  Ever since Flinders Petrie undertook a theodolite survey on the Giza plateau
in 1881 and drew attention to the extraordinary degree of precision with which
the three colossal pyramids are oriented upon the four cardinal directions,
there have been a great many suggestions as to how this was achieved and why it
was of importance. Surprisingly, given the many astronomical hypotheses and
speculations that have been offered in the intervening 130 years, there have
been remarkably few attempts to reaffirm or improve on the basic survey data
concerning the primary orientations.
  This paper presents the results of a week-long Total Station survey
undertaken by the authors during December 2006 whose principal aim was to
clarify the basic data concerning the orientation of each side of the three
large pyramids and to determine, as accurately as possible, the orientations of
as many as possible of the associated structures. The principal difference
between this and all previous surveys is that it focuses upon measurements of
sequences of points along multiple straight and relatively well preserved
structural segments, with best-fit techniques being used to provide the best
estimate of their orientation, as opposed to simple triangulation between
directly identified or extrapolated corners.
  Our results suggest that there is only a very slight difference in
orientation (c. 0.5 arc minutes) between the north-south axes of Khufu's and
Khafre's pyramids, that the sides of Khafre's are more perfectly perpendicular
than those of Khufu's, and that the east-west axis is closer to true
cardinality in both cases. The broader context of associated structures
suggests that the east-west orientation in relation to sunrise or (in one case)
sunset may have been a, or even the, key factor in many cases.
