Python: Drawing a Ring of Circles

Python: Drawing a Ring of Circles

The goal: Draw a number of circles that revolve around the origin (0,0). The center of each circle is rotated counterclockwise. The angle of the rotation is determined by:

a = 360° ÷ n = (2 * π rad) ÷ n

Since the center of each circle is set at (0, 0), the center of each circle is located at (r * cos a, r * sin a) where r is the radius.

Python: Using Turtle (Numworks)

( radius = 50 pixels, n = 8 circles)

The script circring.py imports the Turtle module. The circle command draws a circle starting at the bottom of the circle going counter-clockwise. The bottom of the circle is located at the point (x, y – r) where (x, y) is the center and r is the radius.

Code:

from math import *

from turtle import *

# 2026-07-19 EWS

# turtle version

r=eval(input("radius? "))

n=int(input("# steps? "))

speed(7)

for i in range(n):

  # set angle

  a=i*2*pi/n

  # turtle circle starts at

  # bottom center point

  x=r*cos(a)

  y=r*(sin(a)-1)

  # move to starting point

  penup()

  goto(x,y)

  # draw circle

  pendown()

  circle(r)

  

# make turtle invisible

hideturtle()

Python: Using TI-Draw (TI-84 Evo)

( radius = 50 pixels, n = 8 circles)

The script CIRRNG84.py uses the TI Draw module. The TI-84 Evo (and I think the TI nSpire, not 100% sure) lacks the Turtle module and instead employs a calculator-specific drawing module. The draw_circle command calls for both the center point and the radius. No adjustments are necessary.

Code:

from ti_draw import *

from math import *

# 2026-07-19 EWS

# TI version non turtle

set_window(-160,160,-105,105)

print("grid -160,160,-105,105")

r=eval(input("radius? "))

n=int(input("# steps? "))

clear()

for i in range(n):

  # set angle

  a=i*2*pi/n

  # determine center

  x=r*cos(a)

  y=r*sin(a)

  # draw circle

  draw_circle(x,y,r)

# show picture

show_draw()

Source

Chartier, Tim and Langville, Amy. Nonstandard Notebook: Mathematically Rule Pages for Unruly Thoughts The University of Chicago Press: Chicago and London. 2024 ISBN-13 978-0-226-83090-2 <pg. 61-63>

If you get a chance, please get this book. It’s a journal of interesting curves involving polynomials, circles, lines, and waves. The authors uses these curves to illustrate what ruled paper would look like when it doesn’t consist of all straight lines. The concept of music, earthquakes, and heartbeats are illustrated, including equations for clovers, mandalas, and hearts. This book is an inspiration for me.

Eddie

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