How to draw a circle using turtle in python?

Question

I wanted ask how can I draw a circle using turtle module in python just using turtle.forward and turtle.left? I use the code below:

 for i in range(30):
     turtle.forward(i)
     turtle.left(i)  
 turtle.done()

What I get is that the line does not stop once I get the full cirle. How can I code so that I have a circle of specific radius and that I have a full stop once the circle is drawn (without using turtle.circle).

Answer 1

I made this image as a reference,

Essentially you need to draw the inscribed polygon with n sides.

The initial left turn will be ϴ/2.

Then forward by a = 2rsin(ϴ/2).

Each forward is followed by a left turn of the full ϴ, except that after the last forward we want only a left turn of ϴ/2 so that the heading will be correctly updated to be tangential to the circle (or arc).

Something like this,

import turtle
import math

def circle2(radius,extent=360,steps=360):
    if extent<360 and steps==360:
        steps=extent
    
    theta=extent/steps
    step_size=2*radius*math.sin(math.radians(theta/2))
    turtle.left(theta/2)
    turtle.forward(step_size)
    for i in range(1,steps):
        turtle.left(theta)
        turtle.forward(step_size)
    
    turtle.left(theta/2)
    

turtle.hideturtle()
turtle.speed(0)
turtle.getscreen().tracer(False)

circle2(50)
circle2(100,180)
turtle.up()
turtle.home()
turtle.down()
circle2(130)
circle2(130,360,10)

turtle.update()
turtle.mainloop()