line">\(\mathbb{R}^2\)</span>. However, the overall shape of <span class="math inline">\(S^2\)</span> is not like a plane
in that is compact (i.e., there is a maximum distance between points).
If you set off around the globe in a “straight line” (i.e., a
geodesic), you wind up back where you started eventually; that is why
the geodesics on the sphere (<span class="math inline">\(S^2\)</span>) are called “great circles,” and
why we need to use some clever representations to do circular or
spherical s