Pyramid Geometry
ancient-egypt style geometry for square pyramids
Polyhedral Metric Constraints 🖖
The square pyramid is a fundamental polyhedron where volume and surface area are strictly bound by non-linear trigonometric relationships. The dihedral angle dictates the slant height, structurally mapping base dimensions to three-dimensional polyhedral limits.
Two numbers define the whole pyramid 🖖
A square pyramid is fully fixed by just two measurements: the base side s and the vertical height h. Everything else follows from one right triangle running from the center of the base to the midpoint of an edge. The slant height is its hypotenuse, l = √(h² + (s/2)²), and once you have l, the surface area and volume drop right out. Change one input and every result recomputes together.
How Egyptians measured slope backwards 🖖
The ancient Egyptians used no angles. In the Rhind Mathematical Papyrus they recorded a pyramid's slope as its seked: the horizontal run, in palms, for every royal cubit (7 palms) of vertical rise — essentially the cotangent, the inverse of our modern slope. The Great Pyramid's seked is about 5½ palms, giving a face angle near 51.84°. This tool's seked output revives that 3,600-year-old convention.
Example problems
- school example - School example: compute slant height, area, and volume.
- great pyramid - Great Pyramid scale approximation with real-world dimensions.
- steep face - Steeper pyramid with larger face angle.
- flat face - Flatter pyramid with smaller face angle.