Loxodromes: A Rhumb Way to Go

A rhumb is a course on the Earth of constant bearing. For example, to travel from New York to London a voyager could head at a constant bearing 73◦ east of north. Loxodrome is a Latin synonym for rhumb, and has come to be used more as a geometric term—the course is a rhumb, the curve is a loxodrome. On a surface of revolution, meridians are copies of the revolved curve; on the earth, they are north-south lines of constant longitude. A loxodrome intersects all the meridians at the same angle. A circle of constant latitude is a loxodrome (perpendicular to meridians). Any other loxodrome can be continued forwards and backwards, winding infinitely often around the poles in limiting logarithmic spirals, as in FIGURE 1.