the entire southeastern quadrant in Al-Andalus (Islamic Iberian Peninsula), and the southwestern quadrant in Central Asia, to be valid qibla. Arguments for the validity of jihat al-ka'bah include the wording of the Quran, which commands Muslims only to "turn [one's] face" toward the Great Mosque, and to avoid imposing requirements that would be impossible to fulfill if ayn al-ka'bah were to be obligatory in all places. The Shafi'i school of Islamic law, as codified in Abu Ishaq al-Shirazi's 11th-century Kitab al-Tanbih fi'l-Fiqh, argues that one must follow the qibla indicated by the local mosque when one is not near Mecca or, when not near a mosque, to ask a trustworthy person. When this is not possible, one is to make one's own determination—to exercise ijtihad—by the means at one's disposal. Determination Theoretical basis: the great circle A great circle, also called the orthodrome, is any circle on a sphere whose centre is identical to the centre of the sphere. For example, all lines of longitude are great circles of the Earth, while the equator is the only line of latitude that is also a great circle (other lines of latitude are centered north or south of the centre of the Earth). The great circle is the theoretical basis in most models that seek to mathematically determine the direction of the qibla from a locality. In such models, the qibla is defined as the direction of the great circle passing through the locality and the Kaaba. One of the properties of a great circle is that it indicates the shortest path connecting any pair of points along the circle—this is the basis of its use to determine the qibla. The great circle is similarly used to find the shortest flight path connecting the two locations—therefore the qibla calculated using the great circle method is generally close to the direction of the locality to Mecca. As the ellipsoid is a more accurate figure of the Earth than a perfect sphere, modern researchers have looked into using ellipsoidal models to calculate the qibla, replacing the great circle by the geodesics on an ellipsoid. This results in more complicated calculations, while the improvement in accuracy falls well within the typical precision of the setting out of a mosque or the placement of a mat. For example, calculations using the GRS 80 ellipsoidal model yields the qibla of 18°47′06″ for a location in San Francisco,