Geometry of the Sphere - Spatial Mathematics: Theory and Practice through Mapping - page 6

• To convert this system to an absolute system, that is replicable,
employ some commonly agreed-upon measurement strategy to
standardize measurement. One such method is the assumption that
there are 360 degrees of angular measure in a circle.
− Thus, P might be described as lying 42 degrees north of the
Equator, and 71 degrees west of the Prime Meridian. The
degrees north are measured along a meridian; the degrees
west are measured along the Equator or along a parallel (the
one at 42 north is another natural choice). The north/south
angular measure is called latitude; the east/west angular mea-
sure is called longitude.
− The North and South poles are 90 degrees north latitude, and
90 degrees south latitude, respectively. The angle between the
equatorial plane (Plane B in Figure 1.1 ) and the poles is 90
degrees. The polar axis is perpendicular to a diameter in the
equatorial plane.
− The use of standard circular measure creates a designation
that is unique for P ; at least unique to all whose mathematics
rests on having 360 degrees in the circle.
− Parts of degrees may be noted as minutes and seconds, or as
decimal degrees. A degree (°) of latitude or longitude can be
subdivided into 60 parts called minutes ( ′ ). Each minute can
be further subdivided into 60 seconds ( ″ ). Thus, 42 degrees 30
minutes is the same as 42.50 degrees because 30/60 = 50/100.
Current computerized mapping software often employs deci-
mal degrees as a default; older printed maps may employ
degrees, minutes, and seconds. Thus, the human mapper
needs to take care to analyze the situation and make appro-
priate conversions prior to making measurements of position.
Such conversion is simple to execute using a calculator. For
example (see Figure 1.4 ), 42 degrees 21 minutes 30 seconds
converts to 42 + 21/60 + 30/3600 degrees = 42.358333 degrees;
powers of ten replace powers of 60.
• Figure 1.5 shows the described reference system placed on a sphere.
What might be called a Cartesian grid in the plane is called a grati-
cule on the sphere.
• Points along one parallel all have the same latitude; they are the
same distance above or below, north of or south of, the Equator.
• Points along one meridian all have the same longitude; they are
the same distance east or west of the Prime Meridian.
• Spacing between successive parallels or meridians might be at any
level of detail; however, when circular measure describes the posi-
tion of these lines, that description is unique, according to the
standard of using 360 degrees in a circle.
• One spacing for the set of meridians that is convenient on maps of
the world is to choose spacing of 15 degrees between successive