What a projection gives up

You cannot flatten a curved surface without tearing or stretching it. Every projection therefore preserves at most one of angle, area and distance, and wrecks the others — which makes the choice a statement about what the map is for.

Read the entry

A folded printed sheet map open on a desk with scale bar and legend

Eight from the register

One entry from each section — kept against wrecked

EntryThe trade it namesSection

What a projection gives up You cannot flatten a curved surface without tearing or stretching it. Every projection therefore preserves at most one of angle, area and distance, and wrecks the others — which makes the choice a statement about what the map is for. 01 Projections The Gulf of Guinea problem Coordinates that default to zero land at the origin, off West Africa. The commonest sign that a coordinate system was never set. 02 Datums & Coordinates The length of a coastline Measure with a shorter ruler and it gets longer, without limit. Which means a coastline has no single length, only a length at a scale. 03 Scale & Generalisation Why the map arrives in squares Fixed-size images on a fixed grid cache well and can be served by anything. The whole delivery model follows from that. 04 Tiles & Zoom Geometry on arrival, or pixels in advance Send the shapes and style them in the client, or send a picture already drawn. The choice moves the work and moves the constraints with it. 05 Vector & Raster Two stories, one dataset The same numbers, classified two ways, produce maps that support opposite readings. The method belongs in the legend. 06 Classification What a scale bar promises On most projections it is only true along particular lines, which is rarely stated. 07 Map Furniture Where a coordinate comes from Every position is measured from something else. The chain ends at a physical mark somebody set in the ground. 08 Survey & Measurement

The complete register — thirty entries

Four times as many, every step down

Tile counts in a zoom pyramid

Zoom level01tilethe whole world

Zoom level4256tilescountries readable

Zoom level865,536tilesregional detail

Zoom level12~16.7millionurban neighbourhoods

Zoom level16~4.3billionstreet level

Zoom level20~1.1trillionmost never generated

The pyramid, level by level

Every map projection preserves some geometric property at the cost of distorting others.

What a projection gives up

Figure 01

Three places this register keeps returning to, plotted at their true coordinates: the origin every mismatched file collapses onto, the meridian the norths are measured from, and a mark set in the ground.

Real geometry, unprojected labels. Pins: Greenwich, Quito, Null Island.

Plate 02

One sheet of the Turgot plan of Paris. The city was published as a set of sheets because no single sheet could hold it at this detail.

Photo: Turgot plan of Paris, sheet 18–19 · Norman B. Leventhal Map Center

04 — Tiles & Zoom

A surveyor at a tripod instrument in a field

Plate 03

The instrument reports angles and distances. Everything on the finished map is a computation from readings like these.

Photo: Khoiru Ummah Kendari 24 / Pexels

08 — Survey & Measurement