Spherical degree by area pullback
= Spherical degree by area pullback
{title2=$\deg g=\frac1{4\pi}\int_{S^2}g^*\omega$}
For a smooth map between oriented unit <spheres>, integrate the pullback of the target <area form>. Localizing a normalized top-degree form near a <regular value>, and using <Stokes theorem> to discard exact-form differences, identifies this integral with the <degree as a sum of local degrees>.