TEACHER NOTES

ISSUES RELATED TO THE PROBLEM

This represents a chance to model some motion problems with parametric equations.

Prerequisites

Standard precalculus topics--trig, conics, parametric equations

Time allotment - time management

Good homework project--Have students go home and play with such a door so they can get a feel for what is happening. Some will be able to figure out the paths of points on the two panels is fundamentally different.

Expectations

Fun! Students should quickly get a physical sense of what is being asked. If they don't have the opportunity to study an actual door, reasonable models can be built with a brief case or even a stiff folder. Half the problem (panel A) is deceptively easy. The other seems to be much harder, but order prevails over chaos without much complexity. The power of math to prove a conjecture is impressive.

Future payoffs

Although no calculus is required, this problem is a good review of trigonometry,
conic sections, and parametric equations .

Extensions

This problem could be easily extended to include calculus topics by considering the velocity and acceleration of the points on the door.