# Flag Tutorial: Japan to Burkina Faso

This is more challenging than the Romania to Colombia exercise: turn the Japanese flag into the flag of Burkina Faso. The tricky part is the star in the centre. This time, instead of using colour names, we use hexadecimal codes with two digits for red, two digits for green, and two digits for blue. Here are the details you need to draw the flag of Burkina Faso:

• Red is `#EF2B2D`
• Green is `#009E49`
• Yellow is `#FCD116`
• The star is inscribed inside a circle of radius 33.

Again, you can experiment on your own, or read the rest of the tutorial to learn the concepts you need.

``````### Canvas ###
import turtle as t

white = '#e0e0e0'
red = '#b0000f'

t.bgcolor('skyblue')
t.up()
t.left(90)
t.forward(100)
t.right(90)
t.back(150)

t.write('Japan', font=('Arial', 30))
t.color(white)
t.begin_fill()
for _ in range(2):
t.forward(300)
t.right(90)
t.forward(200)
t.right(90)
t.end_fill()

t.color(red)
t.forward(150)
t.right(90)
t.forward(40)
t.left(90)
t.begin_fill()
t.circle(-60)
t.end_fill()

t.mainloop()
### Goal ###
import turtle as t

red = '#EF2B2D'
green = '#009E49'
yellow = '#FCD116'

t.bgcolor('skyblue')
t.up()
t.back(150)
t.left(90)
t.forward(100)
t.right(90)

t.write('Burkina Faso', font=('Arial', 30))
t.color(red)
t.begin_fill()
for _ in range(2):
t.forward(300)
t.right(90)
t.forward(100)
t.right(90)
t.end_fill()

t.right(90)
t.forward(100)
t.left(90)
t.color(green)
t.begin_fill()
for _ in range(2):
t.forward(300)
t.right(90)
t.forward(100)
t.right(90)
t.end_fill()

t.color(yellow)
t.forward(150)
t.left(90)
t.forward(33)
t.right(90)
t.right(72)
t.begin_fill()
size = 24
for _ in range(5):
t.forward(size)
t.left(72)
t.forward(size)
t.right(144)
t.end_fill()

t.mainloop()
``````

## Polygons

Before you learn how to draw a star, try drawing a pentagon. Turn this green square into a yellow pentagon, by changing the colour, the number of sides, and the angle. Remember, the yellow in the Burkina Faso flag is `#FCD116`. If you have trouble calculating the angle, take a guess, then adjust it until your picture looks like the goal.

If you’re wondering about the `_` in `for _ in range(4):`, it’s a variable name just like `i` or `green`, but it’s often used in Python to mean a variable that we’re going to ignore. Here, we do the same thing for each side of the square or pentagon, so we don’t need to know which side we’re drawing.

``````### Canvas ###
import turtle as t

green = '#009E49'

t.bgcolor('skyblue')

t.color(green)
t.begin_fill()
for _ in range(4):
t.forward(100)
t.left(90)
t.end_fill()

t.mainloop()
### Goal ###
import turtle as t

yellow = '#FCD116'

t.bgcolor('skyblue')

t.color(yellow)
t.begin_fill()
for _ in range(5):
t.forward(100)
t.left(72)
t.end_fill()

t.mainloop()
``````

If you had trouble calculating the angle for the pentagon, you can use the technique in this diagram. Each turn of the turtle is marked by angles 1 to 5. You can see that the turtle turns a full 360° through five turns, so each turn is 360÷5 = 72. Don’t worry about the details of this code, it’s just drawing the diagram to explain how to calculate the turn angle.

``````### Canvas ###
import turtle as t

t.shape('turtle')
for i in range(5):
t.forward(100)
t.stamp()
t.forward(30)
t.left(90)
t.circle(30, 72)
t.circle(30, -72)
t.write(i+1, font=('Courier', 15))
t.right(90)
t.back(30)
t.left(72)

t.mainloop()
``````

## A Star

What’s the difference between a pentagon and a star? Only the angle. Try using your finger or a pencil to trace all the turn angles for the turtle at each point of the star, and count how many complete circles it turns.

``````### Canvas ###
import turtle as t

yellow = '#FCD116'

t.bgcolor('skyblue')

t.color(yellow)
t.begin_fill()
for _ in range(5):
t.forward(100)
t.left(72)
t.end_fill()

t.mainloop()
### Goal ###
import turtle as t

yellow = '#FCD116'

t.bgcolor('skyblue')

t.color(yellow)
t.begin_fill()
for _ in range(5):
t.forward(100)
t.left(144)
t.end_fill()

t.mainloop()
``````

If it wasn’t clear with your finger, look at the marked angles in this diagram. The turtle starts out facing right, turns through corners 1 and 2, then faces right again in the middle of corner 3, and turns a complete second circle through corners 4 and 5. It turns two complete circles in five turns, so each turn is 360*2÷5 = 144.

``````### Canvas ###
import turtle as t

t.shape('turtle')
for i in range(5):
t.forward(100)
t.stamp()
t.forward(30)
t.left(90)
t.circle(30, 144)
t.circle(30, -144)
t.write(i+1, font=('Courier', 15))
t.right(90)
t.back(30)
t.left(144)

t.mainloop()
``````

## Filling the Centre

Notice that the star’s centre isn’t filled in. That’s because the filling technique counts how many edges you have to cross to get to a pixel. If the number is odd, it fills in the pixel. Getting to the centre of the star always crosses two edges, so it isn’t filled in.

To fill in the centre, we can’t draw all those lines through the middle, so we need to draw around the outside of the star. Can you work out what angle you need for the inside corner? Either calculate it with geometry, or keep adjusting it until you get a star.

``````### Canvas ###
import turtle as t

yellow = '#FCD116'

t.bgcolor('skyblue')

t.fillcolor(yellow)
t.begin_fill()
for _ in range(5):
t.forward(50)
t.left(90)
t.forward(50)
t.right(144)
t.end_fill()

t.mainloop()
### Goal ###
import turtle as t

yellow = '#FCD116'

t.bgcolor('skyblue')

t.fillcolor(yellow)
t.begin_fill()
for _ in range(5):
t.forward(50)
t.left(72)
t.forward(50)
t.right(144)
t.end_fill()

t.mainloop()
``````

Here’s how I calculated the turn angle for the inside corner. The yellow triangle is one of the points of the star, and we already know that angle A is 144°. The turtle’s turn angle at the inside corner is marked as C. You can see that A and B add up to 180°, so B must be 36°. B, C, and D are the three angles of the yellow triangle, so they must add up to 180°. Since B is 36°, C+D must be 180° - 36° = 144°. The yellow triangle is an isosceles triangle, so C and D are the same, and C is 144° ÷ 2 = 72°.

``````### Canvas ###
import turtle as t

yellow = '#FCD116'

t.color(yellow)
t.begin_fill()
t.left(72)
t.forward(100)
t.right(144)
t.forward(100)
t.end_fill()
t.goto(0, 0)
t.left(72)

t.color('black')
t.back(25)
t.forward(100)
t.back(50)
t.left(90)
t.circle(25, 72)
t.circle(25, -72)
t.right(90)
t.back(25)
t.write('C', font=('Courier', 15), align='right')
t.left(72)
t.forward(75)
t.write('B', font=('Courier', 15), align='right')
t.right(90)
t.circle(25, 36)
t.circle(25, -36)
t.left(90)
t.forward(55)
t.right(90)
t.circle(-30, 90)
t.write('A', font=('Courier', 15), align='right')
t.circle(-30, 54)
t.circle(-30, -144)
t.left(90)
t.back(30)
t.right(144)

t.forward(100)
t.left(72)
t.write('D', font=('Courier', 15))
t.back(25)
t.left(90)
t.circle(-25, 72)
t.circle(-25, -72)
t.right(90)
t.forward(50)

t.mainloop()
``````

## Inside a Circle

Next, you need to make your star fit inside a circle of radius 33. Can you adjust the Japanese flag’s circle to be the right size?

``````### Canvas ###
import turtle as t

white = '#e0e0e0'
red = '#b0000f'

t.bgcolor('skyblue')
t.up()
t.left(90)
t.forward(100)
t.right(90)
t.back(150)

t.color(white)
t.begin_fill()
for _ in range(2):
t.forward(300)
t.right(90)
t.forward(200)
t.right(90)
t.end_fill()

t.color(red)
t.forward(150)
t.right(90)
t.forward(40)
t.left(90)
t.begin_fill()
t.circle(-60)
t.end_fill()

t.mainloop()
### Goal ###
import turtle as t

white = '#e0e0e0'
red = '#b0000f'

t.bgcolor('skyblue')
t.up()
t.left(90)
t.forward(100)
t.right(90)
t.back(150)

t.color(white)
t.begin_fill()
for _ in range(2):
t.forward(300)
t.right(90)
t.forward(200)
t.right(90)
t.end_fill()

t.color(red)
t.forward(150)
t.right(90)
t.forward(67)
t.left(90)
t.begin_fill()
t.circle(-33)
t.end_fill()

t.mainloop()
``````

Now, change the angle and size of the star to fit inside the circle. You could use trigonometry to calculate the size exactly, but it’s probably much easier to adjust it until it looks good.

``````### Canvas ###
import turtle as t

white = '#e0e0e0'
red = '#b0000f'
yellow = '#FCD116'

t.bgcolor('skyblue')
t.up()
t.left(90)
t.forward(100)
t.right(90)
t.back(150)

t.color(white)
t.begin_fill()
for _ in range(2):
t.forward(300)
t.right(90)
t.forward(200)
t.right(90)
t.end_fill()

t.color(red)
t.forward(150)
t.right(90)
t.forward(67)
t.left(90)
t.begin_fill()
t.circle(-33)
t.end_fill()

t.color(yellow)
t.begin_fill()
star_size = 50
for _ in range(5):
t.forward(star_size)
t.left(72)
t.forward(star_size)
t.right(144)
t.end_fill()

t.mainloop()
### Goal ###
import turtle as t

white = '#e0e0e0'
red = '#b0000f'
yellow = '#FCD116'

t.bgcolor('skyblue')
t.up()
t.left(90)
t.forward(100)
t.right(90)
t.back(150)

t.color(white)
t.begin_fill()
for _ in range(2):
t.forward(300)
t.right(90)
t.forward(200)
t.right(90)
t.end_fill()

t.color(red)
t.forward(150)
t.right(90)
t.forward(67)
t.left(90)
t.begin_fill()
t.circle(-33)
t.end_fill()

t.color(yellow)
t.begin_fill()
t.right(72)
star_size = 24
for _ in range(5):
t.forward(star_size)
t.left(72)
t.forward(star_size)
t.right(144)
t.end_fill()

t.mainloop()
``````

Now that you have all the skills you need, can you solve the challenge at the start of the tutorial?