  A simple geometric construction on the moduli spaces $\mathcal{M}_{0,n}$ of
curves of genus $0$ with $n$ ordered marked points is described which gives a
common framework for many irrationality proofs for zeta values. This
construction yields Ap\'ery's approximations to $\zeta(2)$ and $\zeta(3)$, and
for larger $n$, an infinite family of small linear forms in multiple zeta
values with an interesting algebraic structure. It also contains a
generalisation of the linear forms used by Ball and Rivoal to prove that
infinitely many odd zeta values are irrational.
