def archimedes(q1, q2, q3):
    """
    This is the difference between the lhs and the rhs of the
    TripleQuadForumula.  [MF 124 @ 2:23].

    The TQF is satisfied when this is zero.

    Given:
        TQF: ((q1 + q2 + q3) ** 2) == (2 * (q1 ** 2 + q2 ** 2 + q3 ** 3))

    Define:
        A(q1, q2, q3) = ((q1 + q2 + q3) ** 2) - (2 * (q1 ** 2 + q2 ** 2 + q3 ** 3))

    Claim:
        A(q1, q2, q3) = 4 * q1 * q2 - (q1 + q2 - q3) ** 2
    """
    return 4 * q1 * q2 - (q1 + q2 - q3) ** 2