The analog formula of Euler's formula in terms of the Pauli matrices R ^ ^ ( θ θ , n ^ ^ ) = e i θ θ 2 n ^ ^ ⋅ ⋅ σ σ = I cos ⁡ ⁡ θ θ 2 + i ( n ^ ^ ⋅ ⋅ σ σ ) sin ⁡ ⁡ θ θ 2 for higher spins is tractable, but less simple.