🌐 Sphere Projections
A sphere cannot be unrolled onto a flat surface without distortion — this is guaranteed by Gauss's Theorema Egregium (intrinsic curvature is preserved under isometry). Every map projection therefore compromises: some preserve angles (conformal), others preserve areas (equal-area), and none preserve both. Compare the six classic projections by clicking a point to trace its position. The grid shows lines of latitude and longitude every 30°. 🇺🇦 Українська
Projection
Globe Centre
Overlay
Conformal (angle-preserving). Vertical scale = horizontal scale at each point. Areas near the poles are wildly inflated — Greenland appears as large as Africa.
The Six Projections
Mercator — cylindrical, conformal. x=λ, y=ln(tan(π/4+φ/2)). Used for navigation since right angles = compass bearings. Stereographic — azimuthal, conformal. Projects from one pole through the sphere onto a tangent plane. Used for polar charts and complex analysis (Riemann sphere). Orthographic — azimuthal, perspective from infinity. Shows one hemisphere as the eye would see it from outer space. Azimuthal Equidistant — all distances and directions from the centre are correct. The UN logo uses an azimuthal equidistant centred on the North Pole. Mollweide — pseudocylindrical, equal-area. Whole globe on an ellipse; meridians are ellipses, parallels straight lines. Popular for world thematic maps. Gnomonic — all great circles map to straight lines, making it useful for shortest-path navigation. Cannot show a full hemisphere.