Parabola bounces

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Parabola bounces
On display at MathsWorldUK
Type Hands-on, puzzle
Topics Conics, plane curves

Parabola bounces is an exhibit at MathsWorldUK.


Two balls are released to fall in the parabola

The exhibit consists of a metal band bent in the shape of a parabola (with a big aperture) placed between two large sheets of transparent acrylic plastic walls. All this is supported by a wooden structure, with the axis of the parabola vertical from the floor. The height of the exhibit is around 1m. Users can drop a ball to fall between the two transparent walls. The ball then bounces against the metal parabolic band and hits a bell which is located in the focus of the parabola. The ball eventually reaches the bottom of the parabola and exits the wall through a hole.

The height of the bell can be adjusted, and some tubes help to drop the balls perfectly vertical.

Activities and user interaction

Visitors can try to drop the ball from different distances to the axis, or from different heights. There are practical problems. Since the action is vertical, gravity interferes producing more parabolas after the bouncing. However, this effect is small to be detected in most of the cases with the dimensions of this exhibit. In fact, this sparks discussion amongst adult visitors and even engineers and professors enjoy arguing about the relative effect of different factors.

The exhibit is perceived as a challenge, and it makes a loud noise when the bell is hit, which makes the experience much more attractive.

Mathematical background

Reflective properties of parabolas are classic. A panel with a description of the parabola and some of its properties is next to the exhibit.

History and museology

This exhibit of MathsWoldUK is a prototype for their traveling exhibition, but it has proven to be an attractor of the interest of all visitors.