Ko ha tuliki tafatusa ko e toa fakalongolongo ia ʻo e langa kotoa pē. Tafatusaʻi ʻa e tefito ʻi he kamataʻanga pea ʻe nofo fakanatula ʻa e holisi kotoa pē, ngaahi faʻunga matapā kotoa pē, mo e ngaahi cabinet kotoa pē ʻi honau feituʻu. Hē hono fai pea ʻe ke tipi maʻu pē ha ngaahi packers fakatāfā ʻi he toenga ʻo e langa ke matapuni ai ʻa e ngaahi matapā. Ko e kalakuleita siaki tafatusa ʻa Chippy Tools ko e ʻepi Pythagoras faingofua taha — hū ha loloa mo ha laulahi, maʻu ʻa e laine ʻoku ʻamanaki ki ai, pea fakatatau ki he laine ʻokú ke fua ʻi he feituʻu ngāue. Kapau ʻoku tatau ʻa e ongo fika, ʻoku tafatusa ʻa e ngāue. Kapau ʻoku ʻikai tatau, fakaleleiʻi kimuʻa pea ke toki lilingi ʻa e simā pe tuki ʻa e ngaahi laupapa.
Ko e hā ʻoku fai ʻe he kalakuleita siaki tafatusa
ʻOku ʻave ʻe he kalakuleita siaki tafatusa ʻa Chippy Tools ha ongo meʻa hū:
- Loloa — ko e tafaʻaki ʻe taha ʻo e meʻa fakaloloa ʻokú ke siaki
- Laulahi — ko e tafaʻaki tuʻu fakatuʻu
Pea foki mai ha meʻa ʻe taha:
- Laine — ko e mamaʻo mei he tuliki ki he tuliki ʻe ʻi ai ʻi he meʻa fakaloloa kapau ʻoku tafatusa moʻoni
Fakatatau ʻa e laine kuo lau mo e laine moʻoni ʻokú ke fua ʻaki ha tape ʻi he ngāue. Kapau ʻoku tatau, ʻoku tafatusa ʻa e meʻa fakaloloa. Kapau ʻoku loloa ange ʻa e laine kuo fua ʻi he ʻa ia kuo lau, ʻoku hē ʻa e meʻa fakaloloa ki he tafaʻaki ʻe taha; nounou ange, ʻoku hē ki he tafaʻaki ʻe taha. Fakaleleiʻi kae ʻoua kuo fakatatau.
ʻOku ngāue ʻa e ʻepi fakalokolo ʻi he iOS mo Android taʻe ha ʻinitaneti. Ko e matematika tatau pē ʻo e tapatolu tuliki-tapafā ʻoku ne tekeʻi ʻa e Kalakuleita Sitepu, Kalakuleita Fakaholo ʻo e ʻAto, mo e Kalakuleita Tapatolu — ʻoku tukukehe ʻe he kalakuleita siaki tafatusa ʻa e meʻa pē ko ʻeni ki he palopalema “ʻoku tafatusa ʻa e meʻa fakaloloa ko ʻeni?”.
Ko hono tafatusaʻi ʻo ha meʻa fakaloloa: siaki ʻo e laine
ʻOku tafatusa ha meʻa fakaloloa (ʻa ia ʻoku ʻi ai ha ngaahi tuliki 90° ʻe fā) kapau pea kapau pē ʻoku tatau ʻa hono laine ʻe ua. Ko ia, ʻoku ʻikai ke ke fua ʻa e tuliki ʻe fā ʻaki ha sukuea pe protractor, ka ʻokú ke fua ha laine ʻe ua pea siaki pe ʻokú na fenāpasi — ko e founga vave ʻo e tafatusaʻi ko ia ʻoku ngāueʻaki ʻe he framer kotoa pē.
ʻI he fakatātā: (1) loloa, (2) laulahi, (3) laine, (4) laine fehangaaki (ʻe totonu ke tatau mo e 3).
Ki ha meʻa fakaloloa 4m × 3m, ʻe totonu ke fua tonu ʻa e ongo laine ki he 5m. Kapau ʻoku fua ʻa e laine A ki he 5.05m mo e laine B ki he 4.95m, ʻoku hē ʻa e meʻa fakaloloa ʻo 50mm mei he tafatusa — teke ʻa e tuliki ʻo e laine loloa ki he loto kae ʻoua kuo 5.00m fakatouʻosi ʻa e laine pea fakamālohi kimuʻa ʻi he tuki.
ʻOku foki mai ʻe he kalakuleita siaki tafatusa ʻa Chippy Tools ʻa e laine kuo lau ʻo tuʻo taha. ʻOku ke fua ʻa e ongo laine moʻoni pea fakatatau fakatouʻosi ki he fika kuo lau (mo e niʻihi ʻo e niʻihi). ʻE totonu ke tatau ʻa e meʻa ʻe tolu ʻi he loto ʻo hoʻo ngaahi fakangatangata.
ʻE anga fēfē hono lau ʻo e laine ʻo ha meʻa fakaloloa
Ko e laine ʻo ha meʻa fakaloloa ko e hypotenuse ʻo e tapatolu tuliki-tapafā kuo fakatupu ʻe hono loloa mo hono laulahi:
laine = √(loloa² + laulahi²)
Ki ha fakatātā kuo fai, ko ha tefito 4m × 3m ʻe ʻi ai ha laine ko e √(16 + 9) = √25 = 5m tonu. Ko ha teki 6.0m × 4.5m ʻe ʻi ai ha laine ko e √(36 + 20.25) = √56.25 = 7.5m. ʻOku tokangaʻi ʻe he kalakuleita ʻa Chippy Tools ʻa e matematika ʻo e aka tafatusa — hū ʻa e ongo fua pea lau ʻa e laine fakahangatonu.
Ki ha fakatātā imipealiale, ko ha teki 16-futa × 12-futa ʻe ʻi ai ha laine ko e √(256 + 144) = √400 = futa tonu ʻe 20. Ko e tolu Pythagorean 3-4-5 kuo fakalahi ʻaki ʻa e 4 ʻoku ʻomi ai ʻa e fika 12-16-20, ko e taha kehe ʻo e founga vave lelei ʻi he feituʻu ngāue: ko e loloa 16-futa, laulahi 12-futa, mo e laine 20-futa ʻoku ʻuhinga ʻoku tafatusa tonu ʻa e meʻa fakaloloa.
ʻE anga fēfē hono lau ʻo e laine ʻo ha tafatusa
Ko ha tafatusa ko ha meʻa fakaloloa ʻoku tatau ai ʻa e loloa mo e laulahi, ko ia ʻoku faingofua ange ʻa e laine:
laine = tafaʻaki × √2 ≈ 1.414 × tafaʻaki
Ki ha tafatusa 4m × 4m, ko e laine ko e 4 × 1.414 ≈ 5.66m. Ki ha tafatusa 12-futa × 12-futa, ko e laine ko e 12 × 1.414 ≈ 16.97 futa (16 futa 11¾ ʻinisi). ʻOku tokangaʻi ʻe he kalakuleita ʻa Chippy Tools ʻa e meʻa fakaloloa angamaheni mo e tuʻunga makehe ʻo e tafatusa fakatouʻosi — hū pē ʻa e fika tatau ki he loloa mo e laulahi.
Ki hono siaki ʻo ha fale pe tefito ʻoku fakaʻamu ke hoko ko ha tafatusa moʻoni, fua maʻu pē ʻa e loloa mo e laulahi takitaha ʻo ʻikai ke tui pē ʻoku tatau — ko ha tefito “tafatusa” ʻoku ko e 4.00m × 3.97m moʻoni ʻoku angamaheni ange, pea ko hono tui ʻo e loloa ʻo e tafaʻaki ʻoku ʻuhinga te ke tafatusaʻi ki ha laine taumuʻa hala.
Founga 3-4-5 (mo hono ngaahi fakalahi)
Ko e founga 3-4-5 ko e founga tafatusaʻi motuʻa taha ʻi ha feituʻu ngāue. ʻOku ngāueʻaki ʻe ia ʻa e tolu Pythagorean siʻi taha — ngaahi loloa tafaʻaki fakaʻiniteja ʻe tolu ʻokú na fakahoa mo e a² + b² = c². ʻOku pehē ʻe he 3-4-5: faʻileʻi ʻa e ʻiunite ʻe 3 mei he tuliki ʻi he tafaʻaki ʻe taha, faʻileʻi ʻa e ʻiunite ʻe 4 mei he tuliki tatau ʻi he tafaʻaki ʻe taha, pea ʻe totonu ke fua tatau ʻa e laine ʻi he vahaʻa ʻo e ongo faʻileʻi mo e ʻiunite ʻe 5 ʻi he taimi ʻoku tafatusa ai ʻa e tuliki.
ʻOku kapui ʻe he ngaahi fakalahi angamaheni ʻo e 3-4-5 ʻa e tokolahi ʻo e ngaahi vā ʻo e ʻapi:
| Tafaʻaki 3-ʻiunite | Tafaʻaki 4-ʻiunite | Laine 5-ʻiunite |
|---|---|---|
| 3 ft | 4 ft | 5 ft |
| 6 ft | 8 ft | 10 ft |
| 9 ft | 12 ft | 15 ft |
| 12 ft | 16 ft | 20 ft |
| 3 m | 4 m | 5 m |
| 6 m | 8 m | 10 m |
| 0.9 m | 1.2 m | 1.5 m |
Ko e 6-8-10 ko e tuʻunga ko ia ʻoku ngāueʻaki ʻe he tokolahi ʻo e kau tufunga koeʻuhí ʻoku lalahi feʻunga ʻa e fika ke fakahā ai ʻa e ngaahi hala faʻunga siʻi ka ʻoku iiki feʻunga ke faʻileʻi ʻaki ha tope ʻe taha. ʻOku ngāue ʻa e kalakuleita siaki tafatusa ʻa Chippy Tools ki ha faʻahinga meʻa fakaloloa pē, ʻo ʻikai ki he ngaahi tolu Pythagorean pē — ʻaonga ʻi he taimi ʻoku ʻikai ke maʻa ai ʻa e fika ʻo e tefito, loki, pe teki.
Tafatusaʻi ʻi he Feituʻu Ngāue
Download ʻa Chippy Tools pea ngāueʻaki ʻa e kalakuleita siaki tafatusa ʻi he iOS pe Android. Pythagoras ʻi he taʻomia ʻo ha kī — ngāue taʻe ʻinitaneti, ʻi he metuliki pe imipealiale.
Ngaahi ngāueʻaki angamaheni
ʻOku kapui ʻe he kalakuleita siaki tafatusa ha faʻahinga palopalema “ʻoku tafatusa ʻa e meʻa fakaloloa ko ʻeni?”:
- Ngaahi tefito mo e simā — ki muʻa ʻi hono lilingi ʻo e simā, fakapapauʻi ʻoku tafatusa ʻa e formwork. Ko ha hala 50mm ʻi he tuʻunga simā ko ha hala 50mm ʻi he holisi kotoa pē ki ʻolunga.
- Ngaahi teki mo e poletī — fakatafatusaʻi ʻa e faʻunga bearer-mo-fau kimuʻa pea ke toki tuki ʻa e laupapa teki. Hili ʻa e tuki ʻo e laupapa, ʻoku ʻikai te ke kei lava ʻo fakaleleiʻi.
- Ngaahi loki mo e holisi — fakapapauʻi ʻa e tafatusa ʻo e faʻunga stud-wall kimuʻa ʻi he plasterboard. ʻE fufu ʻe he plaster ha holisi hēhē ka ʻe hā mai ʻi he ʻaho ʻe fakatautau ai ha matapā.
- Fokotuʻutuʻu ʻo e tile mo e paver — fakatafatusaʻi ʻa e fokotuʻutuʻu kimuʻa pea toki tuku ʻa e tile pe paver ʻuluaki. Ko e ngaahi fokotuʻutuʻu taʻe-tafatusa ʻoku ʻuhinga ʻa e ngaahi tipi fakatāfā ʻi he holisi kotoa pē.
- Ngaahi shed, karaisi, mo e ngaahi fale ʻi tuʻa — fakatafatusaʻi takitaha ʻa e simā mo e faʻunga. ʻOku faingofua ange ke hē ʻa e ngaahi shed koeʻuhí ʻoku ʻikai ke fehokotaki mo e fakatataa ʻo e fale.
- Ngaahi ʻā — fakatafatusaʻi ʻa e ngaahi tuliki ʻo e ʻā ʻi hono ngāueʻaki ʻo e founga 3-4-5 kimuʻa pea ke toki fokotuʻu ha pou.
Ki he meʻa kotoa pē ʻo e ngaahi meʻá ni, ʻoku tatau pē ʻa e founga: fua ʻa e loloa mo e laulahi, lau ʻa e laine ʻoku ʻamanaki ki ai, pea fua ʻa e laine moʻoni mo fakatatau.
Ngaahi fakangatangata mo e “tafatusa feʻunga”
ʻE totonu ke tonu fēfē ʻa e laine kuo fua? ʻOku fakatatau ki he meʻa ʻe haʻu hoko mai:
- Joinery mo e ngāue cabinet — ʻi he loto ʻo e 2mm (1/16") ʻi ha avaʻanga angamaheni. Fakangatangata mālohi koeʻuhí ʻoku fakahā ʻe he ngaahi matapā ʻo e cabinet mo e mata ʻo e draws ʻa e hala kotoa pē.
- Faʻunga ʻapi — ʻi he loto ʻo e 5mm (1/4") ʻi ha loki angamaheni. ʻE lava ke fufu ʻe he ngaahi matapā mo e architrave ha ngaahi hala iiki ka ʻe lahi ange ʻi he 5mm pea ʻe matahafe ʻa e vā ʻo e matapā.
- Formwork ʻo e simā — ʻi he loto ʻo e 10mm ʻi ha simā angamaheni. Hili hono lilingi ʻo e simā, ʻoku tuʻumaʻu ʻa e hala — ʻoku sai ange ke 10mm fefeka kimuʻa ʻi hono lilingi ʻi he 10mm māvaʻe hili ia.
- Faʻunga tuai mo e decking — ʻi he loto ʻo e 10–15mm. ʻOku fakamolemoleʻi ʻe he ngaahi laupapa decking ʻa e ngaahi hala iiki ʻi he ngaahi tipi tuʻa; ʻoku fufu ʻa e faʻunga tuai ʻi tuʻa ʻo e cladding.
- Fokotuʻu ʻo e feituʻu — ʻi he loto ʻo e 25mm ʻi ha fakatataa fale. Ngaahi fakangatangata lalahi ʻi he tuʻunga ʻo e ngaahi pou-fanua; ʻoku mālohi ange ʻi he ʻalu hake ʻa e ngāue ʻi he hierarchy fakalāngapu.
ʻOua naʻa taumuʻa ki he zero — ʻoku ʻikai malava ʻaki ha tape ʻi ha feituʻu havili. Taumuʻa ki he “fakatatau pea ʻi loto ʻi he fakangatangata” — ko e laine tatau pē kuo fua tuʻo tolu ʻe ha kakai ʻe toko tolu ʻe totonu ke foaki ʻa e tali tatau ʻi he loto ʻo e fakangatangata.
Ngaahi ʻiunite imipealiale mo metuliki
ʻOku tali ʻe Chippy Tools ʻa e milimita, sentimita, mita, futa, ʻinisi, pe ko e futa mo e ʻinisi ʻi ha tuʻunga pē. ʻOku tokangaʻi ʻe he kalakuleita ʻa e liliu ʻo e ʻiunite ʻi loto koeʻuhí ke ke lava ʻo fefiloi ʻa e ngaahi hū metuliki (ʻi he mm) mo e ngaahi ola imipealiale (ʻi he futa mo ʻinisi) — ʻaonga ʻi he taimi ʻoku ʻi he mm ai ʻa e ngaahi fakatātā fakapotopoto ka ʻoku fakatau ʻa e ʻakau ʻi he futa hangatonu.
ʻOku ʻikai ʻiunite ʻa e lau ʻo e laine — ʻoku tuʻu ʻa e Pythagoras ki ha faʻahinga ʻiunite tutuʻu pē. ʻOku fakapapauʻi pē ʻe he kalakuleita ʻoku liliu hoʻo ngaahi hū ki ha ʻiunite pē ʻe taha kimuʻa ʻi hono lau ʻo e laine pea fakahā leva ʻa e ola ʻi hoʻo ʻiunite kuó ke fili.
Ko e hā ʻokú ke ngāueʻaki ai ha kalakuleita siaki tafatusa ʻi hoʻo telefoni
ʻOku langa ʻa e ʻepi ʻa Chippy Tools ki he kau ngāue ʻa ia ʻoku fie maʻu ha lau ʻi he feituʻu ngāue taʻe ha ʻinitaneti. ʻOku tuʻutuʻuni fakataha ʻa e kalakuleita siaki tafatusa ʻi he ʻepi tatau pē mo e Kalakuleita Sitepu, Kalakuleita Decking, Kalakuleita Fakaholo ʻo e ʻAto, mo e Kalakuleita Tapatolu — tafatusaʻi ʻa e tefito, lau ʻa e teki, pou ʻo e hala-fāʻele, mo e fakaholo ʻo e ʻato ʻi ha founga pē ʻe taha taʻe ha toe hū ʻo e ngaahi fua.
ʻOku maumau ʻa e ngaahi kalakuleita siaki tafatusa ʻi he ʻinitaneti ʻi he tuʻa ʻo ha feituʻu ngāue taʻe ha fakaʻiloa. ʻOku ngāue fakalokolo ʻa e kalakuleita ʻa Chippy Tools — ʻoku ʻi he matavavae ʻa e tali ʻi lalo ʻi he sēkoni ʻe taha. Toho hake ʻa e kalakuleita hangatonu mei hoʻo widget ʻi he matavavae ʻo e ʻapi ʻi he taimi ʻoku fehuʻi ai ha kasitomā “ʻoku tafatusa ʻa e loki ko ʻeni?” ʻi he taimi ʻo e ʻaʻahi.
Ngaahi kalakuleita felāveʻi
- Kalakuleita Tapatolu — matematika tefito ʻo e tapatolu tuliki-tapafā, ʻaonga ki ha faʻahinga fakatataa taʻe-fakaloloa
- Kalakuleita Decking — hili hono tafatusa ʻo e faʻunga ʻo e teki, lau ʻa e ngaahi laupapa teki mo e ngaahi fau
- Kalakuleita Sitepu — Pythagoras tatau pē kuo ngāueʻaki ki he loloa ʻo e pou ʻo e hala-fāʻele
- Kalakuleita Fakaholo ʻo e ʻAto — matematika hake-ki-he-laka tatau pē kuo ngāueʻaki ki he ngaahi ʻakau mo e fakaholo