Exrior Angles

draws in red; fd 100 moves forward; and rt 72 turns right by 72°.

pen red                      # Start drawing in red.
fd 100                       # Move forward by 100 pixels.
rt 72                        # Turn right by 72 degrees.
fd 100                       # Move forward by 100 again.

The command rt 72 turns the turtle, but it does not slide it. To draw an angle, move forward after turning.

• How big is the drawn angle? The 72 degree turtle turn is the supplement of the drawn angle.
• Experiment with other angle sizes. How big is the angle using rt 5?

2. The angle that measures a turtle turn is called an exterior angle. The following special line of code will load a script "/lib/angles.cs" that puts the turtle in a mode that shows all exterior angles when the turtle turns. It waits to finish loading the script before running the rest of your program.

await loadscript '/lib/angles.cs', defer()

pen red                      # Start drawing in red.
fd 100                       # Move forward by 100 pixels.
rt 72                        # Turn right by 72 degrees.
fd 100                       # Move forward by 100 again.
rt 72                        # Turn right by 72 degrees.
fd 100                       # Move forward by 100 again.

You could copy-and-paste the code five times to repeat it five times. Or you can have the program repeat the steps automatically, using a loop.

3. Make a loop. Unlike LOGO, which used "repeat" to make a loop, CoffeeScript uses the word for. Indent the block of code and then write for [1..5] above it, to loop 5 times.

await loadscript '/lib/angles.cs', defer()

pen red                      # Start drawing in red.

for [1..5]                   # Repeat 5 times
  fd 100                     # Move forward by 100 pixels.
  rt 72                      # Turn right by 72 degrees.
  

It is important to line up indented lines neatly in CoffeeScript: the language uses indenting to know which block of lines to repeat under a for.

4. Finally, experiment with variables. We will use s as the length of a side, and n as the number of sides, and a as the measure of an exterior angle.

await loadscript '/lib/angles.cs', defer()

s = 80                       # s is the side length.
n = 6                        # n is the number of sides.
a = 60                       # a is the exterior angle size.

pen red                      # Start drawing in red.

for [1..n]                   # Repeat n times
  fd s                       # Move forward by s pixels.
  rt a                       # Turn right by a degrees. 
  

5. Exercises:

• Try shrinking s down to a size smaller than 10.
  What do you notice about the exterior angles all together?
• What is the sum of all the exterior angles of a polygon? Why?
• What does a need to be to make a polygon when n is 3?
• What should a be when n is 10?
• Find a formula for a in terms of n. Change your program to use the formula.

s = 200
n = 9
a = 360 * 4 / 9
bk 100
pen blue
for [1..n]
  fd s
  rt a 
pen null
jump(-500, 100)

await loadscript '/lib/angles.cs', defer()

s = 10
n = 6
a = 60
pen red

for [1..n]
  fd s
  rt a

6. Extra Credit:

• What would it mean for the turtle to turn a total of 720 degrees?
• Try setting n to 5 and a to 144, and make s 80. Why do you get the shape that you get?
• Can you make a nine-pointed star?
• How many different nine-pointed star shapes can you create?