Near-phi exploratory match

Pyramid of Menkaure

The smallest main pyramid at Giza shows how a declared tolerance changes which proportional patterns enter the comparison set.

PeriodFourth Dynasty, c. 2532–2503 BCE
PlaceGiza, Egypt
Dimensions modelled108.50 m base; 65.50 m heightRoyal cubit and seked reconstruction
Pattern under reviewNear phi slant and 2 pi perimeter within ±0.5
Measured or reconstructed dimensionsCalculated geometryInterpretation labelled

Why this pyramid belongs in the collection

Menkaure prevents Giza from becoming a one-monument pattern story. Its smaller scale, granite casing programme, unfinished surfaces, and later damage create a different evidential problem while retaining the same basic geometric vocabulary.

What can be measured

The calculator uses representative original dimensions of 108.50 metres for the base and 65.50 metres for the height. They produce a face angle near 50 degrees, a slant near 85.05 metres, and an ideal-envelope volume near 257,027 cubic metres. Published base estimates vary, so the selected values are declared rather than hidden.

The native or comparative measure

A seked remains the appropriate cross-scale comparison because it describes run per rise without depending on metres. The selected profile yields about 5.80 palms per royal cubit of rise, not a neat half-palm value.

Calculate this monumentOpen Pyramid of Menkaure 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 slant-to-half-base ratio of about 1.568 enters the chosen broad ±0.5 screen for phi, while the perimeter-to-height ratio of about 6.626 enters the same screen for 2 pi. Both are named patterns under the declared tolerance rather than exact identities.

Interpretive limit

The broad screen intentionally favours pattern visibility. Menkaure's residuals remain substantially larger than Khufu's, so the displayed deltas are essential to comparing the strength of the two results.

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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