Billiard Table Illustrating an Ellipse Inscribed in a Rectangle

① This example uses a billiard table model to vividly demonstrate the geometric property of an ellipse inscribed in a rectangle, where the ellipse is tangent to all four sides of the rectangle and its foci lie inside. ② Core mathematical concepts include the standard definition of an ellipse (constant sum of distances to two foci), the relationship between foci and major/minor axes, and the connection of the ellipse with rectangles and triangles. ③ Construction highlights: using GeoGebra commands such as Mirror, Polygon, Intersect, Point, Segment, Focus, Circle, and Ellipse, the rectangle poly1, the ellipse, and its foci F and F' are constructed, with auxiliary points, segments, and circles revealing tangency points and geometric relations. ④ Suitable for high school or early college analytic geometry lessons, math lab activities, and dynamic geometry explorations to help students understand the conditions for an ellipse inscribed in a rectangle and the properties of its foci.