Global Positioning System Reference
In-Depth Information
FIGURE 3.1.
Constructing a square on level ground, using only a peg and a rope. From
the central peg, mark out a circle. Starting at a point on the circle, stretch the rope to
another point on the circle; repeat until the circle has been divided into six equal seg-
ments. The dashed lines are parallel. Stretch the rope along these lines from the
circle to construct the square shown.
a certain age) was taught in grade school. Consider, for example, figure 3.1,
in which you can see how a peg and rope system can be used to construct a
square. This method is just one way of doing it; there are many others.
The method of figure 3.1 is simple in that it requires no knowledge of
algebra. Thus, it does not assume that the surveyor is aware of Pythagoras's
theorem. But with such extra knowledge, the construction of a square
would be even simpler: the surveyor would equip himself with two ropes,
one the length of a side of the square he sought to lay out, and the second
with a length greater by a factor of
2 . Two such ropes make the con-
struction of a square quite trivial. It is likely that the mathematical knowl-
edge of third-millennium-BCE Egyptians was more sophisticated than that
of their near contemporaries in stone age Britain,
2
and yet we see from
figure 3.1 that even an intuitive knowledge of basic plane geometry, unsup-
ported by theoretical ruminations, is su≈cient for constructing squares.
2. For example, the Egyptians knew about 3-4-5 triangles—that is, if the lengths of the
sides of a triangle are in the ratio 3:4:5, then one of the angles of the triangle is 90\. That
they used geometry when surveying is pretty obvious from their pyramids, which have very
square bases. As for the builders of Stonehenge, the theory that they surveyed the con-
struction site using peg and rope techniques is due to Johnson (2008).
