doomed?

def find_centroid(polygon):
    """Find the centroid of a polygon. If a polygon has 0 area, use the latitude
    and longitude of its first position as its centroid.

    http://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon

    Arguments:
    polygon -- A list of positions, in which the first and last are the same

    Returns 3 numbers: centroid latitude, centroid longitude, and polygon area.

    >>> p1 = make_position(1, 2)
    >>> p2 = make_position(3, 4)
    >>> p3 = make_position(5, 0)
    >>> triangle = [p1, p2, p3, p1] # First vertex is also the last vertex
    >>> round_all = lambda s: [round(x, 5) for x in s]
    >>> round_all(find_centroid(triangle))
    [3.0, 2.0, 6.0]
    >>> round_all(find_centroid([p1, p3, p2, p1])) # reversed
    [3.0, 2.0, 6.0]
    >>> apply_to_all(float, find_centroid([p1, p2, p1])) # A zero-area polygon
    [1.0, 2.0, 0.0]
    """
    "*** YOUR CODE HERE ***"
    def polygon_area_fn(polygon):
        if len(polygon) == 1:
            return 0
        else:
            part_a = ((longitude(polygon[0])*latitude(polygon[1])) -
                      (longitude(polygon[1])*latitude(polygon[0])))
        return (part_a + polygon_area_fn(polygon[1:]))

    def centroid_latitude_fn(polygon):
        if len(polygon) == 1:
            return 0
        else:
            part_x = ((latitude(polygon[0]) + latitude(polygon[1])) *
                      (latitude(polygon[0])*longitude(polygon[1]) -
                       latitude(polygon[1])*longitude(polygon[0])))
        return part_x + centroid_latitude_fn(polygon[1:])

    def centroid_longitude_fn(polygon):
        if len(polygon) == 1:
            return 0
        else:
            part_y = ((longitude(polygon[0]) + longitude(polygon[1])) *
                      (latitude(polygon[0])*longitude(polygon[1]) -
                       latitude(polygon[1])*longitude(polygon[0])))
        return part_y + centroid_longitude_fn(polygon[1:])

    polygon_area = polygon_area_fn(polygon) * (1/2)
    centroid_latitude = (1/(6*polygon_area)) * centroid_latitude_fn(polygon)
    centroid_longitude = (1/(6*polygon_area)) * centroid_longitude_fn(polygon)
    final_list = [centroid_latitude, abs(centroid_longitude), abs(polygon_area)]
         # Trying to do abs(centroid_latitude), centroid_latitude*-1, or
         # anything else gives a ZeroDivisionError.
    return final_list