Nānā
E ʻae i kāu keiki e pāʻani a noʻonoʻo e pili ana i kēia mau noiʻi. Mai wikiwiki. Aia ka waiwai i ka pāʻani a puni a me ka ʻike ʻana i nā ʻano nani. Aia kekahi mau makemakika hohonu i loko o kēia mau hana, akā hiki i kēlā mau manaʻo ke kali a hiki i ka wā e ʻelemakule ai kāu keiki.
Mea Hoʻohui
Pua Pua
I loko o kahi māla kilokilo, aia ʻelua ʻano pua. ʻEhā mau lau o kekahi a ʻehiku mau lau o kekahi. Ua noi ʻia kekahi keiki e ʻohi i kekahi mau pua i hiki ai i ka huina o nā lau he 13. Hiki ke hana ʻia? Pehea e pili ana i 15 mau lau? No nā helu hea o nā lau e hiki ai? No nā helu i hiki, hiki ke hana ʻia ma mua o hoʻokahi ʻano? No ka laʻana, he 32 mau lau he ʻehā 7 a hoʻokahi 4, a he ʻewalu hoʻi 4.
Ma ka hoʻāʻo ʻana i nā hui helu he nui, nui nā laʻana e pāʻani ai. No kekahi mau hui helu, aia kahi manawa e hiki ai nā helu āpau o nā petal, a no nā hui helu ʻē aʻe, ʻaʻohe wahi like. No 4 a me 7, hiki nā helu āpau mai 18 a i luna. No 3 a me 6, ʻaʻohe wahi ma hope o ka puka ʻana o nā helu āpau.
He aha ke ʻano a he aha ka mea e hana ai i kēlā ʻano? He mau nīnau pinepine kēlā e kū mai ana, a ma laila e hana ʻia ai nā mea hoihoi he nui.
ʻOi aku ka maʻalahi o ka ʻike ʻana i ka mea e hana ʻia ke hoʻokaʻawale like kekahi helu i nā helu ʻelua. E lawe i ka 3 a me ka 6 no ka laʻana. E noʻonoʻo i kēia mau helu he 1 x 3 a me 2 x 3. Ke hoʻohui ʻoe i kēia mau helu, e loaʻa mau iā ʻoe kekahi helu o 3. ʻAʻohe ala e hoʻohui ai i nā 3 a me 6 e loaʻa ai ka 10, no ka mea, ʻaʻole he hoʻonui o 3 ka 10.
Ke hoʻokaʻawale like ʻia nā helu ʻelua me 1 wale nō, e hiki mai ana kahi e hiki ai ke loaʻa i kēlā me kēia helu. No 4 a me 7, ʻo ia helu he 18. No ka loaʻa ʻana o kēlā helu, e unuhi i ka 1 mai kēlā me kēia helu o ka pālua a hoʻonui pū i kēlā mau helu hou. I kēia hihia, hāʻawi kēlā i 3 x 6 = 18. ʻO kekahi ʻano hoihoi o kēia kūlana, ʻo ia ka hapalua o nā helu ma lalo o 18 e hiki ke kiʻi ʻia. No ke aha e hana ai kēia, pono kekahi makemakika i ʻoi aku ka paʻakikī no kahi keiki ʻōpio; akā naʻe, he mea leʻaleʻa ka pāʻani me kēia mau helu a ʻo nā ʻike o kāu keiki me kēia mau ʻano e kaomi koke paha i kahi ma hope aku.
Nā ʻanuʻu piʻi - Ehia mau ala?
Ke manaʻo nei kāu keiki makemake e hana i ʻelua mau ʻanuʻu i ka manawa hoʻokahi i kekahi manawa, akā hoʻokahi i ka manawa i nā manawa ʻē aʻe. Inā makemake kāu keiki e piʻi i kekahi mau ʻanuʻu, he nīnau maʻamau kēia: Ehia mau ala e hiki ai ke hana i kēia?
Eia kekahi laʻana, no nā ʻanuʻu 0, hoʻokahi wale nō ala - kū wale ʻoe ma laila. No 1 ʻanuʻu, hoʻokahi ala - lawe ʻoe i hoʻokahi ʻanuʻu. No ʻelua ʻanuʻu, hiki iā ʻoe ke lawe i hoʻokahi ʻanuʻu pālua a i ʻole ʻelua ʻanuʻu hoʻokahi.
Pono kāu keiki e helu pono i nā hihia he nui o kēia a hana i kahi papa o nā hopena. Ke nui ka ʻike, kōkua pinepine kahi papa i ka hoʻonohonoho ʻana i ka ʻike a ʻae i nā ʻano e kū i waho. E like ke ʻano o ka papa me kēia (ʻae, ʻo ka hele ʻana ma mua o 6 e pono ai ka nui o ke ahonui, akā eia nā helu):
1 – 1 – 2 – 3 – 5 – 8 – 13 – 21 – 34 – 55
Ma hope o ka nānā ʻana i kēia mau helu, e ʻike paha kāu keiki e hoʻohui ʻia kēlā me kēia pālua o nā helu e pili ana i ka helu aʻe. No ke aha e hana ʻia ai kēia? Ua kapa ʻia kēia mau helu he mau Helu Fibonacci. ʻO ke kānāwai no ka hana ʻana i nā Helu Fibonacci kūhelu, ʻo kēlā me kēia helu ka huina o nā ʻelua ma mua. Hana pū kēia no nā ʻanuʻu. Hmmm …
E nānā pono kākou i hoʻokahi laʻana - e ʻōlelo i 5 mau ʻanuʻu. ʻO nā hiki 8: 1+1+1+1, 1+1+2+1, 1+2+1+1, 2+1+1+1, 2+2+1, 1+1+1+2, 1+2+2, a me 2+1+2. Hoʻohana nā hiki 5 mua i 1 no ka neʻe hope loa, a hoʻohana nā hiki 3 hope loa i 2 no ka neʻe hope loa. ʻO ia ka wehewehe ʻana - hiki iā ʻoe ke piʻi i 5 mau ʻanuʻu ma ka piʻi ʻana i 4 mau ʻanuʻu a lawe i 1 ʻanuʻu hou aʻe, a i ʻole ma ka piʻi ʻana i 3 mau ʻanuʻu a piʻi i 2 mau ʻanuʻu hou aʻe. ʻO ka helu o nā ala e piʻi ai i 5 mau ʻanuʻu ua like ia me ka huina o ka helu o nā ala e piʻi ai i 4 mau ʻanuʻu me ka helu o nā ala e piʻi ai i 3 mau ʻanuʻu.
Hoʻomaopopo pinepine ʻia nā ʻano maʻamau ma o ka nānā pono ʻana i nā laʻana, ka hoʻonohonoho ʻana i ka ʻikepili, ka nānā pono ʻana i ka ʻikepili, a me ka ʻeli ʻana no nā wehewehe no ke aha e hana ai nā mea e like me kā lākou hana ʻana. He ʻano maʻamau maikaʻi kēia e hoʻomohala ai i kāu keiki.
Kaulike Kaulike
He mea maʻalahi ka unahi kaulike no ka haʻi ʻana i ka wā e like like ai ke kaumaha o nā mea ʻelua. Hoʻolako pinepine ʻia ka unahi me kahi hoʻonohonoho o nā kaupaona i hoʻohana ʻia e ana i ke kaumaha o nā mea ʻē aʻe. Nui nā noiʻi hoihoi hiki iā ʻoe ke hana inā ʻoe e kaupalena i nā kaupaona āu e ʻae ʻia e hoʻohana.
Hoʻokahi ʻAno Kaumaha Manaʻo ʻoe he nui kāu mau kaumaha, akā like lākou a pau - e ʻōlelo, 5 mau anakahi. A laila ʻo nā mea wale nō āu e hiki ai ke kaupaona pololei he mau mea he nui o 5 (e like me ka helu ʻana ma ka 5).
ʻElua ʻAno Kaumaha - Hoʻokahi ʻAoʻao Manaʻo ʻoe he nui kāu mau kaumaha he 4 mau ʻāpana a i ʻole 7 mau ʻāpana a hoʻohana wale ʻoe iā lākou ma kekahi ʻaoʻao o ke kaulike. ʻO nā mea āu e hiki ai ke kaupaona ʻo ia nā helu like āu i loaʻa ai i ka noiʻi ʻana i ka pua pua. No 4 a me 7, e hoʻomaka ana ma 18 mau ʻāpana hiki iā ʻoe ke kaupaona pololei i nā mea āpau. Inā he 4 mau ʻāpana a me 6 mau ʻāpana nā kaumaha, hiki iā ʻoe ke kaupaona i nā helu like e hoʻomaka ana me 4.
ʻElua ʻAno Kaumaha – ʻElua ʻAoʻao Ma hope o ka hana ʻana i ka noiʻi me ʻelua ʻano kaumaha ma kekahi ʻaoʻao, e kahaha paha kāu keiki inā ʻoe e noi iā lākou e kaupaona i kahi mea 3-unit, a i ʻole he mea 1-unit, me 4 a me 7. ʻO ke akamai, ʻo ia ke kau ʻana i kekahi mau kaumaha ma kekahi ʻaoʻao a me nā kaumaha ʻē aʻe ma kekahi ʻaoʻao. No ka laʻana, e hōʻoia i ke kaumaha o kahi mea he 3 mau anakahi ma ke kau ʻana me kahi kaumaha 4-unit a ʻike i kona kaulike me kahi kaumaha 7-unit. Pēlā nō, e hōʻoia i ke kaumaha o kahi mea he 1 anakahi ma ke kau ʻana me kahi kaumaha 7-unit a ʻike i kona kaulike me ʻelua mau kaumaha 4-unit.
Aia kekahi kumumanaʻo makemakika koʻikoʻi i kapa ʻia ʻo Bezout's Theorem i hūnā ʻia i loko o kēia noiʻi. ʻAʻole pono kāu keiki e ʻike e pili ana i kēlā kumumanaʻo i kēia manawa, akā, ʻaʻole anei he mea maikaʻi ke hiki i kahi keiki ʻōpio ke pāʻani a puni me ka makemakika holomua!
Ka Pālua ʻana i nā Kaumaha He aha ka mea e hana ai inā loaʻa iā ʻoe hoʻokahi kaumaha no kēlā me kēia kaumaha i ka holomua pālua 1, 2, 4, 8, a me 16? Ehia mau ala e hiki ai iā ʻoe ke kaupaona i kahi mea he 13 ke kaumaha? He aha ke kaumaha nui loa hiki iā ʻoe ke ana?
Ma hope o kekahi noiʻi ʻana, e ʻike ʻoe hiki iā ʻoe ke kaupaona i nā mea āpau a hiki i hoʻokahi emi ma mua o ka pālua o ke kaumaha kiʻekiʻe loa - ma kēia hihia ʻo ia hoʻi he 31. Eia kekahi, hiki ke kaupaona ʻia kēlā me kēia mea āu e kaupaona ai ma hoʻokahi ala wale nō - no ka laʻana, 13 = 1 + 4 + 8, a ʻaʻohe ala ʻē aʻe e hana ai. Maikaʻi loa! Pili kēia kūlana i ka ʻōnaehana helu binary.
Nā Kaumaha Fibonacci: He aha ka mea e hana ai inā aia nā kaumaha ma nā Helu Fibonacci? Aia ma mua o hoʻokahi ala e kaupaona ai i kekahi mau kaumaha? E ʻimi i kahi palena e hana ai i hoʻokahi wale nō ala no kēlā me kēia kaumaha.
Manaʻo ʻia he hoʻokahi kāu no nā kaupaona 1, 1, 2, 3, 5, 8, a me 13. Me kēia, 10 = 2 + 3 + 5 = 2 + 8 = 1 + 1 + 3 + 5 = 1 + 1 + 8. ʻO ke kumu o ka hana pālua ʻana, ʻo ia ka hana ʻana o ke kānāwai Fibonacci i nā ala he nui e kākau ai i nā helu Fibonacci ma ke ʻano o lākou iho - no ka laʻana, 2 = 1 + 1 a me 8 = 5 + 3. ʻO ke ala e hoʻoponopono ai i kēia pilikia, ʻo ia ke koi ʻana ʻaʻole hiki iā ʻoe ke hoʻohana i ʻelua mau helu Fibonacci e pili ana kekahi i kekahi i ke kaʻina. Ke hoʻohui ʻoe i kēlā palena, ʻo ke ala wale nō e loaʻa ai ka 10 ʻo 2 + 8.