McShane's identity

In geometric topology, McShane's identity for a once punctured torus $$\mathbb{T}$$ with a complete, finite-volume hyperbolic structure is given by


 * $$\sum_\gamma \frac{1}{1 + e^{\ell(\gamma)}}=\frac{1}{2}$$

where This identity was generalized by Maryam Mirzakhani in her PhD thesis
 * the sum is over all (unoriented) simple closed geodesics γ on the torus; and
 * ℓ(γ) denotes the hyperbolic length of γ.