python turtle drawing ellipse

Drawing an Ellipse with Python Turtle

1. Definition and Characteristics of an Ellipse

An ellipse is a geometric figure with a special shape. It is a trajectory on a plane where the sum of the distances from a point to two fixed points varies by a constant. Ellipses have the following characteristics:

• The sum of the distances from any point on an ellipse to its two foci is a constant
• The axis of symmetry of an ellipse is the line connecting the two foci and passes through the center
• The eccentricity of an ellipse is less than 1 and is equal to the ratio of the focal length to the major axis
• The major axis of an ellipse is the reciprocal of the eccentricity, and the minor axis is the square of the reciprocal of the eccentricity

2. Python Turtle Library

Python Turtle is a graphics library that provides simple and intuitive drawing functions, making it ideal for beginners to learn and practice. Turtle can be used to draw a variety of shapes, including ellipses.

3. How to Draw an Ellipse

In Python, you can use the circle function in the turtle library to draw an ellipse. Since the circle function can only draw circles, and an ellipse is a special case of a circle, you need to set appropriate parameters to draw an ellipse.

The method for drawing an ellipse is as follows:

import turtle

# Initialize turtle
turtle.setup(800, 600)
turtle.bgcolor("white")
turtle.fillcolor("pink")
turtle.speed(2)

# Draw an ellipse
turtle.penup()
turtle.goto(0, -100)
turtle.pendown()
turtle.begin_fill()
turtle.circle(200, 90)
turtle.circle(100, 90)
turtle.circle(200, 90)
turtle.circle(100, 90)
turtle.end_fill()

# Hide turtle
turtle.hideturtle()

# Main Loop
turtle.mainloop()

In the above code, the turtle library is first imported and initialized. Then, the ellipse’s appearance is defined by setting properties such as color and speed. Next, the penup and pendown functions are used to move to the ellipse’s starting position. The circle function is called to draw the four parts of the ellipse, and the end_fill function is used to fill the interior of the ellipse. Finally, the turtle is hidden, the main loop is entered, and the window is closed.

4. Run Results

The results of the above code are as follows:
[Ellipse Example Image]

5. Modifying the Shape and Size of the Ellipse

If you want to change the shape and size of the ellipse, you can modify the parameters of the circle function. The first parameter represents the radius (or equivalently, the diameter of the circle), and the second parameter represents the degree of the circle, which represents the portion of the circle to be drawn. By adjusting the values of these two parameters, you can draw ellipses of different shapes and sizes.

6. Summary

Using the turtle library, we can easily draw a variety of shapes, including ellipses. By adjusting the parameters of the circle function, we can change the shape and size of the ellipse.