Overview
This lecture explains the technology, mathematics, and methods used in constructing the pyramids of Giza, focusing on how ancient Egyptians achieved this with available tools.
Religious and Social Motivation
- Egyptians believed preserving the body and building strong tombs was necessary for afterlife entry.
- Pharaohs used their power and wealth to commission pyramids and develop embalming techniques.
Orientation and Layout of Pyramids
- Pyramids are oriented almost perfectly to the cardinal points (N, E, S, W).
- Orientation was likely achieved using observations of the North Star and the shadow of a vertical stick at noon.
- The pyramid's base was constructed as a perfect square aligned to cardinal directions using ropes and geometric techniques.
Quarrying, Cutting, and Transporting Stones
- Most blocks were limestone (density 2.6 gm/cm³), quarried nearby, and cut with copper tools.
- Levers were used to loosen stones; sleds, pulled by many men, transported them.
- Sleds reduced friction, and water or oil lubrication further decreased resistance, making transport feasible.
Block Transportation Mathematics
- Average block was ~1 m³, weighing about 2.86 tons.
- With lubricated sleds, twenty men could move a 3-ton block using about 30 lb of force each on level ground.
- Steeper inclines required more manpower or assistance.
Construction Rate and Workforce
- Great Pyramid volume: 2.59 million m³, requiring about three million blocks.
- Construction needed ~35 blocks delivered per hour, with around 100,000 workers in shifts over twenty years.
Raising Blocks and Pyramid Structure
- Egyptians had only basic machines: levers, inclined planes, and lacked wheels, rollers, pulleys, and abundant wood.
- The pyramid slope (Khufu: 57.6°) was too steep for block transport without ramps.
- Pyramids were likely built as step pyramids, with steps matching their measured angle.
Block Lifting Method
- Causeways (ramps) were built flush with pyramid steps along each face.
- Two crews pulled ropes attached to sleds or blocks up the causeways.
- Each crew of 40 men needed to pull about 71.4 lb per person when moving heavy blocks up steep slopes.
- Most blocks were used in lower levels, with smaller stones placed at the top.
Finishing Touches
- After the final layer, the pyramid was clad in white limestone.
- Some cladding remains visible on the Chefren Pyramid today.
Key Terms & Definitions
- Cardinal Points — The four main directions: North, East, South, West.
- Inclined Plane — Sloped surface used for lifting or moving heavy objects.
- Cubit — Ancient Egyptian unit of length (about 20.7 inches), divided into palms and digits.
- Shekel — Egyptian measure (here refers to the tangent of an angle).
- Causeway — Ramp used for moving blocks up pyramid sides.
- Coefficient of Friction — A measure of how much a surface resists sliding.
Action Items / Next Steps
- Review geometric techniques for orienting structures.
- Practice calculating force requirements for moving objects on inclined planes.
- Read about other ancient construction projects for comparison.