@lisyarus Under "Quaternions in Clifford (aka geometric) algebra" near the end, there's a problem with your definition of i, j, and k. Notice that ij ≠ k, but instead ij = −k, so these are not actually isomorphic to the quaternions. You need to negate all three bivectors so that i = −e₂₃, j = −e₃₁, and k = −e₁₂.