Maps
The Maps domain tests how maps are made, measured, and misread: scale, projections and distortion, coordinate systems, topographic symbols, thematic map types, and geospatial technologies.
Scale
Scale is the ratio of map distance to ground distance, expressed as a representative fraction such as 1:50,000, a verbal statement, or a graphic bar. A large-scale map, such as 1:10,000, covers a small area in detail; a small-scale map, such as 1:5,000,000, covers a large area with little detail. Generalization, including selection, simplification, smoothing, and displacement, increases as scale shrinks.
Projections
Every projection distorts shape, area, distance, or direction. Mercator is conformal: angles and local shapes are preserved, rhumb lines are straight, but area inflates toward the poles. Robinson and Goode homolosine are compromise or equal-area choices for world maps. Conic projections suit mid-latitude countries; azimuthal or planar projections suit polar regions. A secant projection intersects the globe along standard lines, reducing distortion there.
Coordinates and topographic maps
Latitude and longitude give absolute location; UTM is a metric grid; the Public Land Survey System divides much of the United States into townships and ranges. Contour lines connect equal elevation; the contour interval is the elevation change between adjacent lines. Closely spaced contours mean steep slopes; hachures point downhill. Magnetic declination is the angle between true north and magnetic north.
Thematic maps and GIS
Choropleth maps shade administrative units by rate; dot maps show raw counts; graduated symbols vary size; isoline maps connect equal values; cartograms distort area by value. GIS stores layers and performs overlay and buffer analysis; remote sensing records reflectance; GPS gives position.
Worked example
A map has a representative fraction of 1:24,000. A measured 4 cm on the map equals 4 times 24,000 = 96,000 cm = 0.96 km on the ground. Reasoning: multiply the map measurement by the denominator in the same unit, then convert centimeters to kilometers.
Traps
- Reversing large and small scale: a small-scale map covers a large area.
- Treating a representative fraction as having units; it is unitless.
- Assuming Mercator preserves area; it preserves shape and direction instead.
- Confusing magnetic declination with grid convergence.