About two years ago, after running through a series of second-hand compact cameras, I went looking for a compact of my own. I’m not entirely sure what the requirements were – availability, mostly – but I ended up grabbing a Panasonic Lumix DMC-TZ80. One of the neat features about this camera is its whopping 30× zoom: 4.3–129 mm, or “24–720 mm” as the “35 mm equivalent”.[1] That makes it a pretty versatile unit, but that far end of the range ended up being more useful than I anticipated, because it turns out what I want to photograph …

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 …