days before or after each event, still show accurate directions with negligible difference. On the world map Spherical trigonometry provides the shortest path from any point on earth to the Kaaba, even though the indicated direction might seem counterintuitive when imagined on a flat world map. For example, the qibla from Alaska obtained through spherical trigonometry is almost due north. This apparent counter-intuitiveness is caused by projections used by world maps, which by necessity distort the surface of the Earth. A straight line shown by the world map in using the Mercator projection is called the rhumb line or the loxodrome, which is used to indicate the qibla by a minority of Muslims. It can result in a dramatic difference in some places; for example, in some parts of North America the flat map shows Mecca in the southeast while the great circle calculation shows it to the northeast. In Japan the map shows it to the southwest, while the great circle shows it to the northwest. The majority of Muslims, however, follow the great circle method. A retroazimuthal projection is any map projection which preserves the angular direction (the azimuth) of the great circle path from any point of the map to a point selected as the center of the map. The initial purpose of its development was to help finding the qibla, by choosing the Kaaba as the center point. The earliest surviving works using this projection were two astrolabe-shaped brass instruments created in 18th-century Iran. They contain grids covering locations between Spain and China, label the locations of major cities along with their names, but do not show any coastline. The first of the two was discovered in 1989; its diameter is and it has a ruler with which one can read the direction of Mecca from the markings on the instrument's circumference, and the distance to Mecca from the markings on the ruler. Only the second one is signed by its creator, Muhammad Husayn. The first formal design of a retroazimuthal projection in the Western literature is the Craig projection or the Mecca projection, created by the Scottish mathematician James Ireland Craig, who worked at the Survey Department of Egypt, in 1910. His map is centered in Mecca and its range is limited to show the predominantly Muslim lands. Extending the map further than 90° in longitude from the center will result in crowding and overlaps.