1. The graticule is made up of vertical lines, called lines of longitude, and horizontal lines, called lines of latitude. Because the earth is spherical, these lines form circles.

3. Sphere vs. spheroid
A sphere is the three-dimensional form of a circle. A spheroid is the ellipsoid that is very close to the shape of a sphere.

4. The assumption that the earth is a sphere simplifies mathematical calculations and can be used for small-scale maps (i.e., less than 1:5,000,000). To maintain accuracy for larger-scale maps (1:1,000,000 or larger), however, the earth must be treated as a spheroid.

5. Datums
A datum is a point of reference used to measure locations on the surface of the earth. It defines the origin and orientation of the lines of latitude and longitude.
A datum is always related to a spheroid.
There are two types of datums: earth-centered and local.
The origin of the 1983 North American Datum (NAD83) is very close to the earth's center of mass and is the most commonly used datum for North America.
A local datum is aligned so that it closely corresponds to the earth's surface for a particular area. An example is the 1927 North American Datum (NAD27) which uses Meades Ranch, Kansas as the point of origin for all measurements.

7. Map Projections
The term "map projection" was coined because early cartographers employed the concept of projecting light from a source through the earth's surface and onto a two-dimensional surface. The light source could be placed at the center of the earth, the opposite side of the earth, or at some location distant from the earth. The two-dimensional surface could be a cylinder, plane, or cone.

9. Projections (cont’d)
Although maps are created using mathematical formulas rather than projecting light through the earth's surface onto a flat surface, the concept is valid and cartographers use the term "projection" to describe the set of rules that control or predict the distortion inherent on any map.

10. Projections (cont’d)
Today, all projections use formulas—mathematical expressions that convert data from a geographic location (latitude and longitude) on the earth to a representative location on a flat surface. Most modern projections are variations of the three original surfaces.
Cylindrical
Plane
Cone

14. Distortion
The conversion of geographic locations from a spherical coordinate system to a Cartesian coordinate system causes distortion. The projection process will distort one or more of these four spatial properties:
Shape
Area
Distance
Direction
Distortion of these spatial properties is always inherent in a Cartesian coordinate system.
No projection can preserve all four properties.

16. Distortion (cont’d)
These examples show how four different projections distort the earth's surface. A Mercator projection maintains true shape, a Sinusoidal projection maintains true area, an Equal-Area Cylindrical projection maintains true area (notice how different it looks from the Sinusoidal projection), and a Robinson projection does not enforce any properties but is widely used because it makes the earth's surface and its features "look right."

17. Projected coordinate systems are based on Cartesian coordinates which use a grid. Feature locations are measured using x and y coordinate values from the point of origin.

18. The Universal Transverse Mercator grid that covers the conterminous 48 United States comprises 10 zones—from Zone 10 on the west coast through Zone 19 in New England.

19. UTM
The northing values are measured continuously from zero at the Equator, in a northerly direction.
A central meridian through the middle of each 6° zone is assigned an easting value of 500,000 meters. Grid values to the west of this central meridian are less than 500,000; to the east, more than 500,000.

20. State Plane Each zone has its own projection
LCC (long axis E-W) or Transverse Mercator
Covers smaller geographic area than UTM
Each zone has a central meridian
False origin SW of each zone
Unit of measure is feet
X direction measured in eastings, Y direction measured in northings