If you want to calculate the perimeter (circumference) of an ellipse, you must use an approximation.

Project #1

The perimeter of an ellipse is very difficult to calculate.

In this problem use the ellipse perimeter infinite series equation. For more information about the equation click HERE .

Show the results of using

1. term 0
2. terms 0 to 1
3. terms 0 to 2
4. terms 0 to 3
5. terms 0 to 4
6. terms 0 to 5
7. terms 0 to 6
8. terms 0 to 7

Create an interactive program to calculate (approximate) the perimeter of an ellipse.

1. ask the user for input
   What should the user be ask to input?
   • major and minor axis
   • semi-major and semi-minor axis
   • the eccentricity
   • coordinates
   • bounding box
   • ...
2. calculate the ellipse's perimeter
3. display pertinent information
4. loop

Image From: commons.wikimedia.org

Note:

• The center of an ellipse is the midpoint of both the major and minor axes.
• The semi-major (a) and semi-minor (b) axes of an ellipse are half the length of the major and minor axes.

Project #2

Use graphics.py. It is a simple graphics library. Click HERE for more information. (download, install, documentation, ...)

Recreate project #1, but instead draw the ellipse using the data the user entered. (Ellipse centered at the origin 0,0) For more information click HERE .

Note:

• draw points on the ellipse perimeter (not lines)
• points evenly spaced along the X axis

Project #3

Recreate project #2, but center the ellipse at 100,200. For more information click HERE .

Project #4

Recreate project #2, but allow the user to specify an angle for the major axis (above or below the X axis). (i.e. Draw the ellipse at a "tilt" angle centered at the origin 0,0.) For more information click HERE .

Project #5

Combine project #3 and Project #4. (Use a transformation matrix?) For more information click HERE .

Project #6

Create an interactive program that

1. ask the user for the semi-axes of an ellipse
2. display the size of the
   • axes
   • perimeter
   • area
3. loop

Project #7

Create an interactive program that

1. ask the user for the semi-axes of an ellipsoid
2. display the size of the
   • axes
   • surface
   • volume
3. loop

Links

Why is there no equation for the perimeter of an ellipse? (YouTube)

Perimeter of Ellipse

Ellipse (Wikipedia)

Perimeter of an ellipse (Wikipedia)

Orbit (Wikipedia)

Ellipsoid (Wikipedia)

Miscellaneous