Project Euler Search Results: Tutorials on Elementary Problems, Only Euler's 18th-Century Ellipse Work Substantive — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Search results are mostly tutorial videos on elementary Project Euler problems (figurate numbers, palindromes, factorials, name scores) — no genuinely unsolved or deep mathematical discoveries; the only substantive research item is Euler's 18th-century work on minimal-area/perimeter ellipses through fixed points. | MATH: Figurate numbers: P(s,n) = ((s-2)n² - (s-4)n)/2 for s-gonal numbers (e.g., heptagonal s=7). Euler's ellipse problem: given m points, find ellipse minimizing area A = πab or perimeter (elliptic integral, no closed form) subject to passing through all points — an early constrained optimization in projective/affine geometry. | CONNECTION: Figurate numbers relate to polygonal numbers, which connect to lattice points on triangular grids (2D root system A₂) — but no golden ratio or base-60 appears in the cited problems. Euler's ellipse extremization touches on affine geometry, where ellipse area is invariant under affine transforms (det = 1) — a symmetry group (SL(2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222297850
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