In geometry, a ball is a region in space comprising all points within a fixed distance from a fixed point. An n-ball is a ball in n-dimensional Euclidean space. The volume of an n-ball is an important constant that occurs in formulas throughout mathematics.
== Formulas ==
=== The volume ===
The n-dimensional volume of a Euclidean ball of radius R in n-dimensional Euclidean space is:
V
n
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R
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A drunk man will find his way home, but a drunk bird may get lost forever.
This encodes the fact that a 2-dimensional random walk is recurrent (appropriately defined for either the discrete or continuous case) whereas in higher dimensions random walks are not. More details can be found for ...
Is there any polynomial $f(x,y)\in{\mathbb Q}[x,y]{}\ $ such that $f:\mathbb{Q}\times\mathbb{Q} \rightarrow\mathbb{Q}$ is a bijection?
