Map Projections and Distortion Questions and Answers

Answer: A

Conformality means that angles measured at a point are correct and shapes are true over a very small area, though not over a large one. Equal-area preserves relative size, equidistant preserves distance from certain points, and azimuthal preserves direction from a centre.

Answer: B

An equal-area projection reports every region at its correct proportion of the whole, which is what a map comparing the extent of countries or land cover requires. Shapes are stretched to achieve it, often noticeably at high latitudes.

Answer: C

It follows from Gauss's theorem that no projection can preserve both angles and areas, so the two must be traded against one another. That impossibility is the reason so many projections exist rather than one correct answer.

Answer: D

A tiny circle on the globe becomes an ellipse on the map, and the shape and size of that ellipse record what the projection has done at that point. Plotting many of them across a map makes the pattern of distortion visible at a glance.

Answer: A

Correct answer: departure from conformality

The indicatrix is the image of an infinitesimal circle on the globe. Its two axes are the principal scale factors, so a circle that comes out elliptical means the scale differs with direction - which is exactly what destroys angles and shapes. The *area* of the ellipse carries the other message: unchanged area means an equal-area projection. A conformal projection therefore gives circles of varying size; an equal-area one gives ellipses of constant area.

Answer: B

If every ellipse encloses the same area the projection is equal-area, whatever their shapes. Eccentricity is the separate signal and reports on angles, which is why the two properties can be read independently from the same diagram.

Answer: C

Distance can be held true along particular lines or from particular points, but not between every pair of places at once. Claims that a map preserves distance always carry an unstated qualification about where and from what.

Answer: D

A developable surface can be unrolled flat without stretching, and the sphere by definition cannot, which is the whole problem. The cylinder, cone and plane can, which is why projections are traditionally grouped by them.

Answer: A

Azimuthal projections show true direction from the point of tangency, which makes them natural for polar maps and for anything organised around a single centre. Cylindrical and conic forms wrap different surfaces around the globe instead.

Answer: B

Correct answer: At the point or line of contact

The projection surface touches the globe along the point or line of tangency, so the scale there is true and the distortion is zero. Away from it the surface separates from the globe and the distortion grows with the separation. Using a secant surface instead trades a small distortion between the two standard lines for a smaller maximum overall - the same idea applied twice.