KEY PROBLEM
PROJECT 03 · COMPUTATIONAL GEOMETRY · OPEN RESEARCH · VERIFICATION
Triangle Packing Atlas
A living, reproducible map of what fits, what is proven, and what remains open.
311verified records
THE SYSTEM
Triangle Packing Atlas maps dominant observed packing patterns across triangle geometry and rectangle aspect ratio. Every published record carries coordinates, provenance, an evidence state, and enough information for independent replay.
LIVE RESEARCH ATLAS
Move through shape space and watch the dominant pattern change.
Explore the phase map, inspect verified records, compare constructions, and browse explicitly open problems.
OPEN FULL EXPERIENCE ↗
APPROACH
I built a versioned research dataset, a deterministic solver portfolio, a phase-map interface, and separate JavaScript and Python verification paths. The atlas exposes optimality gaps and labels unsupported or open claims rather than hiding uncertainty.
HOW IT WORKS
A chain of evidence—not merely a gallery of dense layouts.
- 01Canonical problem definitions and versioned coordinate records
- 02Lattice, exact-discrete, local, and evolutionary solver portfolio
- 03Independent overlap, boundary, and evidence verification
- 04Interactive phase maps, record inspection, and contribution reports
DIFFICULT DECISION
The defining decision was to keep mathematical truth separate from presentation. Software can promote a candidate to a verified construction, but only reviewable bounds and human-reviewed proof can justify a proven-optimal claim.
EVALUATION
The 1.0.0 release candidate replays every research record through independent JavaScript and Python geometry implementations. Shared-budget solver traces preserve orientation, iterations, density, algorithm version, and deterministic seed.
RESULT