5½-palm seked
Seven palms of rise for 5½ palms of run produces the exact 14:11 triangle in the conventional cubit model.
Model variance: 0%Flagship interactive exemplar
Giza: one slope, three readings
A dynamic comparison of the Great Pyramid's 5½-palm seked with the famous pi and phi interpretations generated by the same triangle.
One base, three height rules
Compare what each reading actually changes.
The base remains fixed at 440 royal cubits. Each model asks what height would make one rule exact, then compares that ideal with the conventional 280-cubit reference.
Historically grounded model
Selected height rule
5½-palm seked
280royal cubits high
A 5½-palm horizontal run for each royal cubit of rise gives the 14:11 profile.
Matches the 280-cubit reference exactly in this conventional model.
Reference profile440 base × 280 height
Pi comparison
For 440 by 280 cubits, perimeter divided by height is 44/7. This is close to 2π.
Variance: 0.0403%Phi comparison
Slant height divided by half-base is close to φ, producing a near Kepler triangle.
Variance: 0.0344%The central finding
The three results are mathematically dependent.
The standard 440-by-280-cubit model produces a half-base of 220 and a height of 280. Reduce that triangle and the rise-to-run ratio is 14:11. The seked is therefore 5½ palms. Perimeter divided by height becomes 44/7, close to 2π. The slant ratio becomes close to φ.
Those are not three independent codes discovered in separate parts of the monument. They are three descriptions of one slope. A deliberate 5½-palm construction choice could create both modern comparisons without the architect selecting π and φ as abstract targets.
Interpretive boundaryThe numerical closeness is measured. Claims about what Khufu's designers intended are interpretations. No surviving Fourth Dynasty design text names π, φ, or a Kepler triangle.
What the evidence can support
Petrie's survey supports careful reconstruction of the monument. The royal-cubit system is supported by physical rods and architectural analysis. Egyptian seked mathematics is documented in the later Rhind Mathematical Papyrus. Together they make a practical slope model historically plausible while leaving intention open.
Read the monument dossier · Test the 440 × 280 model · Use the sacred-geometry evidence framework