Designing an Elliptical Pool Table
Students learn about the mathematical characteristics and reflective property of ellipses by building their own elliptical-shaped pool tables. After a slide presentation introduction to ellipses, student “engineering teams” follow the steps of the engineering design process to develop prototypes, which they research, plan, sketch, build, test, refine, and then demonstrate, compare and share with the class. Using these tables as models to explore the geometric shape of ellipses, they experience how particles rebound off the curved ellipse sides and what happens if particles travel through the foci. They learn that if a particle travels through one focal point, then it will travel through the second focal point regardless of what direction the particle travels.
A student-designed elliptical pool table.Copyright 2016 Fatma Tamer, RET Program, Cullen College of Engineering, University of Houston
Civil engineers, architects and acoustic engineers use ellipse’s reflection property to create whispering galleries, which are structures that enable a whispering person at one location in the space to be heard clearly by someone in another area of the space, but not by anyone else in the room. Ellipses also explain planetary motion; as stated by Kepler’s first law of planetary motion, the path of each planet is an ellipse with the sun at the focus.
After this activity, students should be able to:
- Use the equation of an ellipse to calculate the various properties of an ellipse.
- Design an elliptical pool table that ensures players can always make the shot.