I wanted to draw a triangle, so I sat down on the ground and thought about it for a while.

When it all comes down to it. What it is, you see. How it works. Well a triangle has. It has 3.

• 3 points.
• 3 corners.
• 3 angles.

It's 3 lines really.

So I want to draw 3 lines.

The lines are all the same size.

An equal triangle. An equilateral triangle.

(Are the lines the same because the angles are the same or are the angles the same because the lines are the same? It's a trickly-pickly question and you might think that both are true—but one of these is the MOST true—and you can work it out if you consider shapes with more than 3 sides)

So I'll have:

Draw a line

Draw a line

Draw a line

...but I need something in between.

I need to turn the paper around.

Or if I can't turn the paper, I could turn myself.

I imagine I am a turtle. And for a moment I wonder if I have always been a turtle. Perhaps I have just been a turtle pretending to be a human boy. At last: I am turtle again. And I speak the language of turtle.

I will draw a line. Length 200. A good length for a line. I will draw 3. And I will turn myself around in between each line. (The paper will not move)

fd 200
rt 120
fd 200
rt 120
fd 200
rt 120

Same thing is repeated three times.

I picked the angle of 120° because... well I've played this game before.

I know if we are drawing a shape with 3 sides then we get a circle, of 360°, and divide it into 3 equal turns.

360/3 = 120

If we were drawing a shape with 36 equal sides we would have:

360/36 = 10

I should make the looping more obvious.

repeat 3 [
fd 200
rt 120
]

Now I want to draw something fun with this triangle.

I have read something about drawing the mid point on each of the lines and joining it up to something.

I make a function, mark, that scratches a little line at the mid-point of each line.

to mark
lt 90
fd 5 
rt 180
fd 10
rt 180 
fd 5
rt 90
end
repeat 3 [
fd 100
mark
fd 100
rt 120
]

What I want to do is join the midpoint to the opposite corner.

I have a way of doing that.

to extrabit 
rt 30
fd 200
rt 180
fd 200
rt 180
lt 30
end
repeat 3 [
fd 200
rt 120
extrabit
]

to splity :angle :length
rt (180 - :angle)
pu
fd :length
rt 180
pd
fd :length
rt :angle
end
to extrabit :length
splity 52.5 :length
splity 45 :length
splity 30 :length
splity 15 :length
splity 7.5 :length
end
to side :length
fd :length
extrabit :length
rt 120
end
repeat 3 [
side 780
]

Here's what it looks like with some of the areas shaded: