Baha'i News -- Which way is Jerusalem? Which way is Mecca?
Which way is Jerusalem? Which way is Mecca? The direction-facing problem in religion and
geographyWhich way is Jerusalem? Which way is Mecca? The direction-facing problem in religion and
Determining the direction in which to face another location on the
globe is a problem with significant social and religious meaning, and
one with a rich and interesting history in the Western world. Yet a
fully satisfying geographic solution to this problem is hindered bv
our intuitive perception of the world as a flat surface-- where a
"straight" path (1) is the shortest distance, and (2) maintains a
constant angle. On a curved surface, however, only one of these two
properties can be satisfied: the first, by a great circle; the
second, by a rhumb line. These two solutions are analyzed, compared,
and applied to the direction-facing problem.
Key Words: direction facing religion, great circle, rhumb line
Why would a mosque in New York City face toward the northeast when
"everyone knows" that Mecca is south and east of New York? This
question is an example of the direction-facing problem in geography:
When standing at a particular point on the globe, in what direction
is another point elsewhere on the globe? As in the above example of
the New York mosque oriented more or less toward Greenland, the
answers can be surprising. Perhaps even more surprising, though, is
that, from the perspective of mathematics and cartography, there is
not just one scientific answer to the direction-facing problem, but
two potentially valid mathematical answers. As we shall see, the
reality of compass direction on a round earth does not always fit
with what our intuitive notions of distance and direction would have
For religious Jews and Muslims, for example, this issue is not
merely academic. In both faiths, worshippers have been conducting
their prayers for centuries while facing a holy city: for Jews,
Jerusalem; for Muslims, Mecca. Thus, beyond its usual importance to
social science, public policy, and industry, the tools and techniques
of geographic analysis in this case have significant social (even
theological) meaning to religious institutions as well. Although
religions have relied upon various folk traditions and rules of
thumb, modern worshippers might also wonder if mathematics,
geography, and cartography can provide a scientific answer to the
direction-facing problem. Yet, deciding what exactly is the direction
in which to face another point on the globe turns out, for
theoretical reasons, to be far from straightforward, even
scientifically. In fact there are two potential mathematical
solutions to the direction-facing problem: either the initial compass
direction of a great circle (i.e., the shortest path) connecting the
two locations; or the constant direction of a rhumb line (i.e., the
path of constant compass direction) connecting the two locations. In
this article-designed to spark the interest of students of geography
and requiring no more than high-school trigonometry-I review the
diverse history of prayer orientations and then describe how and why
we might use the great circle versus the rhumb line to solve the
DIRECTION FAcING IN WESTERN RELIGIONS
Several major religions-Judaism, Christianity, Islam, and Baha'i-
have historically observed the practice of orienting prayer in a
particular geographic direction. Moreover, over time, these groups
have approached the direction-facing problem in a number of different
The tradition among Jews to face in the direction of Jerusalem
while praying is an ancient, biblical one. According to the Bible,
King Solomon (10th century B.C.E.) built the first Temple in
Jerusalem and then stated when dedicating that structure that the
Israelites would "pray to the Lord in the direction of the city which
You have chosen [Jerusalem], and in the direction of the House
[Temple] which I built to Your name" (I Kings 8:44). After the
destruction of this Temple, the Bible notes that Daniel (6th century
B.C.E.), while in exile in Babylonia, faced in the direction of
Jerusalem while praying (Daniel 6:11). After the final destruction of
the second Jewish Temple (70 C.E.), located on the same site as the
first, this tradition remained and was soon codified into Jewish law.
For the most part, however, it appears that in actual practice Jews
have had a rather flexible attitude toward the direction of Jerusalem
and moreover, even in theory, have never been extraordinarily precise
about determining its direction.
The earliest rabbis, whose views were first recorded around the
year 200 C.E., believed that Jews should physically face Jerusalem
when praying, but added that someone on a boat could simply direct
his "heart" to the site of the destroyed Temple in Jerusalem
(Babylonian Talmud, B'rachot 28b). Another source from the same time
period elaborated, "Those in the north face the south, those in the
south face the north, those in the east face the west and those in
the west face the east so that all Israel [i.e., the Jewish people]
prays toward one place" (Tosefta B'rachot 3:16). By the late 5th
century, subsequent rabbis had reiterated this viewpoint but added
the opinion that a blind man or someone who does not know the
direction should simply direct his "heart" towards his Father in
heaven (Babylonian Talmud, B'rachot 30a). Archaeological evidence
confirms that 2nd- to 5th-century synagogues were roughly oriented to
face Jerusalem (Avi-Yonah 1971).
As Jews migrated to North Africa and Europe, later commentaries on
this Jewish law-e.g., rabbis writing in 13th-century Germany
(Mord'khai, B'rachot 30a) and in 14th-century Spain (Tur, O.H. 94)-
noted simply that Jews to the west of the Land of Israel should face
eastward. Interestingly, in Arab lands-where Muslim astronomers and
others focused intensely on the direction-facing problem-medieval
Jewish scholars showed no interest in treating more scientifically
the direction of prayer (Goldstein 1996). Perhaps the only scientific
treatment of this issue was by a 15th-century Jewish astronomer in
Lisbon who wrote in Hebrew of finding the direction of Jerusalem
using geographic coordinates, although he did not indicate what
method he used or what direction he found (Langermann 1999). By the
16th century in Poland, one legal codifier (a rabbi) wrote of facing
eastward, but then added that Jews should build a synagogue such that
the direction of prayer is actually southeast, since facing directly
east (toward where the sun rises) is the way Christians pray (Mappah,
O.H. 94:2). Subsequently, another 16th-century scholar-one who lived
in Prague, Venice, and Poland-- also expressed concern about directly
emulating the Christian custom of facing due east, and further wrote:
For all the lands in which we dwell are all northwest of the Land
of Israel, and we are not located due west of the Land of Israel.
Therefore it appears to me to be the proper thing to do that, when we
make a synagogue, we should be careful when we make the eastern wall-
where we place the ark and we pray opposite it-that it should lean a
little towards the southeast. (L'vush, as quoted in Mishna B'rurah,
However, a rabbi writing in 17th-century Prague noted that he had
only witnessed Jews facing directly eastward. He therefore concluded-
even though his own opinion was to face southeast-that most Jews must
be taking the view that simply choosing one of the four compass
directions mentioned 1,400 years earlier in the Talmud was sufficient
(Divrei Hamudot, B'rachot 30a). In fact, most synagogues from the
middle ages to the 18th century placed the ark along a wall that was
due east; one notable exception, though, was the 16th/17th-century
"Spanish synagogue" in Venice, which was oriented to face south by
southeast (Kashtan 1971). At the turn of the 20th century, yet
another Jewish legal authority-one who lived in Lithuania and Poland-
again reiterated that Jews in Europe should face southeast; that is,
toward where the sun is 30-60 minutes after sunrise in the spring or
fall (Mishna B'rurah, O.H. 94:2). Despite these admonitions, however,
today all, or nearly all, synagogues in Europe and North America (if
they have any intentional geographic orientation at all) are oriented
to face due east.
Besides praying in the direction of Jerusalem, 3rd-- to 5th-
century rabbis also applied the direction-facing principle to a
Jewish law that one should avoid showing disrespect by relieving
oneself while facing the Temple in Jerusalem when it is in view.
These early rabbis debated and differed over whether this prohibition
applies when the Temple is not in existence (i.e., after 70 C.E.), or
when Jerusalem is not in sight, or when one is not due north or due
east of Jerusalem, or when one is outside the Land of Israel
entirely. Interestingly, those who followed this prohibition would
avoid facing Jerusalem and avoid turning their backs to it; thus,
many rabbis argued that someone to the east of Jerusalem should face
north or south when relieving himself (Babylonian Talmud, B'rachot
61b). Many centuries later, Jewish burial also became associated with
the direction of Jerusalem. One early-19th-century European rabbi
wrote that, although it is not mentioned in ancient or early Jewish
texts, it had become an established Jewish custom in Europe to bury a
person with the legs to the east (or sometimes south) "as symbolic of
the faith in resurrection of the dead, indicating that he will stand
up from his gr\ave and leave..to travel to the Holy Land [when the
Messiah comes and ends the Jewish exile]" (Responsum Hatam Sofer Y.D.
part 2, section 332). This rabbi also noted that the journey from
Europe to the Holy Land starts out on either a southerly route (that
then turns east) or an easterly route (that then turns south), so
either direction for burial is proper. Again, we see that Jews
typically have been content, even in theory, to approach the
direction of Jerusalem with approximate solutions.
The "early Christian practice of facing the east for
prayer...could well have begun in conscious contrast to the Jewish
custom [of facing Jerusalem], but it would also have been influenced
by the general pagan understanding of the time that the east is the
direction in which the good divine powers are to be found, a view
originally connected with sun worship" (Davies 1986, 421). Along with
these particular rationales, however, Christian scholars and
theologians have also offered numerous other historical, theological,
or biblical explanations for the custom of facing eastward (Davies
1986; Hassett 1913; Lang 1989; Yarnold 1994). In addition, a related
custom has been the practice among some Christians of burying the
dead with the lay person's feet placed to the east (Lang 1989).
Interestingly, the early Church's adult baptism (i.e., conversion)
ceremonies-instituted after the Roman Empire legalized Christianity
in the 4th century-included having the candidate face west to
renounce the devil, then turn away in the opposite direction "to face
Christ, the source of light, in the east" (Yarnold 1994).
Historically, this custom of facing eastward has found expression
in the geographic orientation of churches. From the 4th century to
the 8th century, Christian basilicas in the Western world were
typically built with their entrance on the east side, whereas later
basilicas, influenced by Orthodox and French church architecture
(Foley 1991; Redmond 1967), came to be built with the opposite
orientation, with the apse (i.e., the area containing the altar,
opposite the entrance) on the east side. In both cases, however,
apparently the "presider stood on whichever side of the altar allowed
him to face east, the place of the rising sun and a symbol of the
resurrection" (Foley 1991, 70). The latter custom of both presider
and congregation facing eastward continued in Roman Catholic churches
until the decades after World War II, when priests gradually switched
their orientation so that they now face the congregation, even though
this change means that the priests may thus be facing westward (Cross
and Livingstone 1983). Protestant ministers have generally faced the
congregation since the Reformation, although their churches have not
been oriented in any particular direction (Cope 1986). In fact,
throughout Christian history, from the earliest days to the present,
"orientation has never been considered absolutely essential and many
churches have been built regardless of it to accommodate them to the
site available" (Davies 1986, 421).
In contrast, Islam has been perhaps the most concerned among the
major Western religions with the direction-facing problem.
Interestingly, among Muslims the direction of prayer (qibla, in
Arabic) was initially, as it is among Jews, toward Jerusalem.
However, within a year or two of Muhammad's founding of Islam (7th
cent.), the Muslim qibla (also spelled kibla) was changed from
Jerusalem to Mecca, due perhaps in part, some have speculated, to
Muhammad's disappointment that few Jews were converting to Islam
(Wensinck 1986). Thus, Muslims were instructed, `Turn then your face
in the direction of the Sacred Mosque: wherever you are, turn your
faces in that direction" (Koran 2:144); that is, in the direction of
the Ka'ba (sacred mosque), which is in Mecca. To this day whenever a
mosque is constructed, the building is oriented to face in the
direction of this qibla (Wensinck 1986). In addition to its
considerable importance in Muslim prayer, "according to Islamic law,
certain ritual acts such as reciting the Qur'an, announcing the call
to prayer, and slaughtering animals for food, are to be performed
facing the Ka'ba. Also Muslim graves and tombs were laid out so that
the body would lie on its side and face the Ka'ba" (King 1999, 47).
In addition, "it is forbidden to turn towards Mecca when relieving
nature" (Wensinck 1986, 82).
Historically, Muslims have used a number of different approaches
in determining the direction of Mecca. In the first two centuries of
Islam, for example, the qibla was sometimes determined by using the
direction of the road on which pilgrims left for Mecca (Goldstein
1996), or it was simply to face south because "the Prophet Muhammad
had prayed due south when he was in Medina (north of Mecca)" (King
1993,1253). Later in the medieval period, however, two main
traditions, each existing alongside the other, emerged: mathematical
astronomy, which used geographic coordinates and trigonometric
formulas, and legal scholarship, which used a number of different
rules of thumb not requiring computations. Interestingly, as King
(1993, X 8) notes, "It is quite apparent from the orientations of
mediaeval mosques that astronomers were seldom consulted in their
construction. Indeed...several different and often widely-divergent
kiblas were accepted in specific cities and regions."
The medieval legal scholars, drawing on a kind of folk astronomy,
began with the observations that the Ka'ba, a rectangular-shaped
building, is oriented so that, roughly speaking, (1) the two shorter
walls face the rising point of the star, Canopus, (2) the two longer
walls face the summer sunrise or winter sunset, and (3) each of the
walls face head on into one of the four Arabian winds. These
observations were then combined with a view of the Ka'ba, in Mecca,
as the center of the world. Muslim legal scholars then divided the
world into either 4, 8, 11, 12, or 72 sectors radiating out from the
Ka'ba, so that each sector of the world could be said to face a
particular section of the perimeter (or wall) of the Ka'ba. Muslims
living in a particular sector could then determine the qibla based on
the rising (or setting) of the sun or stars or the winds in their
location. Thus, the legal tradition's
attempts to define the kibla for different localities in terms of
astronomical risings and settings [or even of wind directions] stem
from the fact that these localities were associated with specific
segments of the perimeter of the Ka'ba, and the kiblas adopted were
the same as the astronomical directions which one would be facing
when standing directly in front of the appropriate part of the Ka'ba.
(King 1993, XI 12)
So, for example, early Iraqi mosques faced the winter sunset, and
early Egyptian mosques, the winter sunrise, so that these mosques
would be in some sense "parallel" to the relevant wall of the Ka'ba.
Nevertheless, even within the same city "there were differences of
opinion, and different directions were favoured by particular groups"
(King 1993, 1255).
Although the increasingly accurate approximations and formulas of
mathematical astronomers from the 8th to 15th centuries were
circulated only within the scientific community, and were largely
ignored by Muslim legal scholars and by the wider community, this
mathematical approach eventually, by the modern era, came to
dominate. Today, mosques are built according to the qibla found by
calculating the initial compass direction of the shortest distance to
Mecca (i.e., the great-circle route) using precise geographic
coordinates (King 1993).
The Baha'i faith, which began in the Middle East in the mid-19th
century and today has millions of followers worldwide, has its own
qiblih for the direction of certain prayers. Individual Baha'is
recite the daily obligatory prayer while facing in the direction of
the tomb of Baha'u'llah, located at Bahji, just north of Acre, Israel
(near Haifa). According to Baha'u'llah's Book of Laws, "When ye
desire to perform this prayer, turn ye towards the Court of My Most
Holy Presence, this hallowed Spot that God hath... decreed to be the
Point of Adoration for the denizens of the Cities of Eternity (Kitab-
i-Aqdas, 16). In addition, this qiblih towards Acre is used during a
communal prayer recited twice per year and whenever visiting two
particular Baha'i shrines. It is also customary for Baha'is to be
buried with their feet in the direction of Acre (Yancy 2000).
Like modern-day Muslims facing Mecca, Baha'is compute their qiblih
based on the initial compass direction of the great-circle route to
Acre. So, for example, in North America's Baha'i House of Worship,
which was designed in the mid-1920s and is located just north of
Chicago, the chairs in the auditorium face roughly northeast, or east
by northeast (Stockman 2000; Yancy 2000). Interestingly, though,
local folklore at this particular House of Worship near Chicago has
it that the sidewalk leading (in a southeasterly direction) from the
temple to the nearby intersection forms an "arrow" pointing towards
Acre (Yancy 2000). This southeastward sidewalk is fairly consistent
with a rhumb line from Chicago to Acre, although, as already noted,
the actual seating inside the temple is based on the initial compass
direction of the great-circle route (i.e., people face northeast). In
practice, many Baha'i followers, like Jews facing Jerusalem, are not
especially strict about following the qiblih towards Acre (Brown and
Bromberek 2000; Yancy 2000). For those followers who are interested,
though, the Baha'i Computer and Communication Association has created
a "web-based calculator" that will compute the qiblih to Acre based
on the initial compass direction of the great-circle route from any
latitude and longitude entered (Brown and Bromberek 2000).
Thus, for these world religions, the meaning of physical space and
geography h\as a strong spiritual component. In orienting the
direction of prayer, these faiths have historically made use of
scientific methods on occasion but also other rules of thumb for
determining the proper direction. Moreover, the knowledge by
worshippers that all of their co-religionists are praying in the same
direction, or in the direction of the same place, can be a source of
unity in a number of ways among these worshippers-particularly among
Jews, Muslims, and Baha'is, who are facing a specific location.
Synchronizing geographic direction plays a symbolic role in
supporting theological notions of unity, such as unity of faith, of
the divine, of a people, or of humankind; it plays a social role in
creating a sense of community and fellowship among worshippers even
if they are scattered all over the world; and it plays an
institutional role in supporting the process of building and
maintaining cross-national linkages and unity among members of the
same religious organizations.
The Earth Is Round
Yet, ironically, the question of which way to face, despite its
purpose as a source of unity, lacks, geographically speaking, the
unity of a single answer that worshippers in the modern era might
expect. That is, over short distances we can simply assume that the
two points essentially lie on a flat surface, and we can draw a
straight line between them to determine the compass direction. As the
two locations in question become farther and farther apart on the
earth, however, the question of which way to face ceases to be just a
straightforward math problem. Indeed, for longer distances, we are
forced to take into account that the earth's surface is actually
curved and thus we must add the constraint that the "line" connecting
the two points must remain on the curved surface. With this
constraint, however, the very notion of a "straight" line between two
points becomes considerably less intuitive than it was on the flat
surface, for no line on a curved surface is truly straight; it is, by
Thus, we need some sort of curved-surface analog to the notion of
a straight line on a flat surface.
We all know, for instance, what a straight line is. It is the
shortest distance between two points, and it is, well, straight
[i.e., it forms a constant angle]. But when we try to draw a straight
line on the surface of the globe, it is immediately apparent that we
can't draw any sort of line which even begins to meet our intuitive
idea of what a straight line should be. (Reid 1963, 149)
Since our intuitive notions of direction and distance are derived
almost entirely from our visual perception of and interaction with a
flat (Euclidean) world, we must make conceptual compromises when
defining a "straight" line on the surface of the earth. This
divergence between intuitive concepts based on plane geometry and the
realities of spherical geometry (especially for long-range distances)
leads to two possible definitions of a curved-surface "straight"
line. On a flat surface, a straight line has two properties: (1) it
is the shortest distance between two points, and (2) it maintains the
same direction (angle) all along its path; psychologically, we take
these two properties for granted. On a curved surface like the earth,
however, it turns out that we can choose only one of these two
properties to define a "straight" line. As a result, two definitions
of a "straight" path on a curved surface emerge: the great circle
(the line of shortest distance) and the rhumb line (the line of
The shortest distance between two points on a sphere is along a
great circle, or orthodrome, defined as a "circle on a sphere
produced by any plane which passes through the center of the sphere"
(Raisz 1962, 292) and through the two points in question. If one
point is due north or south of the other-that is, if both points lie
along the same meridian (those lines of longitude that converge at
the north and south poles)-then the great circle connecting the two
points is the meridian itself along which both points lie. More
typical is the case of an oblique great circle, a great circle
connecting two points (not on the equator) with different longitudes.
One answer to the question, then, of what is the direction of another
point elsewhere on the globe is to say that it is the initial compass
direction-known as the azimuth-of the great-circle path, starting at
the initial location. That is, in what direction would we start
traveling if we were to trace the shortest path (the great circle) to
the destination point.
This particular definition of a "straight" path on the surface of
a globe emphasizes the notion of distance. For if the "true" distance
between two points, even on a curved surface, is to mean anything,
this argument-popular among geographers and mathematicians-goes, it
must mean the shortest distance (i.e., along the great circle)
between those two points (Reid 1963; Kramer 1970; Robinson et al.
1995). This definition is also the consensus among Muslims in
choosing a direction in which to face Mecca (King 1986) and among
Baha'is for facing Acre (Brown and Bromberek 2000).
To compute the initial azimuth (angle), Z, between the line
extending due north from point 1 and the great-cir. cle route
connecting points 1 and 2 on a sphere, the following equation is
In this equation ALo is the absolute value of the difference in
longitude between the two points (minimum of 0 and maximum of 180 deg
), and Lat, is the latitude of point 1 (Lat^sub gamma^ of point 2);
note that, in this equation, Lat should be a negative number for
latitudes south of the equator. The solution provided by this
equation was first determined in Damascus by the 14th-century
astronomer al-Khalili, who developed a qibla table for each degree of
longitude and of latitude in the Muslim world (King 1986).
Choosing the initial direction of a great-circle route, however,
does have some drawbacks. For one, "the navigator thinks of an
oblique great-circle course as a line of inconstant direction. Though
it is indeed the shortest, most direct route between two points on
the earth's surface, you must be ever changing your compass direction
with respect to those converging meridians if you would stick to the
oblique great-circle route" (Greenhood 1964, 130). In other words,
the initial compass direction of a great-circle route will be
incorrect as soon as the journey begins, because an oblique great
circle's direction (with respect to the north-south meridians) is
different for every point along the route (see Fig. 1). This lack of
consistency between the initial direction of the great circle versus
subsequent compass headings along it seems to violate part of what it
means for a path to be "straight": it must maintain the same
direction (angle) all along the line. A related difficulty arises
when we examine the special case of two points on the earth that are
due east or west of each other. In this special case, a person at the
more western location who believes that a "straight" path, first and
foremost, should have a constant direction, would face due east along
the same line of latitude shared by the city he or she is facing,
even though that path is not the shortest. This reasoning is probably
closer to the views of the 3rd-century Jewish rabbis who said to face
eastward when one is west of Jerusalem (Tosefta B'rachot 3:16).
In contrast to a great circle, a rhumb line, or loxodrome, is a
"line which Crosses the successive meridians at a constant angle"
(Raisz 1962, 296). In other words, a path connecting two points on
the earth along a rhumb line-- though it will likely not be the
shortest path-will maintain the same constant compass direction all
the way along the path. Thus, a second definition of a "straight"
line on a curved surface assumes that if the "true" direction between
two points-even on a curved surface and even if it is not the
shortest route-is to mean anything, it must mean the same direction
all along the line between those two points (i.e., along the rhumb
line). So of the two possible mathematical solutions to the direction-
facing problem, the great circle distorts our intuitive notion of
direction (i.e., that direction is constant all along a "straight"
line), whereas the rhumb line distorts our intuitive notion of
distance (i.e., that the distance along a "straight' line is the
shortest distance between two points). In practice, if "the two
points are within a few hundred miles, there is little difference
between the two [methods], but at great distances they differ widely"
(Raisz 1962, 150) in providing an initial compass direction.
The rhumb line is closely tied with perhaps the most well-known
map projection-popular in many classrooms-the Mercator projection,
which shows all latitude (east-west) lines as horizontal and all
longitude (north-- south) lines as vertical. Although Gerhard
Mercator's map does, at any given location, show the same scale in
both directions-thereby preserving the two-dimensional shape of any
small area (i.e., the map is conformal)-the scale itself becomes
enormously exaggerated at locations toward the poles: "South America
is over nine times the size of Greenland, but who would believe it
from this map?" (Greenhood 1964, 128). The most notable feature of
Mercator's map, however, is that a straight line drawn between two
points on the map is the rhumb line between those points:
"If you wish to sail from one port to another,' the Flemish map-
maker wrote of his work when he first brought it out in 1569, "here
is a chart, and a straight line on it, and if you follow this line
carefully you will certainly arrive at your destination. But the
length of the line may not be correct. You may get there sooner or
may not get there as soon as you expected but you will certainly get
there." (Greenhood 1964, 128)
Thus, whe\n navigators talk of Mercator sailing, or of "flying a
Mercator course," they mean traveling along a rhumb line, which cuts
every meridian (north-south line) at the same angle.
To determine the angle (direction), Z, of a rhumb line between two
locations on a sphere, we can simply place a straight edge and a
protractor on top of a Mercator map. A more precise method, however,
is the following mathematical equation:
In this equation DeltaLo is the absolute value of the difference
in longitude between the two points (minimum of 0 deg and maximum of
180 deg), In is the natural log, and Lat is the latitude of point 1
(for M^sub 1^) and of point 2 (for M^sub 2^); again, Lat should be a
negative number for southern latitudes.
Adjustments to the angle Z, depending on whether or not Z is
positive or negative and on the orientation of point 1 vis-a-vis the
destination city (Jerusalem or Mecca),3 are given in Table 1 for the
great circle and for the rhumb line.
I estimate the coordinates for the site of the destroyed Jewish
Temple in Jerusalem as 31 46'40"N latitude, 35 deg 14'04"E longitude
(American Practical Navigator 1981; Survey of Israel 1994; 1995), and
for the Ka'ba in Mecca as 21 deg 25'17"N latitude, 39 deg 49'32"E
longitude (Saudi Publishing House 1970; American Practical Navigator
1981). For 21 selected cities, most with large Jewish populations
(Institute of the World Jewish Congress 1998), Table 2 shows the
compass direction for facing Jerusalem. Anchorage, with only 2,300
Jews (Schwartz and Scheckner 1999), and Tokyo, with only 1,000 Jews
(Institute of the World Jewish Congress 1998), are included here
because of their interesting geographic location. Table 3 shows the
compass direction for facing Mecca from 21 selected cities, most with
large Muslim populations (Johnson 1996; Nanji 1996a; 1996b). In both
tables the cities are listed in order from west to east. The
"direction to face" should be interpreted using the compass of Figure
2, where 0 deg is due north, 90 deg is due east, and so on.
The difference between the great circle versus the rhumb line
methods, shown in the last column of Tables 2 and 3, is minuscule for
cities, such as Tel Aviv and Haifa in Table 2, that are within 100
miles of the destination city. In contrast, among the cities listed,
the two methods yield markedly different outcomes for the cities of
North America. The primary reason for this divergence is that, when
two points are located very far apart from each other but are on the
same side of the equator (e.g., New York and Mecca), the shortest
path between them (i.e., the great circle) "swings by" the nearest
pole (see Fig. 1). For example, Mecca is south and east of New York,
yet the great-circle route from New York to Mecca begins by facing
northeast (58) and goes up along the Canadian coastline, then across
the North Atlantic, before returning south through Europe and the
Mediterranean to arrive in Mecca; in contrast, the rhumb line-which
is 400 miles longer-goes southeast straight across the warm waters of
the Atlantic and then North Africa, facing 101 deg the whole time.
When the destination is Jerusalem or Mecca-both of which are in
the northern hemisphere-the only major cities far enough away but
still also in the northern hemisphere are those in North America and,
to a lesser extent, in East Asia. Thus, while the choice of great
circle versus rhumb line is, in general, a significant theoretical
decision in choosing which compass direction to face, as a practical
matter, the difference between the two methods are of major
consequence only in North America. Given the long history of Judaism
and Islam, then, the problem of which mathematically derived
direction-facing method to choose is, relatively speaking, a rather
Which method is better for solving the direction-- facing problem:
the great circle, with its shortest distance, or the rhumb line, with
its constant angle? Historically, Muslims and Baha'is have favored
the great-circle definition of a "straight" line on the globe (King
1986), although this choice has occasionally generated considerable
controversy among North American Muslims (Eissa 1996). Jews have not
chosen any particular definition, and often use only approximate
solutions to the problem, such as choosing a direction only among
north, south, east, or west. In any event, for most cities around the
world, with the exception of North America, the differences between
the two methods outlined here are fairly small (see Tables 2 and 3).
This question of which method is better, however, is not one we
can answer with sophisticated maps and formulas; it is a theoretical
issue that ultimately depends on which of the two components of the
"straight"-path concept we choose to emphasize, distance or
direction. In fact, this issue is analogous to instances in other
fields of ambiguous or indeterminate concepts open to rival
interpretations. For example, many in political science have
concluded that no objective and nonpartisan criteria exist for
determining the "fairness" of a redistricting plan (Levin 1988).
Similarly, in the field of organization management, researchers have
concluded that no objective, mutually agreed-upon criteria exist for
evaluating the "effectiveness" of an organization (Hirsch and Levin
1999). Ultimately, then, the definition of the "straight-line-on-a-
curved-surface" concept is likely to remain unsettled and open to
Thus, the direction-facing problem, in addition to its importance
to major religious institutions, underscores an important point about
the inter-connections among social ideas, intuitive assumptions, and
scientific analysis. For when social ideas, such as unity among a
group's members, are translated into concrete action, such as having
a central location for directing thoughts and prayers, the actions
will likely be based on prevailing-often unstated-- norms and
assumptions (DiMaggio and Powell 1983); in this case, the assumption
that a "straight" path (even on a curved surface) has a unique
meaning. When confronted with new realities, however, such as
immigration to North America, where the two possible geography-based
"straight"-line options differ markedly, problems may arise.
Ultimately, while a mathematical and geographic analysis of the
direction-facing problem can help frame the scientific issues, it
cannot solve the problem fully-this task is a theoretical (even
theological) matter, with which the relevant groups and institutions
themselves must grapple. Still, students of geography should realize
the next time they are in a synagogue, church, mosque, or temple that
even here we can apply the principles and techniques of geographic
The author wishes to thank Michael Balinsky, Keith Burns, Ruth
Dick, Muhammad Eissa, Bernard Goldstein, John Hudson, Jonathan Levin,
Azim Nanji, Eric Restuccia, Robert Stockman, K. Jim Stein, Lynn
Yancy, and Noam Zohar for advice and assistance.
1. Note that the equations used in this article assume that the
earth is a perfect sphere, although it is in fact spheroidal,
flattened slightly at the poles. "On the spheroidal earth the
shortest line is called a geodesic. A great circle [however] is a
near enough approximation of a geodesic for most problems of
navigation" (American Practical Navigator 1981, 700) and is therefore
used here. Readers interested in the (extraordinarily complicated)
formula for the initial angle of a geodesic may wish to consult a
text on geodesy (e.g., Bomford 1983).
2. For even greater precision in determining a rhumb line, one can
take into account that the earth is not a perfect sphere by slightly
modifying the equation for M (see Pearson 1984, 83); I have found,
however, that this result rarely differs by more than one-sixth of a
degree, so the more complicated rhumb line formula is not used here.
3. To calculate the Baha'i qiblih, based on the great-circle path
toward Acre, see Brown and Bromberek (2000).
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Daniel Z. Levitt (Ph.D., Northwestern University, 1999) is an
assistant professor of organization management at Rutgers University.
Ordinarily, his research interests include organizational learning,
change, and innovation, but they also extend to intellectually
interesting problems in social science, geography, and the overlap
between the two.
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