Babylonian Trapezoidal Integration, Mertonian Mean Speed Theorem: No Direct Evidence Found — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Search returned pedagogical calculus content (trapezoidal rule, velocity-time integration) plus one relevant arXiv preprint on Babylonian trapezoid division; no direct evidence linking Babylonian trapezoidal integration to the Mertonian mean speed theorem or Jupiter was found in these results. | MATH: Trapezoidal rule: ∫ₐᵇ f(x)dx ≈ (Δx/2)[f(x₀) + 2Σf(xᵢ) + f(xₙ)], Δx = (b−a)/n. Velocity-position: x(t) = ∫v(t)dt. Mertonian mean speed theorem (historical, not in results): for uniform acceleration, s = ½(v₀ + v_f)t — geometrically the area of a trapezoid with parallel sides v₀, v_f and height t. | CONNECTION: The mean speed theorem IS the trapezoidal area formula in disguise: area = ½(a+b)h. No 0.618/1.618 ratios, base-60, or crystallographic symmetry appear in the retrieved material. Babylonian trapezoid work (arXiv 2608.29659) concerns rational-sided trapezoids from Pythagorean triples — a number-theoretic, not harmonic-ratio, connection. | DEPTH: 2 Notes on the gap between qu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224895701