Cartographic Projection
every map is wrong, and by exactly how much
Theme

The thread: Every figure here is a projection

The page is flat, so there is no way to show the sphere except by projecting it. Even the globes are projections with their own distortion, and no picture here is the undistorted truth.
planeK = 0 — unrolls flatcylinderK = 0 — unrolls flatconeK = 0 — unrolls flatsphereK = 1.00torusK = 1.79pseudosphereK = -1.00K computed at each centretwo routes, one answer The impossibility

No map is faithful

Not "no map yet", and not "no map at page size". Gaussian curvature can be computed from inside a surface, a sphere has some and a plane has none, and that closes the question permanently.

 LondonTokyosolid: shortest · dashed: constant bearing+18.2% for the rhumbdrawn in Mercator Paths and directions

The shortest route is not straight

The shortest path between two points on a sphere is an arc of a great circle, and on almost every map it is a curve. The straight line on a Mercator chart is a different route entirely, and on some journeys it is twenty-eight per cent longer.

All themes