I'm trying to follow Schwabl Thermodynamics, and I found the following equation for the surface area of a unit d-sphere:(adsbygoogle = window.adsbygoogle || []).push({});

$$ \int d\Omega_d = \frac{2 \pi^{d/2}}{\Gamma(d/2)} $$

But this formula clearly fails for d=1:

should be $$\pi$$

and d=2:

should be $$ 4 \pi $$. What gives?

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# Surface area of a d-sphere

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