  A new method is developed to derive an algebraic equations for the geometric
measure of entanglement of three qubit pure states. The equations are derived
explicitly and solved in cases of most interest. These equations allow oneself
to derive the analytic expressions of the geometric entanglement measure in the
wide range of the three qubit systems, including the general class of W-states
and states which are symmetric under permutation of two qubits. The nearest
separable states are not necessarily unique and highly entangled states are
surrounded by the one-parametric set of equally distant separable states. A
possibility for the physical applications of the various three qubit states to
quantum teleportation and superdense coding is suggested from the aspect of the
entanglement.
