Pyramid 11:7 — shape, scale and 10 comparisons (G2, English)
Instructions, scope and sources
Explore a square pyramid using independent sliders. q = B/h changes shape, while s uniformly scales the whole pyramid: B = 11s, h = 11s/q. Initial values and reset: q = 11/7, s = 1, base side B = 11, height h = 7.
Select one comparison #1–10: π, γ, √3, √6, √2, √5, Tribonacci, Brun, 1/φ or φ. The panel shows the segments, formula, result, reference, relative error and 0.1% tolerance. 3D / Copies switches between source segments on the pyramid and two chains of copies using one common scale factor 1/s. Changing s alone does not change the ratios. Pyramid and Other slant heights toggle contextual geometry. If needed, zoom out in 3D; a wide screen is recommended.
√2 is an exact identity of every square. Other matches at 11:7 are numerical approximations, and several results are algebraically dependent. Brun uses an adopted estimate with unspecified rigorous reference uncertainty. Agreement does not prove historical intent or a physical pyramid function. Comparisons #11–13 remain planned.
The English file passed 12,849/12,849 mathematical and construction checks for 64 configurations, plus 40/40 language checks, also after reopening the exported file in a fresh GeoGebra instance. Installed Classic 6, phone, accessibility and offline use are not verified.
Project concept: Michał Przybylski — prylski.dev
Koncepcja projektu: Michał Przybylski — prylski.dev
GitHub: https://github.com/MichaelZP/
Polish edition: https://www.geogebra.org/m/mwvagws2
Detailed project documentation and sources (Polish): https://michaelzp.github.io/great-pyramid-11-7-lab-edu/education/geogebra/g2/
Sources: Euclid — classical geometry; Euler and Mascheroni — γ; M. Feinberg and OEIS A058265 — Tribonacci; Viggo Brun, Thomas R. Nicely and OEIS A065421 — the adopted B₂ estimate. GeoGebra Team supplies the software. Full attributions and limits of evidence are in the documentation.