Drawing polygon with turtle graphics

Question

I am trying to draw a polygon in python using the turtle library. I want to set the size to fit the screen size but I don't know how. For now I tried two ways and it does work but I want that no matter the size the polygon fits in the screen. For example if I put size = 50 and n = 100 it will not show in the screen.

from turtle import * 
def main():
    sides = int(input('Enter the number of sides of a polygon: '))
    angle = 360/sides
    size = 500/sides
# =============================================================================
#     if sides <= 20:
#         size = 50
#     else: 
#         size= 10
# =============================================================================
    for i in range(sides):
        forward(size)
        left(angle)
        i += 1
    hideturtle()
    done()   
main()

Answer 1

If I understand correctly, you are asking how to choose a size (side length) such that the shape fills but does not exceed the screen. First, we need to check the height or width of the screen (whichever is smaller):

min_dimension = min(screensize())  # by default, 300 pixels

The circumradius is the radius of the circle that passes through all the points of the polygon . For the polygon to fit in the screen, the circumradius should be equal to min_dimension . Reversing the formula for the circumradius we can write a function to determine the appropriate side length:

def side_length(circumradius, number_of_sides):
    return circumradius * 2 * math.sin(math.pi / number_of_sides)

To fill the screen we should start drawing near the bottom of the screen rather than in the center.

def main():
    sides = int(input('Enter the number of sides of a polygon: '))
    angle = 360/sides
    min_dimension = min(screensize())
    size = side_length(min_dimension, sides)
    right(90 + angle / 2)
    
    # Start from near the bottom of the screen
    penup()
    forward(min_dimension)
    left(90 + angle / 2)
    pendown()

    # Draw polygon
    for _ in range(sides):
        forward(size)
        left(angle)
    hideturtle()
    done()   

(Technically, this makes the shape slightly smaller than the screen, especially for low numbers of sides. The apothem should be used instead of the circumradius.)