E noʻonoʻo i ka honua (ma ke ʻano he pōʻai me \(r_1 = 6370km\) ) a me ka pī (ma ke ʻano he pōʻai me \(r_2 = 2mm\) ) a e hoʻohola i kahi kaula ma o ka equator e moe paʻa i ka ʻili. I kēia manawa, e hoʻonui i nā kaula ʻelua i hoʻokahi mika. Pono nā kaula ʻelua i kēia manawa e hoʻopaneʻe loa ʻia ma luna o ka equator - akā ʻaʻole lākou ma luna o ka ʻili, akā lana ma luna o ka equator. Pehea ke kiʻekiʻe ma luna o ka ʻili e lana ai ke kaula ma luna o ka honua, pehea ke kiʻekiʻe ma luna o ka pī?
ʻO ka lōʻihi o nā kaula ʻelua i ka wā mua:
$$
l_1 = 2\cdot 6370 km \cdot \pi \Leftrightarrow r_1 = 6370 km = \frac{l_1}{2 \cdot \pi}
$$
e like me
$$
l_2 = 2 \cdot 2mm \cdot \pi \Leftrightarrow r_2 = 2mm = \frac{l_2}{2 \cdot \pi}.
$$
Akā i kēia manawa aia ma hope o ka hoʻolōʻihi
$$
r_{1 NEU} = \frac{l_1 + 1m}{2\cdot \pi}
$$
e like me
$$
r_{2 NEU} = \frac{l_2 + 1m}{2\cdot \pi}.
$$
Akā kupaianaha kēia manawa
$$
r_{1 NEU} - r_1 = \frac{l_1 + 1m}{2\cdot \pi} - \frac{l_1}{2\cdot \pi} = \frac{l_1 + 1m - l_1}{2 \cdot \pi} = \frac{1m}{2 \cdot \pi} = 0.159m
$$
e like me
$$
r_{2 NEU} - r_2 = \frac{l_2 + 1m}{2\cdot \pi} - \frac{l_2}{2\cdot \pi} = \frac{l_2 + 1m - l_2}{2 \cdot \pi} = \frac{1m}{2 \cdot \pi} = 0.159m.
$$
Pēlā ka mamao mai ka ʻilikai i kūʻokoʻa i ka \(l_1\) a i ʻole \(l_2\) , ʻo ia hoʻi he kūʻokoʻa i ka radii \(r_1\) a i ʻole \(r_2\) nā ʻāpana. Penei ka pane kupaianaha: lana nā kaula ʻelua i ke kiʻekiʻe like \(0.159m\) ) ma luna o ka ʻili.