetho ngqo;
• Uhambo lwendiza;
• Lathiso ngqo;
• Kwaye njalo.

Kwimeko nganye, inkcazelo yentsingiselo iya kuhluke ngokupheleleyo, nangona kusetshenziswe igama elifanayo kuyo yonke inhlanganisela yegama. Ngokomzekelo, ukhokelo ngqo lubonisa nje indlela yokuhambisa. Ukuhamba ngokukhawuleza ngumyalezo othi isithuthi sisuka kwenye indawo ukuya kwelinye ngaphandle kokuyeka nokutshintsha indlela.

Indlela yokwahlula umgca ochanekileyo, upheleleke kwikota

Yintoni ngqo? Kwiincwadi zeJometri kukho inkcazo yale ngcamango. Umgca ochanekileyo ubizwa ngokuba ngumlinganiselo we- geometric elula - umgca onqamlekileyo ongenaso isiqalo okanye ukuphela. Inxalenye yomgca olawulwa ngamacandelo amabini kuthiwa ikhefu. Uluphi umgca ochanekileyo kunye nesiqwengana, siqikelele.

Naliphi na into enokukhishwa okanye i-wavy, oko kukuthi, ijika. Ukuba iqela elithile elizimeleyo "elongeziweyo" lixhumeke ngokulandelanayo ngaphandle kokuqwalasela ulwalathiso olulodwa (kwimizila eyahlukileyo), kwaye i-curve okanye umgca ophukileyo uya kufumaneka. Xa umgca unamarcs, ugoba kwaye uguqulwe, ubizwa ngokuba yi-curve, wavy. Yintoni umgca kwijometri? Ukuba uhamba ukusuka kwelinye icala, yile yile mgca ongaphenduliyo, i-wavy, ephukile okanye ephihliweyo.

Yintoni eqhelekileyo phakathi kwengxoxo ecacileyo kunye nentetho ethe ngqo

Ukuqwalasela ngcaciso yezichazi-magama ezigunyazayo, ingxoxo ecacileyo yintetho enzulu, efuna ukunyaniseka nokunyaniseka kubo bonke abathathi-nxaxheba kule nkqubo. Ukwenza oku, akuyimfuneko ukwazi ukuba yintoni intetho ngqo, ngokwaneleyo ukuthetha malunga noko kuceliwe, okanye wenze iziphakamiso ezithile ngaphandle kokucasha. Ngexesha lokuxoxa ngokuthe ngqo, ngamanye amaxesha iimfihlelo ezahlukeneyo okanye iinkcukacha ezifihliweyo zeemeko zicacisiwe. Ngokuqhelekileyo iingxoxo ezinjalo zivela phakathi kwabantu abasondeleyo, abahlobo okanye izalamane.

Kodwa ukuze uhanjiswe ngokuchanekileyo okanye urekhode le ngxoxo ephepheni, kubalulekile ukukhumbula amanqaku okubhala, yintoni intetho ngqo, amagama omlobi kunye neminye imibhalo yabalobi.

Upelo ludinga ukuba amagama esithethi ahlukaniswe ngamazwi omlobi (umlandisi) ngekholoni, icatshulwa, ii-commas kunye nokudibanisa. Ulwabiwo lwamagama luthonyelwa indawo yokuba igama elithi "hero" kwisicatshulwa, kumhlathi, kumgca, njalo njalo. Okokuthi, intetho ngokuthe ngqo kuthiwa ngamazwi omntu, afakwe kwisigqibo esona sihloko.

Inyoni enamaphiko kunye namazwi aphiko

Sifumene into echanekileyo kwijometri kunye neencwadi, ixesha lokuhamba phambili. Ngendlela, kwisigwebo esandulelayo, elinye lamagama lisetyenziswe ngomqondo ongokomfanekiso (ukuhamba). Okokuthi, okwesibini, ingeyona intsingiselo ngqo, ehambelana negama eliphambili kuphela lenziwa. Kukho ukutshintshwa kwegama ngamanyathelo. Kuvela ukuba amanye amagama esiwasebenzisayo aneentsingiselo ezahlukeneyo:

• Ngokuthe ngqo, okanye isiseko;
• I-Portable, okanye yesibini.

Iyintoni intsingiselo ngqo yegama? Impendulo ihleli kumbuzo ngokwawo. Leli gama lento, isenzo, into, okanye into eyenzekayo ngokukhawuleza, kungakhathaliseki ukuba imeko. Ukungaqondakali kwengcamango yenziwa ngokudlulisela igama kwenye into, engaxhunyiwe naluphi na indlela kunye nesiseko esisisiseko, esithetha ngokuthe ngqo kwegama. Umzekelo:

• Hambisa kwinqwelo - hlela kwileta;
• Iigrawu zeGolide - izandla zegolide;
• Ikhekile le-ushokolethi - i-tshokolethi.

Yiyiphi ikhoneni elungileyo

Okokuqala, nayiphi na i-angle iyimifanekiso ye geometri. Ukuba sidibanisa iingongoma ezintathu ezingekho phantsi komgca ofanayo, ngoko i-point (okanye i-vertex) yalo lwakhiwo iya kuba yinkalo. Ukuba kukho imigca yokudibanisa emininzi ithatyathwa kuyo nayiphi na ingqungquthela, iimbombo eziliqela kunye namaxabiso amabini ayenziwa kwinqanaba le-intersection. Inani labo liya kulingana nenani lemizila edityanisiweyo, ephindwe kabini.

Zonke ii-angles zilinganiswa ngama-degree, kwaye ixabiso elipheleleyo lemali yeengalo zonke kwisangqa ngama-360 degrees. Iibona zibukhali kwaye zibukhali, zichanekile kwaye zivelele, ezikufutshane, ezicacileyo nezongezelelweyo.

Yiyiphi ikota elungileyo? Ndingayifumana njani, kuphi na ukuyifumana? Ngaphakathi kwesangqa, ehlulwe ngamacangca amabini ajikelezwayo phakathi kwawo, ama-angles afanayo afakwe. Zibizwa ngokuba yimigca ecacileyo kwaye intsingiselo yazo nganye yi-90 degrees.

Indlela yokwakha ikona elungileyo ngaphandle kweprotractor

Ngamanye amaxesha kubomi obuqhelekileyo kubalulekile ukufaka isicelo okanye ukubala inani elichanekileyo le-angle. Zininzi iindlela ezilula zokwenza oku.

• Ukuba uthatha iphepha kwi-notebook okanye kwincwadi, zonke ii-angles zayo zilingana nama-90 degrees.
• Xa uthabathe iphepha elinjalo ngokulungelelanisa okuchanekileyo kwamacandelo amabini ajikelezayo, i-angle engama-degrees ama-45 yenziwa.
• Ukuba ulinganisa i-10 cm kwicala elinye le-tetrad okanye nayiphi na iphepha eliphepheni, kwaye enye-17.3 cm, uze udibanise la manqaku ngomgca, unokufumana itemplate eneengalo ezingama-90, ama-60 ne-30 degrees.

Yintoni ekuxhomekeke ngokuthe ngqo kwiphumo kwizenzo? Izinto ezahlukeneyo zinokuchaphazela impendulo ethile. Into enye ayitshintshiyo: ukuba ulandela amanyathelo ngendlela elungileyo, thabatha amanyathelo angaguqukanga kwaye usebenzise ulwazi olufunyenweyo ngokwenza oko, isiphumo siya kuba nesimo esihle.

Kwihlabathi eliqhelekileyo elithe ngqo kunye nelifa

Yintoni ngqo? Ingongoma ingundoqo yejometri, yinto engenazo iinxalenye. Umgca, ulungelelwano olungenanto kunye nesiqalo nesiphelo, esinombalo ongapheliyo weengongoma, uchanekile.

Ukucacisa ukuba zeziphi iindlela ezifanayo, izibalo zisebenzisa izichaso ezahlukeneyo kunye nokuthelekiswa. Nantsi enye yeexixi: imigca eqondileyo engabikho kwaye ayikwazi ukunxibelelana. Ungasebenzisa enye indlela yokwenza ukucacisa ukulandelana kwemigca. Ukuba ukusuka kwinqanaba ngalinye kwelinye lemizila eqondekileyo ukuba ibe yi-perpendicular (oko kukuthi, ngakwii-angles ezifanelekileyo) ukuya kwinqanaba elingana elilinganayo, ke le miqolo ayikwazi ukudibanisa kwaye iya kuba yinto efanayo.

Yintoni efana ngqo, icacile. Kwaye oku kuhambelana njani nehlabathi elimangalisayo? Impendulo ilula, kuba kule meko kukho ukudluliselwa kweengcamango, esixoxe ngazo ngasentla. Into eyenzekayo engabonakaliyo, kodwa ikhona kufuphi neyethu, kwisithuba esifanayo kunye nexesha, kunye nehlabathi elifanayo. Kucatshangelwa ukuba iinjongo ezenzeka apho azichaphazeli ihlabathi lethu nangaliphi na indlela.

Axioms ezininzi ezaziwayo

Kwilizwe leemathematika, i-axiom yinto ekungqiniswanga ngayo. Ngezantsi ezinye zezi nyaniso.

1. Naluphi na ijometri okanye ezinye iimoko zinganyuswa ngokuhambelana nokulinganisela.

2. Imigca emibini eqondekileyo eyahluka kwelinye icala iya kuguqulwa kwelinye.

3. Ukuba imigca emibini echanekileyo iyafana neyesithathu, ngoko iyafana.

4. Ukuba iindlela ezimbini eziqhelekileyo zithelana, ziza kuhamba ngolunye usuku.

5. Ukuba imigca ihamba kunye, ayikwazi ukuhlakaza kwinqanaba elifanayo ngaphandle kokuwela.

6. Ngamaphi na amabini amanqaku, unokwenza isangqa okanye umgca ochanekileyo.

7. Isibalo seengqungquthela ezintathu silingana nazo zonke i-triangles, kwaye lilingana namandla ombini.

8. Ixande lingumfanekiso onobuso abane.

Khawucinge nje ngehlabathi ngaphandle kwejometri

Ukwazisa yintoni umgca ochanekileyo, isigaba, ingongoma, i-angle, ayifuni kuphela abafundi nabafundi ukuba bafumane amabakala amahle. Zisetyenziswe ngabacwangcisi kunye nabaqulunqi, abaxhasi kunye nabakhi, ii-geodesist kunye ne-geologists, abenzi befenitshala kunye nabakhi be-automakers, kunye nenani elikhulu lezinye iingcali. Ngaba umntu ufuna ukugqoka iingubo ezimbi okanye ahlale endlwini eneziphambeko, iindonga eziwa?

Yiyiphi ikota elungileyo? Imigca, iigqeba, iiplani, iingongoma kunye nama-angles - oku, unokuthi, isiseko sezakhiwo. Isayensi yokwakha indlu ayinakwenzeka ngaphandle kokubala kweemathematika kunye neengcamango zejometri, njengencwadi ngaphandle kwamagama, amanqaku, ii-commas, amanqaku okumemeza kunye nentetho ethe ngqo.

Iyiphi indlela echanekileyo? Le yindlela ekhokela kwinqanaba elinye ukuya kwelinye (okanye ukusuka kwimiqondo ethile ukuya kwelinye, ukusuka ekungazini ukuya kwi-erudition, umzekelo), kunye nokuyeka ukuhamba ngexesha, kodwa ngaphandle kokuphambuka kwindlela ekhethiweyo.