Nā ʻĀpana Conic Elliptical: Manaʻo, Nā Hoʻohana, a me ke Pili i ke Ola o kēlā me kēia lā Hoʻolauna ʻO nā ʻāpana Conic kahi manaʻo koʻikoʻi i ka makemakika a me ke geometry. ʻEhā ʻano nui o nā ʻāpana conic: nā pōʻai, ellipses, parabolas, a me nā hyperbolas. E kālele ana kēia ʻatikala i hoʻokahi ʻāpana conic hoihoi nona nā noi ola maoli: ka ellipse. … E heluhelu hou aku
Nā ʻĀpana Conic Parabolic: Ke Hoʻomaopopo nei i ko lākou mau ʻAno a me nā Waiwai ʻO nā ʻāpana Conic ka hoʻonohonoho o nā piʻo i loaʻa mai ka hui ʻana o kahi cone me kahi mokulele. ʻEhā ʻano nui o nā ʻāpana conic: circular, elliptical, parabolic, a me hyperbolic. Loaʻa i kēlā me kēia nā waiwai kū hoʻokahi a me nā ʻano e hoʻolilo ai i mea nui i nā ʻano aʻo like ʻole, mai ka makemakika a i ka physics a me ka ʻenekinia. Ma kēia ʻatikala, mākou… E heluhelu hou aku
Ke Kūlana o ʻElua Pōʻai: He Loiloi Geometric I ka makemakika, ʻoi aku hoʻi i ke geometry, he kuleana koʻikoʻi ka hoʻomaopopo ʻana i ke kūlana o ʻelua pōʻai. ʻO ka pōʻai kekahi o nā ʻano geometric kumu i loaʻa pinepine ʻia i nā noi kumumanaʻo a me nā hana. Hāʻawi ke kūlana o ʻelua pōʻai i ka ʻike i ka pilina o kēia mau ʻano ʻelua i ka wā e kau ʻia ai i loko o kahi mokulele hoʻokahi. Hoʻokomo kēia haʻawina i kahi loiloi o… E heluhelu hou aku
ʻO ke kaulike o kahi tangent i kahi pōʻai. ʻO nā pōʻai kekahi o nā mea geometric kumu loa a loaʻa pinepine ʻia ma nā ʻano like ʻole, mai ka makemakika kumu a i ka ʻenekinia kīwila a me ke kuhikuhipuʻuone. ʻO kekahi o nā manaʻo nui e pili ana i nā pōʻai i ka geometry analytical ʻo ia ka kaulike o ka tangent i kahi pōʻai. ʻO ka hoʻomaopopo ʻana i ka kaulike o kahi tangent i kahi pōʻai e wehe i kahi ʻike hohonu o… E heluhelu hou aku
Ke Kūlana o nā Laina e Pili Ana i nā Pōʻai ʻO nā pōʻai kekahi o nā kinona kumu i ke geometry a he nui nā noi ma nā ʻano like ʻole, mai ka makemakika a i ka physics a me ka ʻenekinia. ʻO kahi ʻano koʻikoʻi o ke aʻo ʻana i nā pōʻai ʻo ia ka hoʻomaopopo ʻana i ke kūlana o nā laina e pili ana i nā pōʻai. He mea koʻikoʻi kēia kūlana i nā kūlana he nui, e like me ka hoʻolālā geometric, ka nānā ʻana i ke ʻano, a me ke aʻo ʻana i ka logic… E heluhelu hou aku
Ke Kūlana o kahi Kiko e Pili Ana i kahi Pōʻai ʻO ka pōʻai kahi ʻano geometric kumu i loaʻa pinepine ʻia i ke ola o kēlā me kēia lā a ma nā lālā like ʻole o ka ʻepekema, e like me ka makemakika a me ka physics. ʻO kahi hanana i kūkākūkā pinepine ʻia ma ke ʻano o nā pōʻai ʻo ia ke kūlana o kahi kiko e pili ana i ka pōʻai. Hiki ke hoʻoholo ʻia ke kūlana o kahi kiko e pili ana i kahi pōʻai ma muli o kona mamao… E heluhelu hou aku
Ka Hoʻohālikelike Pōʻai: Manaʻo, ʻAno, a me nā Hoʻohana ʻO nā pōʻai he mau ʻano geometric i loaʻa pinepine ʻia i ke ola o kēlā me kēia lā, inā paha ma ke ʻano o nā huila, nā papa, a i ʻole nā ʻano like ʻole. I ka makemakika, ʻo ka pōʻai ka hōʻiliʻili ʻana o nā kiko āpau i loko o kahi mokulele he mamao mau mai kahi kiko paʻa i kapa ʻia ʻo ke kikowaena. Ua ʻike ʻia kēia mamao mau ʻo ia ka radius o ka pōʻai. I loko o … E heluhelu hou aku
Wehewehena o ka Pōʻai ʻO ka pōʻai kekahi o nā ʻano geometric kumu loa a ua hoʻopio i ke kanaka mai ka wā kahiko. I ka makemakika, ua wehewehe ʻia ka pōʻai ʻo ia ka hoʻonohonoho ʻana o nā kiko āpau i loko o kahi mokulele e like ka mamao mai kahi kiko paʻa. Ua kapa ʻia kēia kiko paʻa ʻo ke kikowaena o ka pōʻai, a ʻo ka mamao mai ke kikowaena a i kekahi kiko ma ka pōʻai ua kapa ʻia ʻo ka radius. 1. Wehewehena o ka Pōʻai… E heluhelu hou aku
Nā Pōʻai a me nā Tangents: Nā Manaʻo, nā Waiwai, a me nā Hoʻohana ʻO nā pōʻai he mau ʻano geometric e pili ana i nā piʻo pani maʻalahi. Loaʻa i nā pōʻai nā ʻano hoihoi like ʻole i lilo i kumuhana o ke aʻo makemakika no nā kenekulia. ʻO kekahi manaʻo koʻikoʻi e pili ana i nā pōʻai ʻo ia ka laina tangent. E kūkākūkā kēia ʻatikala i ke ʻano o nā pōʻai a me nā tangents, ko lākou mau waiwai, a… E heluhelu hou aku
ʻO ke Geometry Analytical: Hoʻohui i ka Algebra a me ke Geometry ʻO ke geometry analytical kahi lālā o ka makemakika e hoʻohui i nā manaʻo mai ka algebra a me ke geometry e aʻo i nā pilina geometric a me nā waiwai me ka hoʻohana ʻana i nā kaulike algebraic. Hoʻomohala kūʻokoʻa ʻia e René Descartes lāua ʻo Pierre de Fermat i ke kenekulia 17, hāʻawi ke geometry analytical i ke kumu no nā manaʻo he nui i ka makemakika hou, physics, a me ka ʻenekinia. ʻO kēia ʻatikala… E heluhelu hou aku