tatistics.</p>
<p>Even though <span class="math inline">\(S^{n-1}\)</span> behaves locally like <span class="math inline">\(\mathbb{R}^{n-1}\)</span>, there is no
way to smoothly map between them. For example, because
latitude and longitude work on a modular basis (wrapping at <span class="math inline">\(2\pi\)</span>
radians in natural units), they do not produce a smooth map.</p>
<p>Like a bounded interval <span class="math inline">\((a, b)\)</span>, in geometric terms, a sphere is
compact in that the dis