- #1

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

But this formula clearly fails for d=1:

should be $$\pi$$

and d=2:

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

- Thread starter onanox
- Start date

- #1

- 15

- 0

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

But this formula clearly fails for d=1:

should be $$\pi$$

and d=2:

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

- #2

mathman

Science Advisor

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http://en.wikipedia.org/wiki/N-sphere

- #3

- 15

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yea, you're right. Schwabl must be counting the dimension its embedded in or something.

- #4

HallsofIvy

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