Qibla is an Arabic word meaning "direction". As it pertains to Muslims, it refers to the direction in which Muslim face when performing salat. It is also the direction one points an animal when slaughtering it. Lovemaking is also preferred to be done facing the Qibla.

Masajid are oriented with a wall with a niche called a mihrab which indicates the Qibla so that no one has to pull out the compass when attending Jumah or going there for other prayers.

The Qibla was pointed towards Jerusalem during the early days of Islam. On February 11, 624 A.D., it was changed to Makkah. The Qur'an says this regarding the change:

The foolish will now ask and say:
"What has made the faithful turn away
from the Qibla towards which they used to pray?"
Say: "To God belong the East and West.
He guides who so wills to the path that is straight."
Orientalists have theorized that the change was the result of Muhammad giving up on designs to convert the Jews of the area to the fledging religion, deciding rather to concentrate on the Arabs. The Muslim POV is obviously that God ordered that the change occur and his slave, Muhammad (SAW) obeyed.

To clarify robwicks' writeup with regards to the change in the direction of the Qibla: There is another reason that Muslims believe that Muhammad may have been ordered to change the direction, related to the level of faith of his followers.

Initially, when Muhammad's mission began (around 610CE), the Kaaba was full of idols. Since the greatest sin in Islam is worshipping someone together with God, idols were considered a total no-no -- in fact, Muhammad's rejection of the idols is what got him into so much trouble in the first place.

In order to break connections with the Kaaba and the association of the Kaaba with idolatry, Muhammad was initially ordered to pray towards Jerusalem.

However, over the next 14 years, the faith strengthened and people came to know what it stood for; so it was no longer necessary to not face Mecca.

Four years after the change in Qibla, Muhammad conquered Mecca bloodlessly and the idols were destroyed.

This change was not an isolated incident. Another example of a change was the visiting of graveyards. In the early days of Islam, this was prohibited, as the graveyards were home to superstitious beliefs, many of them in conflict with the unity of God. This was later changed, allowing both men and women to visit graves.

Pace asterphage, the qibla is specifically the direction of the Kaaba. That's at 21° 25' 24" N, 39° 49' 24" E, if you're into blasphemous geocaching.

Since the earth is a sphere (more or less), determining the qibla is more than just a matter of drawing a line on a map. On that map, for example, the direction from my apartment, in a heavily Pakistani neighborhood in Brooklyn, to Makkah would appear to be southeast.

The qibla, however, is the shortest distance on a Great Circle arc. If I were to convert to Islam, I'd actually have to pray facing northeast*. The exact direction is calculated using spherical trigonometry -- at my apartment it's roughly 58 degrees from true north.

*It's for similar reasons that the flight paths on the maps in airplane magazines are arcs rather than straight lines: on a globe, those are straight lines.

Source: http://www.salon.com/tech/col/smith/2003/03/07/askthepilot31/

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