Revision as of 19:37, 21 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div> {{Alert-warning|This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion. }}Prove that the area of the unit sphere in <math>\mathbb R^N</math> is given by <math display="block"> A=\left(\frac{\pi}{2}\right)^{[N/2]}\frac{2^N}{(N-1)!!} </math> with our usual convention <math>N!!=(N-1)(N-3)(...")
BBot
Apr 21'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.
Prove that the area of the unit sphere in [math]\mathbb R^N[/math] is given by
[[math]]
A=\left(\frac{\pi}{2}\right)^{[N/2]}\frac{2^N}{(N-1)!!}
[[/math]]
with our usual convention [math]N!!=(N-1)(N-3)(N-5)\ldots[/math] for double factorials.