Stage: 2 Challenge Level: 
Describe what is happening in these pictures.
Do the pictures appear to be coming towards you, or going
away?
How many squares are there in each picture?
If the side of the smallest square is 1 unit, how many units
is the side of the next square?
And the next?
How many units is the side of the largest square?
What is the area of the smallest square?
What is the area of the next square? And the
next?
The smallest square is one unit of area. How many more units are in the second square?
What is the sequence of the areas of the squares?
The smallest square is one unit of area. How many more units are in the second square?
How many more units of area are in the third square
than in the second square?
Look at the top picture. Start from the largest square and think of it as shrinking as it turns.
What is the rule for building the squares?
Look at the top picture. Start from the largest square and think of it as shrinking as it turns.
Through what angle has it turned when it has
changed to the smallest square?
Is it the same in both pictures?
What is the angle of rotation as one square
changes to the next?
Is it the same in both pictures?
Make a similar picture. You could change
the rules if you would like to.
This image, along with the questions and notes, features on the Exploring Squares CD-ROM, developed by members of the NRICH Team and published by Virtual Image Publishing Ltd. For more details, please see our publications page .
Investigations. Working systematically. Rectangles. Area. Circles. Visualising. Angles. Perimeters. Squares. Interactivities.
Published January 2007.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk
