Monte Carlo Simulation: The Area of an Ellipse

Overview: Use Monte Carlo simulation to estimate the area of an ellipse.

• Use the spinners to select the lengths of the major and minor axes of the ellipse.



• Draw rectangle checkbox: When this is selected, random points are chosen from within a 2a x 2b rectangle containing the ellipse.



• One quadrant checkbox: When this is selected, points are selected in the first quadrant only.



• Using the buttons, points can be generated 50, 200, or 1000 at a time. The total number of points generated and the number of points inside the ellipse are reported.



• Use the 'On,' 'Off' radio buttons to toggle animation.

1. Set a and b to determine the lengths of the axes of the ellipse.
2. Select the 'Draw rectangle' checkbox to draw the rectangle with side lengths 2a and 2b enclosing the ellipse.
3. Find the area of the rectangle.
4. Use the buttons to generate random points.
5. Consider the number of random points that were within the ellipse and the total number of points generated. How can you use this information to estimate the area of the ellipse?
6. If you choose more random points, how do you expect your estimate to change?
7. How would you use the 'one quadrant only' checkbox to estimate the area of the ellipse?