Paths of constant bearing (known as ‘loxodromes’ or ‘rhumb lines’) are often mentioned in the context of the Mercator projection, as they are always straight lines on the map. It’s often emphasised that this is not the shortest route between two locations, but something I feel is glossed over is the direct consequence that these paths are not straight on a sphere, even though the bearing is consistent. In general, following a steady course on a compass requires turning slightly along the entire journey. Perhaps the most obvious indication of this is to imagine travelling due east when only …

Everyone loves the azimuthal equidistant projection; some just don’t yet realise it. For that latter camp, a quick refresher: azimuthal equidistant maps show all courses from the centre point at the appropriate angle and with correct scale – a ray from the centre to any point shows the initial bearing and length of the direct route to that point. The azimuthal equidistant projection, which unfortunately lacks a more concise name (‘Postel’?), is quite popular with some rather diverse groups, including the contemporary ‘zero-Gaussian-curvature Earth’[1] crowd. Perhaps more perplexing than this movement’s modern resurgence, is their insistance on the …