# AZIMUTHS

## (THINKING IN CIRCLES)

 "Well, Lou, the best way to learn about compasses and direction is to start thinking in circles...."
 "Catch this dizzy dame!"
 "Don't be nervous, Lou! OK. Here's a circle. It has a center and an outside, called the CIRCUMFERENCE."
 "Now, let's divide the circumference into parts. (Each part is called an arc.) Divide it into 2 equal parts, and what do you have? Two equal arcs called SEMI-CIRCLES. And if you divide it into four equal arcs, each arc is a 'quarter circle' or 'QUADRANT.' Now comes the fancy part: divide the circumference into 360 equal arcs, and each arc is called a DEGREE. So tell me, Lou, how many degrees is a semi-circle? How many degrees is a quadrant?"
There are degrees in a semi-circle...and there are in a quadrant.

Click the "SEMI-CIRCLE" button to see if you have the correct number of degrees in a semi-circle:-

Click the "QUADRANT" button to see if you have the correct number of degrees in a quadrant :-

 "Now suppose we want to number each of the 360 degrees...."
 "How about 'first degree', 'second degree' and then the third one could be 'the third degree'! (Heh heh!)"
 "Once again, Lou, you've hit it on the head. But 'third' from where? Some place on the circle has to be called the beginning, that is, called zero degrees. And then you can start counting, so every degree has a number. (Numbers of degrees are indicated by a little circle above and to the right of the number; for example seven degrees is 7°.) Notice that '0°' is the same as '360°' because you've gotten back to where you started. That's the way it is when you go around in a circle!"

 "Now, let's orient the circle so that the line going from the center of the circle to the '0°' (or 360°) is pointing North. Then the '90°' points to the East, '180°' to the South, '270°' to the West, and so on. That system of stating direction according to the number of degrees clockwise from the zero is known as the azimuth system!"

 "And the circle with radiating lines and the directions marked on it or next to it is called a COMPASS ROSE! You'll find them on maps and navigation charts!!"
 "I see that on our compass rose the azimuthal (gulp) direction 45° is called 'northeast' (NE), and 135° is called 'southeast' (SE), etc. Thank goodness!! 'North', 'south', 'northeast', 'southeast'...that's how I'm used to giving directions! I'm much more comfortable with names than numbers! "

 "There's a reason for the numbers, Lou! 'North', 'south', 'east' and 'west', and 'northeast', 'southeast', and so on are OK as names without numbers! But all the directions in between them are too vague! The names need numbers attached to them!      Look at the diagram! Consider the direction in which the green arrow is pointing. To get its azimuth, you measure the angle it makes with 0°. That angle is 103°! That's pretty easy, isn't it??!!"

 By the way, for azimuth 0° people often say 'due' north ('due' means 'exactly'), and for 90° they say due east, for 180° due south and for 270° due west!"
"Now, Lou, check out your understanding of direction by doing some exercises!"

DIRECTIONS:
(READ ALL THE DIRECTIONS BEFORE YOU CLICK ON ANY BUTTONS!)
1. Click on the pink button to print out instructions on how to use the "Distance and Directions on Maps: Exercises."
2. Click on the top blue button to go to the Exercises.
3. There you will find exercises with maps that use a
• Bar Scale (Lower Manhattan)
• Statement of Equivalency (Northeast US)
• Representative Fraction (Western US)
4. For each map, answer the questions about direction. Questions about distance or scale may be ignored until you have studied 'Distance'.
5. Do as many of the exercises as are needed for you to feel confident that you understand the material.
6. Check your understanding by doing the "Additional Exercises" (click the bottom blue button).
 PRINT INSTRUCTIONS FOR EXERCISES