Knowing even just that the
3-4-5 triangle is a
right triangle is enough to do
geometry in the field. Apparently the
ancient Egyptians knew this fact, and used it (all of
Egyptian mathematics was devoted to
tax inspection, for which being able to measure an
area is crucial). Given a
rope of
length 12, knotted at every
unit distance, you can build a right triangle by ensuring
two of the edges have lengths
3 and
4.
It is a shame that people are unable to do the same, 3000 years later.