Qibla, and Related, Map Projections

The Qibla problem determination of the direction to Mecca has given rise to retro-azimuthal map projections, an interesting, albeit unusual and little known, class of map projections. Principal contributors to this subject were Craig and Hammer, both writing in 1910. The projections thus introduced are examined. An unusual recent discovery from Iran suggests that Muslims might have been prior inventors of a similar projection, by at least several centuries. A property of retroazimuthal projections is that the parallels are bent downwards towards the equator. The resulting maps, when extended to the entire world, thus must overlap themselves. A later corollary by Schoy leads to a new “cylindrical” azimuthal map projection with parallels bending away from the equator, here illustrated for the first time.