The Case of the Diminishing Square

A small square EFGH is constructed within a larger (unit) square, OABC, as shown.

The point W gives the position of the defining point D and the AREA of the smaller square.

Can you find an algebraic model which best describes this relationship?

Drag the point D to explore this problem.

Double-click anywhere on the worksheet to open a full version of the software, and try some functions to try and match the motion of W.

Steve Arnold, 21/09/2006, Created with GeoGebra

This problem may also be modelled using CabriJr on the TI-83/84 series calculator. Click on the graphic below to download the file and try it yourself!

Try having students work in pairs: one generating data points using the CabriJr model and the partner entering these into lists to plot and then to help build their algebraic model!

Just wait until you try this with TI-nspire CAS!

And you may want to have a look at Geometry Expression.