3:4:5 face triangle

Pyramid of Khafre

A near-rival to Khufu's pyramid whose representative original dimensions resolve into a particularly clear rational face triangle.

PeriodFourth Dynasty, c. 2558–2532 BCE
PlaceGiza, Egypt
Dimensions modelled215.25 m base; 143.50 m heightRoyal cubit and seked reconstruction
Pattern under reviewHalf-base : height : slant = 3 : 4 : 5
Measured or reconstructed dimensionsCalculated geometryInterpretation labelled

Why this pyramid belongs in the collection

Khafre belongs beside Khufu because visual prominence can mislead. Its higher bedrock position and surviving summit casing make it appear taller from some viewpoints, even though its reconstructed original height is lower. The calculator returns attention to the measured profile.

What can be measured

Using a representative base side of 215.25 metres and original height of 143.50 metres, the half-base is 107.625 metres and the calculated slant is 179.375 metres. Those values reduce exactly to a 3:4:5 right triangle for the selected model. Survey estimates and casing reconstruction still carry archaeological uncertainty.

The native or comparative measure

The most historically plausible design language is a cubit divided into palms and digits, expressed through a seked. The selected dimensions return a 5.25-palm seked. That rational slope is easier to construct and communicate than a retrospective decimal angle.

Calculate this monumentOpen Pyramid of Khafre in the pyramid calculator. The shared tolerance and rounding rules make its result directly comparable with the other seven pyramids.

The pattern worth testing

The exact 3:4:5 relationship is stronger than the slant ratio's looser proximity to phi. This is a useful example of why the calculator ranks a direct rational construction above a nearby named irrational constant.

Interpretive limit

The clean ratio belongs to the selected reconstruction, not automatically to every survey line or surviving course. A ratio can be geometrically exact inside a model while the original intention remains an archaeological argument.

A repeatable investigation

Begin with the published or reconstructed dimensions and state the shape assumption. Calculate the seked and ordinary geometry before testing a named constant. Keep the chosen broad ±0.5 exploratory screen fixed across the full collection, display the residual for every match, and treat a numerical result as evidence of intention only when independent historical evidence supports it.

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