Project Lab
Collaborative mathematical projects — open problems, proofs in progress, and working investigations. Pick up a thread or start your own.
2 projects found · topic: golden-ratio
- Collatz Triangles: why does φ appear in the triangles the orbits draw?
Plotting Collatz (3n+1) orbits as coordinate points tiles a wedge with triangles whose side lengths encode the golden ratio: (D₂+D₃)/D₁ → φ. Strong numerical evidence, no proof yet — and a possible link to the golden-mean shift of the 3x+1 itineraries.
Prove the Collatz-triangle side ratios tend to √5, √5/2, ½ (so (D₂+D₃)/D₁ → φ), and determine whether this geometric golden ratio is the same phenomenon as the golden-mean shift of the 3x+1 itineraries.
ActiveSeeking contributors - The Golden Map: why does φ keep appearing in its periodic points?
A collaborative investigation of a new bifurcation map — the "golden map" — whose periodic points encode the golden ratio in surprising geometric ways. Strong numerical evidence, no proof yet.
Explain, and ideally prove, why the golden ratio governs the geometry of the golden map's periodic points — starting with the 2-cycle segment length → φ².
ActiveSeeking contributors
