Map Projections
The only true representation of the earth, free
of distortion, is a globe. Maps are flat, and the process by which geographic
locations (latitude and longitude) are transformed from a threedimensional
sphere to a twodimensional flat map is called a projection.
PROPERTIES
Every map projection distorts at least three, and sometimes all four,
of the following properties: Shape, Area, Distance, and Direction.
Conformal: No map can preserve the shape of large areas,
but a conformal projection maintains shape in small, localized areas.
Equal Area: These projections show the areas of all regions
on the map in the same proportion to their true areas on the globe.
Equidistant: No map can show distance correctly between
all points on the map, but only from one, or at most two, points to any
other point.
Azimuthal: This projection correctly shows directions
(azimuths) from a single point to all other points on the map. 
To better understand what happens
during the projection process, imagine the earth as a large inflated balloon.

Cut it apart, and flatten it to make
a map. It will be stretched in some places, shrunk in others. Think of
where and how the original balloon has been distorted.

VISUAL COMPARISONS
Visualize the properties of a map projection by comparing the arrangement
of its meridians and parallels with the characteristics of the graticule
on the globe: Parallels are spaced equal distances apart.

The equator is the longest parallel. Length of parallels decreases moving
toward the poles (which are points).

All meridians are of equal length.

Meridians converge at the poles.

At a given latitude, meridians are equally spaced.

Latitude and longitude meet at right angles.
This diagram illustrates how a Mercator (cylindrical) projection distorts
the relative sizes of areas on the earth. Note how areas are increasingly
enlarged towards higher lattitudes. 
CLASSIFICATION OF PROJECTIONS
One method of classifying map projections is to group them by the type
of surface onto which the graticule is theoretically being projected: Cylindrical,
Conic, and Azimuthal. Map projections that do not fit within these three
classes are described as Pseudo or Miscellaneous projections. Though few
maps are truly the result of such projection (most are derived from mathematical
formulas), it is a useful way to visualize and understand the transformation
process. Where the projection surface touches (is tangent to) the globe,
scale is true. This can be at a point, or along one or two lines (called
standard lines, or, if along a line of latitude, standard parallels). Distortion
increases with increasing distance from the standard point or lines. 
CYLINDRICAL
Imagine a light bulb in the center of a globe, with a sheet of paper
wrapped around it in the form of a cylinder. Meridians and parallels would
be "projected'' onto the cylinder as straight, parallel lines. Because
meridians on these projections do not meet at the poles, as they do on
the globe, these maps are increasingly stretched and distorted toward the
poles.
Pseudocylindrical projections normally have straight parallels and curved
meridians (usually equally spaced). The Robinson Projection is a popular
example. It was created to make the world "look" right by keeping angular
and areal distortions to a minimum. 

AZIMUTHAL
A perfectly flat piece of paper (a plane) would touch the globe at a
point. This projection is a good choice for maps with circular or square
shapes. When the point of tangency is one of the poles, meridians are shown
as straight lines radiating from the pole. If parallels are then drawn
as equally spaced concentric circles, this projection would be equidistant
(scale is true along any line radiating from the center point, in this
case the pole).
Gnomonic Projection: Great circle routes (the shortest
distance between two points on the globe) appear as straight lines on this
Azimuthal 

CONIC
A cone of paper placed over a globe would touch its surface along one
standard line (usually a parallel). A cone that sliced through the globe
would intersect it twice, creating two standard parallels. Such a projection
is wellsuited for showing areas in the middlelatitudes with a mostly
eastwest extent (like the United States). 

