The narrator just called DNA a time machine. π
They were good at Geometry
**Yes β they were very good at the geometry that mattered to them.**
Their geometry was practical and applied, not the abstract, theorem-proving style later developed by the Greeks. It was the geometry of surveyors, architects, and administrators, and the surviving evidence shows they handled it with real competence.
### What the sources show
The main evidence comes from two mathematical handbooks:
– **Rhind Mathematical Papyrus** (copied c. 1650 BCE from an older Middle Kingdom original)
– **Moscow Mathematical Papyrus** (roughly the same period)
These contain worked problems on:
– **Areas**: rectangles, triangles, trapezoids, and circles. For a circle they used a formula equivalent to Ο β 256/81 β 3.16 β a good practical approximation.
– **Volumes**: cylindrical granaries, rectangular storage bins, and (most impressively) the correct formula for the volume of a truncated square pyramid (frustum). The Moscow Papyrus gives the procedure that matches the modern formula.
– **Pyramid slopes**: they used the *seked* β the horizontal run for a given vertical rise (essentially the cotangent of the face angle). Problems calculate height from base and *seked*, or *seked* from base and height. This is exactly what pyramid builders needed.
### Practical mastery on the ground
After every Nile flood the land had to be re-surveyed and boundaries restored. The βrope-stretchersβ (*harpedonaptai*) did this work. Greek writers later credited them with the origins of geometry. They almost certainly used knotted ropes to lay out right angles (the 3-4-5 triangle is the simplest reliable method and fits the evidence).
The precision of the major pyramids themselves is the strongest practical proof. Bases are square to high accuracy, sides are aligned to the cardinal directions, and the slopes are consistent. That level of execution required solid geometric control, not just rule-of-thumb building.
### Limits
They did not develop an axiomatic system, formal proofs, or general theorems in the Euclidean sense. Their texts give recipes that work for the problems at hand. Within those practical bounds, however, they were skilled, systematic, and effective. The geometry they needed for surveying, architecture, and administration, they largely mastered.
