Degree 4: Cassini ovals
Exploring Cassini Ovals
This construction creates a Cassini Oval, the set of all points P(x, y) such that the product of the distances from P to two fixed points A and B is constant.
By adjusting the slider k, students can visualize how the shape of the Cassini Oval changes — from two loops, to a figure-eight (lemniscate), and finally to a single oval as k increases
Drag Test
- Drag points A and B — the curve should update automatically, maintaining its defining property.
- Move the slider k — observe how the Cassini Oval morphs in real time.
- Verify symmetry about the x-axis.
- When k is small, the Cassini Oval splits into two separate loops.
- As k increases to a critical value (around the half distance between AAA and BBB), the shape becomes a lemniscate of Bernoulli — a figure-eight curve.
- For larger k, the curve merges into one connected oval, resembling an ellipse.
1.
What happens when the foci A and B move farther apart?
2.
How does changing k affect the shape’s symmetry and connectedness?