The Lewis World Map
A novel cartographic projection derived from structured mathematical principles — delivering measurable advantages in area distortion, coordinate addressing, and built-in error detection.
Begin the Journey →Mathematical Foundation
Every design decision in the Lewis World Map traces to a mathematically justified principle — no arbitrary choices.
Optimal Sphere Sampling
A structured angular distribution achieves near-uniform coverage at any resolution level, with proven minimum area distortion benchmarked against established alternatives.
Learn more →Hierarchical Addressing
Every location on Earth carries a canonical address derived from a structured numerical sequence. Addresses are self-correcting — single-cell errors are detected automatically without external look-up tables.
Learn more →Geometric Constructibility
All structural parameters are finitely constructible — no transcendental constants enter the projection. Every calculation terminates in exact arithmetic, enabling reproducible results across all computing environments.
Learn more →Projection Comparison Journey
Explore the evolution from classical projections through modern approaches to the Lewis World Map. Each chapter presents a different cartographic solution with its mathematical foundation and distortion characteristics.
The Fundamental Problem
Why perfect maps are mathematically impossible — and how we measure the compromise.
Mercator Projection
1569 · Conformal cylindrical · Navigation standard for 450 years.
Gall-Peters Projection
1855 · Equal-area cylindrical · Political fairness at the cost of shape accuracy.
Winkel Tripel
1921 · Compromise · National Geographic standard since 1998.
Fuller Dymaxion
1954 · Icosahedral · Pioneered the polyhedral approach to minimising local distortion.
Structured Sphere Sampling
The angular distribution principle that achieves uniform coverage at every resolution level.
The Lewis World Map
The novel projection — combining optimal sampling, hierarchical addressing, and integrity checking.
Distortion Comparison
Quantitative analysis: Lewis World Map vs. all established projections.
Resolution Hierarchy
Canonical zoom levels from a structured numerical sequence — not arbitrary power-of-two levels.
Polyhedral Geometry
Why icosahedral structure minimises per-face distortion — and the geometric properties that make it constructible.
Coordinate Integrity
Built-in error detection via mathematical identity relationships — no external validation required.
Mathematical Discovery
Explore the symbolic relationships underlying the system architecture using protected notation.