Nā nīnau hoʻohālike e kūkākūkā ana i ke kūlana o nā pōʻai ʻelua
Pendahuluan
ʻO ka pōʻai kekahi o nā kinona kumu i ke geometry a mākou e ʻike pinepine ai i nā pilikia makemakika like ʻole. ʻO ke aʻo ʻana i ke kūlana o nā pōʻai ʻelua he kumuhana koʻikoʻi ma muli o kāna mau hoʻohana he nui i ke ola o kēlā me kēia lā. I ka makemakika, hiki ke kālailai ʻia ke kūlana o nā pōʻai ʻelua ma ka nānā ʻana i ko lākou mau kūlana pili ma muli o ka mamao ma waena o ko lākou mau kikowaena a me ko lākou mau radii.
Ke Manaʻo o ke Kūlana o nā Pōʻai ʻElua
No ka hoʻoholo ʻana i ke kūlana o nā pōʻai ʻelua, hoʻohana mākou i kekahi mau palena nui:
1. Radius o ka pōʻai mua (r1)
2. ʻO ke anawaena o ka pōʻai ʻelua (r2)
3. Ka mamao ma waena o nā kikowaena o nā pōʻai ʻelua (d)
Ma muli o kēia mau waiwai, aia kekahi mau kūlana o nā pōʻai ʻelua:
1. He tangent ka pōʻai mai waho mai
– Hana ʻia inā ʻo d = r1 + r2.
2. Ke hui pū nei nā pōʻai mai loko mai
– Hana ʻia inā d = |r1 – r2|.
3. Nā pōʻai e hui pū ana
– Hana ʻia inā |r1 – r2| < d < r1 + r2. 4. Ua kaʻawale nā pōʻai - Hana ʻia inā d > r1 + r2.
5. Hoʻokahi pōʻai i loko o kekahi pōʻai me ka ʻole o ka hoʻopā ʻana
– Hana ʻia inā ʻo d < |r1 - r2|. 6. E hui pono nā pōʻai i kekahi i loko o kekahi – Hana ʻia inā ʻo d = 0 a ʻo r1 = r2 (ʻo lāua ʻelua ka pōʻai like). Nā Nīnau Hoʻohālike a me ke Kūkākūkā E nānā kākou i kekahi mau nīnau hoʻohālike e hoʻomaopopo maikaʻi i ke kūlana o nā pōʻai ʻelua. Laʻana Nīnau 1: E hui pū nā pōʻai ma waho Nīnau: Hāʻawi ʻia i ʻelua pōʻai me nā kikowaena ma nā kiko A a me B, a ʻo ka mamao AB he 10 cm. ʻO ke anawaena o ka pōʻai mua he 6 cm, ʻoiai ʻo ke anawaena o ka pōʻai ʻelua he 4 cm. E hoʻoholo i ke kūlana o nā pōʻai ʻelua. Kūkākūkā: - Hāʻawi ʻia: - ʻO ke anawaena o ka pōʻai mua, r1 = 6 cm - ʻO ke anawaena o ka pōʻai ʻelua, r2 = 4 cm - ʻO ka mamao ma waena o nā kikowaena o nā pōʻai, d = 10 cm No nā kūlana tangent waho: \[ d = r1 + r2 \] E hoʻokomo i nā waiwai: \[ d = 6 + 4 \] \[ d = 10 \] ʻOiai ʻo d = 10 cm, ʻo ia hoʻi ka huina o r1 a me r2, he tangent waho nā pōʻai ʻelua. Laʻana Nīnau 2: Nā Pōʻai Tangent Kūloko Nīnau: ʻElua mau pōʻai me nā radii o 8 cm a me 3 cm ka mamao ma waena o nā kikowaena o 5 cm. E hoʻoholo i ke kūlana o nā pōʻai ʻelua. Kūkākūkā: - Hāʻawi ʻia: - ʻO ke anawaena o ka pōʻai mua, r1 = 8 cm - ʻO ke anawaena o ka pōʻai ʻelua, r2 = 3 cm - ʻO ka mamao ma waena o nā kikowaena o nā pōʻai, d = 5 cm No nā kūlana tangent kūloko: \[ d = |r1 - r2| \] E helu: \[ d = |8 - 3| \] \[ d = 5 \] ʻOiai ʻo d = 5 cm, ʻo ia hoʻi ka ʻokoʻa o r1 a me r2, e hui pū ana nā pōʻai ʻelua i loko. Laʻana Nīnau 3: Nā Pōʻai e Hui Pū ana Nīnau: ʻO nā radius o ʻelua pōʻai he 7 cm a me 5 cm me ka mamao ma waena o ko lākou mau kikowaena he 9 cm. E hoʻoholo i ke kūlana o nā pōʻai ʻelua. Kūkākūkā: - Hāʻawi ʻia: - Radius o ka pōʻai mua, r1 = 7 cm - Radius o ka pōʻai ʻelua, r2 = 5 cm - Ka mamao ma waena o nā kikowaena o nā pōʻai, d = 9 cm No ke kūlana e hui pū ana: \[ |r1 - r2| < d < r1 + r2 \] E helu: \[ |7 - 5| < 9 < 7 + 5 \] \[ 2 < 9 < 12 \] ʻOiai ʻo ka waiwai o d e hāʻule ma waena o |r1 - r2| a me r1 + r2, a laila e hui pū ana nā pōʻai ʻelua. Laʻana Nīnau 4: Nā Pōʻai i Hoʻokaʻawale ʻia kekahi i kekahi Nīnau: ʻO nā pōʻai me nā radius o 2 cm a me 3 cm he mamao ma waena o ko lākou mau kikowaena o 7 cm. E hoʻoholo i ke kūlana o nā pōʻai ʻelua. Kūkākūkā: - Hāʻawi ʻia: - ʻO ke radius o ka pōʻai mua, r1 = 2 cm - ʻO ke radius o ka pōʻai ʻelua, r2 = 3 cm - ʻO ka mamao ma waena o nā kikowaena o nā pōʻai, d = 7 cm No nā kūlana i hoʻokaʻawale ʻia kekahi i kekahi: \[ d > r1 + r2 \]
Helu:
\[ 7 > 2 + 3 \]
\[ 7 > 5 \]
No ka mea, ʻoi aku ka nui o d ma mua o ka huina o r1 a me r2, ua hoʻokaʻawale ʻia nā pōʻai ʻelua kekahi i kekahi.
Laʻana Nīnau 5: Hoʻokahi Pōʻai i loko o kekahi me ka ʻole o ka hoʻopā ʻana
Nīnau:
ʻElua mau pōʻai me nā radius o 8 kenimika a me 2 kenimika ko lāua mamao ma waena o ko lāua mau kikowaena o 5 kenimika. E hoʻoholo i ke kūlana o nā pōʻai ʻelua.
Kūkākūkā:
– Ua ʻike ʻia:
– ʻO ke anawaena o ka pōʻai mua, r1 = 8 kenimika
– ʻO ke anawaena o ka pōʻai ʻelua, r2 = 2 kenimika
– Ka mamao ma waena o nā kikowaena o nā pōʻai, d = 5 kenimika
No ke kūlana o kekahi i loko o kekahi me ka ʻole o ka hoʻopā ʻana:
\[ d < |r1 - r2| \] E helu: \[ d < |8 - 2| \] \[ 5 < 6 \] ʻOiai ʻoi aku ka liʻiliʻi o d ma mua o ka ʻokoʻa ma waena o r1 a me r2, aia kekahi pōʻai i loko o kekahi me ka ʻole o ka hoʻopā ʻana. Hopena Hiki i ka hoʻomaopopo ʻana i ke kūlana o nā pōʻai ʻelua ke kōkua iā mākou i nā noi like ʻole o ke geometry a me ka hana maoli. Ma ka ʻike ʻana i ka pilina ma waena o ka radius o kahi pōʻai a me ka mamao ma waena o kona mau kikowaena, hiki iā mākou ke hoʻoholo inā pili nā pōʻai ʻelua i waho a i loko paha, e hui pū ana, a i ʻole e hoʻokaʻawale ʻia. Ma o nā laʻana ma luna, manaʻolana ʻia e hiki i ka poʻe heluhelu ke hoʻomaopopo maikaʻi i kēia manaʻo a hoʻopili iā ia i nā kūlana makemakika like ʻole. E hoʻomau i ka hoʻomaʻamaʻa ʻana i nā pilikia me nā ʻano like ʻole e hoʻomaikaʻi i kou mau mākau loiloi a me ka hoʻomaopopo ʻana i ke kūlana o nā pōʻai ʻelua. ʻO ka nui o kāu hoʻomaʻamaʻa ʻana, ʻoi aku ka maʻalahi iā mākou ke hoʻoponopono i nā pilikia like ʻole e pili ana i nā pōʻai i ke geometry.
