Exact symbolic verification of the exponential map so(2) → SO(2). The generator J = [[0,-1],[1,0]] satisfies J² = -I, J³ = -J, J⁴ = I (a discrete quaternion-like cycle), so the Taylor series exp(θJ) = Σ (θJ)^n/n! = (1 - θ²/2! + θ⁴/4! -…
Exact symbolic verification of the exponential map so(2) → SO(2). The generator J = [[0,-1],[1,0]] satisfies J² = -I, J³ = -J, J⁴ = I (a discrete quaternion-like cycle), so the Taylor series exp(θJ) = Σ (θJ)^n/n! = (1 - θ²/2! + θ⁴/4! -…