How can $\pi$ be defined as a surreal number. I want to express $\pi$ in the Surreal Number notation $\{L|R\}$. What is the most natural or intuitive way of doing so, seeing as there are many (possibly infinite) ways of expressing the same surreal number.

Perhaps a more natural construction would be to consider the sequences $I_n$ and $C_n$ of $n$-gons (a) inscribed in and (b) circumscribing a circle of unit diameter for $n\in\mathbb{N}$. Now takes $i_n$ to be the circumference of $I_n$ and $c_n$ the circumference of $C_n$. $i_n$ and $c_n$ are algebraic, so can certainly be constructed without first constructing $\pi$, so it makes sense to set
$$\pi = \{ i_n \mid c_n \}$$
