Exploring a Perimeter-Area Relationship

Great news statistics fans: A version 3 beta of the Common Online Data Analysis Platform (CODAP) is now available. To quote the CODAP website, “[The new CODAP] is a powerhouse under the hood, handling much larger datasets, drawing graphs and maps faster, animating more smoothly, and responding instantly.”

CODAP is the successor to Fathom, both developed by my former KCP Technologies colleague, Bill Finzer.

The experiment that follows began as a Fathom activity and is now available as a CODAP document. I liked the experiment so much that I felt compelled to build a Web Sketchpad version as well.

The websketch below displays rectangle ABCD. Pressing Make New Rectangles randomly and repeatedly animates vertices A and C. For each new rectangle, the point (perimeter, area) is plotted. Before you press the button, make a prediction: What do you think the scatterplot will look like as you let the experiment run for a while?

The result may surprise you! Can you explain what you’re noticing?