Te Hiranga o ngā Tau Matua
He ariā taketake ngā tau matua i roto i te pāngarau e whai wāhi nui ana ki ngā momo mara o te pūtaiao me te hangarau. Ko te tau matua he tau pai me ngā tauwehe e rua anake: 1 me ia anō. Ko ngā tauira o ngā tau matua ko te 2, 3, 5, 7, 11, 13, me ētahi atu. I roto i tēnei tuhinga, ka matapakihia e mātou te hiranga o ngā tau matua, mai i te tirohanga pāngarau noa ki ā rātou tono mahi i roto i te ao hou.
Hītori me te Ako i ngā Tau Matua
Kua mōhiotia te hiranga o ngā tau matua mai anō i ngā wā onamata. Neke atu i te rua mano tau ki muri i akohia ai e ngā Ihipiana, e ngā Kariki, me ngā Pāpuroni. Ko tētahi o ngā tino tangata i roto i te hītori o ngā tau matua ko Euclid, he tohunga pāngarau Kariki i noho i te rautau tuatoru BC. I roto i tana mahi whakahirahira, "Elements," i whakamatau a Euclid he mutunga kore te maha o ngā tau matua. Koinei tētahi o ngā taunakitanga pāngarau tuatahi, ā, kei te whai pānga tonu ki tēnei rā.
Te Tūranga o ngā Tau Matua i roto i te Pāngarau
Ariā Tau
I roto i te pāngarau, ka mahi ngā tau matua hei "ngota" mō ngā tauoti. Ko ia tauoti pai nui atu i te 1 ka taea te whakaatu hei hua o tētahi, neke atu rānei o ngā tau matua. Hei tauira, ka taea te wehewehe i te tau 12 ki te 2 × 2 × 3. E mōhiotia ana tēnei ko te whakawehenga tau matua.
He maha ngā pānga nui o te whakawehe matua. Hei tauira, ko tētahi kōrero taketake i roto i te ariā tau e mōhiotia ana ko te "Fundamental Theorem of Arithmetic" e kī ana he ahurei te whakawehe matua o tētahi tauoti engari ko te raupapa o ōna tauoti.
Ngā Mahi me te Tohatoha o ngā Tau Matua
Hei tāpiritanga, ko te ako i te tohatoha o ngā tau matua—te tohatoha o ngā tau matua i waenga i ngā tau katoa—he wāhanga nui anō hoki o te pāngarau. Ko tētahi o ngā hua rongonui o tēnei mara ko te Ariā Tau Matua, e kī ana ko te tohatoha o ngā tau matua i waenga i ngā tau katoa e whai ana i tētahi tauira ka taea te matapae mā te whakamahi i te logarithm maori.
Ngā Raru Tuwhera
Ahakoa he nui ngā mōhiotanga mō ngā tau matua, he maha tonu ngā pātai kāore anō kia whakautua. Ko tētahi o ngā mea rongonui ko te Whakapae Riemann, e hono ana i te tohatoha o ngā tau matua ki ngā kore o te mahi zeta Riemann. Nā Bernhard Riemann i whakaaro i te tau 1859, kāore anō kia whakamātauhia tēnei whakapae, ā, ko tētahi o ngā "Raru Mileniuma" e whitu, me te taonga kotahi miriona tāra e whakawhiwhia ana ki te tangata e taea te whakamātau, te whakahē rānei.
Ngā Whakamahinga o ngā Tau Matua i roto i te Hangarau
tuhi tuhi
Ko tētahi o ngā whakamahinga tino nui, tino rongonui hoki o ngā tau matua i te ao hou ko te whakamunatanga, inā koa ko te whakamunatanga kī tūmatanui. Ko ngā kawa pēnei i te RSA (Rivest-Shamir-Adleman) e whakawhirinaki ana ki te meka ahakoa he ngāwari te whakarea i ngā tau matua nui e rua, he tino uaua ki te tauwehe i a rātou ki ngā tau matua nui e rua (te raruraru tauwehe).
Hei tauira, ki te whiriwhiria e tetahi ngā tau matua nui e rua, ā, ka whakareatia, ka puta he tau tino nui e whakamahia ana hei kī tūmatanui. Ki te kore e mōhio ki ngā tau matua taketake, he tino uaua ki te wetewete i ngā mōhiohio kua whakamunahia ki taua kī, ā, ka noho haumaru ngā raraunga. He mea nui te haumarutanga kei muri i tēnei whakamunatanga mō ngā tauwhitinga pūtea, ngā whakawhitiwhitinga haumaru, me te maha atu o ngā āhuatanga o ō tātou oranga matihiko.
Whakawhitiwhiti Kōrero me te Whatunga
Ka whakamahia hoki ngā tau matua i roto i ngā pūnaha whakawhitiwhiti kōrero me te whatunga hei whakaputa i ngā raupapatanga rūpahu-matapōkere, he mea nui mō te whakarerekētanga raraunga me ngā waehere whakatika hapa. Hei tauira, i roto i ngā whakawhitiwhiti kōrero horapa, ka taea te whakamahi i ngā tau matua hei whakaputa waehere horapa hei āwhina i te whakatika i ngā tohu kua pakaru ina tukuna ngā raraunga i ngā tawhiti roa, i ngā hongere rānei me te pokanoa.
Ariā Whakawaehere
Ka whakamahia nuitia hoki e te ariā waehere ngā tau matua hei whakapai ake i te whai huatanga me te haumarutanga o te tuku raraunga. Ko ngā waehere whakatika hapa pērā i a Reed-Solomon, e whakamahia pinepine ana i roto i ngā CD, DVD, me ngā whakawhitiwhiti raraunga, ka whakaurua hoki ngā tau matua ki roto i ā rātou rauropi.
Te Tūranga o te Mātauranga
He mea nui te whakauru i ngā tau matua ki ngā taumata tuatahi me ngā taumata tuarua hei whakawhanake i te māramatanga taketake o ngā ākonga ki te pāngarau. Mā te ako i ngā tau matua, ka taea hoki e ngā ākonga te whakapai ake i ō rātou pūkenga tātari me te whakaoti rapanga. Ka taea te whakaako i ngā tau matua mā roto i ngā huarahi maha, mai i ngā kēmu pāngarau māmā ki te whakauru i ngā ākonga ki ngā kaupapa rangahau poto wero.
Hei tauira, ka taea e ngā kaiako te tono i ngā ākonga ki te rapu i ngā tau matua i roto i ngā awhe rerekē, ki te mārama ki ngā tauira e puta ake ana, ki te tūhura rānei i ngā ariā matatau ake pērā i te Sieve of Eratosthenes, he rauropi tawhito engari māmā e whakamahia ana hei kimi i ngā tau matua tae atu ki tētahi rohe.
Whakamutunga
Ehara i te mea he mea pāngarau noa iho ngā tau matua; koinei te pūtake o ngā āhuatanga nui o te pūtaiao me te hangarau. Mai i te ariā tau me te rangahau pūtaiao ki ngā tono mahi i roto i te whakamunatanga me ngā whakawhitiwhiti kōrero, he mahi nui tā ngā tau matua.
Mā te tūhura tonu i ngā tau matua ka taea hoki ngā kitenga hou me ngā mahi auaha ka taea te whakarerekē i te huarahi e whakawhitiwhiti kōrero ai tātou, e tatau ai, e tiaki ai hoki i ngā mōhiohio i te ao hou. Nō reira, ko te māramatanga hohonu ake ki ngā tau matua ehara i te mea ka whakarei ake i ō tātou mōhiotanga pāngarau engari ka whai wāhi nui hoki ki ngā whanaketanga hangarau ā muri ake nei.
I te mea ka nui haere te whakawhirinaki o te hapori ki te hangarau me te haumarutanga matihiko, ko te mārama me te maioha ki te hiranga o ngā tau matua he taahiraa nui ki te mārama whānui ake ki te ao e karapoti nei i a tātou. Mai i te mātauranga tuatahi ki te rangahau matatau, ka noho tonu ngā tau matua hei kaupapa matua i roto i te pāngarau me te hangarau, pērā i ngā mano tau kua pahure.
