He aha te mea he taupū kōaro?

Te Middle ake e mohiotia ana ko te wa o te haere me ngā āhuatanga matawhenua. Ko te ara anake ki whakatutukitanga o te haere roa-tawhiti ko te rerenga e te e pā ana ki te whakatinanatanga o buka nui o tātaitanga whakaterenga tonu. He uaua ki te whakaaro i te tukanga o fakaongosia tātaitanga i roto i te whakarea, wehenga o tau e rima-mati "i te ringa". Dzhon Neper, he teolosia e te āhua o tona mahi matua, mahi i roto i te rēhia tātaitanga pākoki fifili whakakapi tukanga kaimahi o te whakarea i te tua ohie. Ia ia i mea ai ko tana whāinga ki "te pehea o te fifi, me te takeo o tātaitanga, e deters tokomaha i te ako o pāngarau." Tautooraa ki angitu - i hanga pāngarau taputapu i huaina pūnaha taupū kōaro.

Na he aha te mea he taupū kōaro? Ko te pūtake o te tätaitanga taupū kōaro ko tetahi kanohi o: hei utu o te pūnaha tūnga tikanga, rite matou whakamahia, māngai te maha o te te rite te kaha o te faaiteraa, te wahi etahi tau te noho N, ka karanga he wāhi turanga e whakaarahia ki te n tohu, e te hua ko te tau A. Ko te kupu , n - ko te taupū kōaro ki te turanga N. he kōwhiringa o pakiaka āta te ingoa o te pūnaha. Hoki taupū kōaro ira ohie vichisleny tono pūnaha, me i roto i te pūtaiao, me te hangarau, ko te pūnaha whānui whakamahia o te taupū kōaro tūturu, te turanga ko ai he e tau noatia = 2,718. Ko te kīanga tautuhi i te taupū kōaro o te maha o te, i roto i te reo o te pāngarau te tuhituhi e whai ake:

n = roko (N) A, te wahi N - turanga tohu.

taupū kōaro-ira, me te taiao i to ratou tuhituhi motuhake haapotohia - LGA ko lnA, aua.

Ko te tātaitanga pūnaha whakamahi i taupū kōaro o tātaitanga, te huānga matua ko te faafariuraa o te tau ki te puka mana e taupū kōaro o etahi tepu turanga, hei tauira 10. Ko te māmā tenei whawhe. Next, te whakamahi i te mana taonga o tau, arā, i roto i te meka e ka tini haere e te tohu o to ratou taiepa. I roto i te mahi, tenei te tikanga e whakakapi whakarea o tau ki te kanohi taupū kōaro e mā te tāpiri ratou mana. Na reira, ko te pātai "he aha te mea te kōaro o te" ki te he te reira ki te haere tonu ki te "me te aha tatou e hiahia reira," ko te whakahoki ohie - ki te faaohie i te tukanga mō te whakareatanga-wehenga o tau mati-maha - no te tua "i roto i te tīwae" Ko nui māmā ki te tini "i roto i te tīwae". Ko wai e kore e whakapono - kia tamata ia ki te takoto ki raro, me te tini haere rua tau moka-waru.

Ko te tepu tuatahi o te taupū kōaro (ki te turanga ki te tau tūturu), whakaputaina i roto i te 1614 Dzhon Neper, a tino noa o te kōwhiringa hapa, me te tae atu i te tepu o te taupū kōaro noa, puta i roto i 1857 me te mohiotia rite tepu Bremikera. Mā te taupū kōaro ki te turanga i roto i te puka o te tau noatia no te tau, ko te, tino whiwhi noa i roto i te raupapa Taylor he whānui tono i roto i te wāhi me te pārōnaki tuanaki.

Ko te ngako o tenei pūnaha rorohiko whakarato te whakautu ki te pātai "He aha te mea te kōaro" me whai reira i te tuakiri taupū kōaro taketake: N (taupū kōaro turanga) whakaarahia ki te mana n, rite ki te taupū kōaro o te tau A (logA), he rite ki te A. tenei maha I roto i tenei take, A> 0, arā takoto taupū kōaro te anake hoki ngā tau pai, a ka he nui atu i te 0 me te kore rite ki te 1. I runga anō i te i mua i te turanga roko tonu, kia whakatakoto ai i nga āhuatanga o te taupū kōaro tūturu e whai ake:

1. Mara o te taupū kōaro tūturu - tuaka tau katoa mai i te 0 ki te mutu-.
2. ln x = 0 - he putanga o te hononga mohiotia - tetahi maha o kore tohu he 1.
3. ln (X * Y) = ln X + lnY - tino nui mō te taonga whawhe tātai - te taupū kōaro o te hua o ngā tau e rua ramen moni o nga taupū kōaro o ia.
4. ln (X / Y) = ln X - lnY - taupū kōaro o te huawehe o ngā tau e rua he rite ki te rerekētanga o te taupū kōaro o enei tau.
5. ln (X) n = n * ln X.
6. Ko te taupū kōaro tūturu ko te mahi maha ohu differentiable, ai ln 'X = 1 / X
7. takiuru (N) A = K * ln A - taupū kōaro rite ki tetahi pai, me te tahi atu atu i te e turanga o taiao anake rerekē i te ōwehenga.

Na nga schoolchild matau e ko te taupū kōaro, engari kua riro whakawhetai ki mua i roto i te mara o tīpakongia raruraru engineering rorohiko o te mahi tātai. Heoi, taupū kōaro, kua rite te taputapu pāngarau e whakamahia ana i roto i te whakaoti whārite ki taurangi i roto i te taupū roto i te kīanga mō te kimi i te wa te pirau o iratuki huānga me i ētahi atu wāhanga o te pāngarau, te ahupūngao me te tatauranga.