Direction

In geography, the four principal directional indicators are marked as points or arrowheads on a traditional compass rose. Called cardinal directions, they are north, east, south and west. There are simple specific means to establish each direction which should work anywhere on Earth where there is a view of the sky. North and south are oriented toward their respective poles near each end of the Earth's axis. The Earth's rotation upon that axis can define the orientation of east and west.

Scale

The scale of a map is the ratio of a single unit of distance on the map to the equivalent distance on the ground. The scale can be expressed in four ways: as a ratio, a fraction, in words and as a graphical (bar) scale.

A scale expressed as a ratio of say 1:25,000 means that one unit on the map represents 25,000 units on the ground.

Scale expressed as a fraction, 1/25,000, means that any distance on the map is 1/25,000 the distance on the ground. It expresses the amount of reduction of distances used to represent detail on the map. The 25,000 value is called the scale denominator.

A graphical (bar) scale is a ruler with ground distances added, included in the margin of most maps. The graphical scale is used to measure distances on the map. The distance on the map is marked on the edge of a sheet of paper, which is then placed over the graphical bar scale and the distance read.

On this map of the southern tip of Manhattan we have a graphical scale that tell us that the length of the scale bar equals 5000 feet.

We place a ruler over the scale and we see that 2 inches on the map represent 5000 feet on the ground.

If we wanted to measure the distance between the Tenement Museum and the Brooklyn Navy Yards we measure the distance in inches between the two places and then translate this distance to feet on the ground in this case 7500 feet.

On the map above determine what is the distance between Salt Lake City and Denver in miles and in kilometers.

Azimuth direction - Azimuth is a mathematical concept defined as the angle, usually measured in degrees (°), between a reference plane and a point. This concept is used in many practical applications including navigation, astronomy, mapping, mining and artillery. The word azimuth is derived from the Arabic ('as-sumut') which means the ways, referring to the ways or directions a person faces.

In the example above the town of Newville is located at 234^{o from North on the SW quadrant.}

^{What is the azimuth direction on the map above?}

Latitude and Longitude

Any location on Earth is described by two numbers: its latitude and its longitude. If a pilot or a ship's captain wants to specify position on a map, these are the "coordinates" they would use. Actually, these are two angles, measured in degrees, "minutes of arc" and "seconds of arc." These are denoted by the symbols ( °, ', " ) e.g. 35° 43' 9" means an angle of 35 degrees, 43 minutes and 9 seconds (do not confuse this with the notation (', ") for feet and inches!).

A degree contains 60 minutes of arc and a minute contains 60 seconds of arc, and you may omit the words "of arc" where the context makes it absolutely clear that these are not units of time.

Practice map - Give the latitude and the longitude of the following points