Spiraling Squares Pretty. And interesting, we think. Do you see a lot of spirals in this image? 1. Carefully add to this picture as many spiraling arcs that you can discern. I made this shape by starting in the middle. I placed 12 squares in a circle evenly spaced. 2. What would be the central angle that surrounds each square? Let's just say that those first squares had side 1 cm. The next round of squares had sides that were the same size as the diagonal of the first square. 3. Using the Pythagorean theorem, what size are the sides of those next squares in the second round? 4. Continue to calculate the sides of the squares in this pattern. I drew some golden lines along the sides of some of the squares. The golden lines seem to make a lovely arc. 5. What can you figure out about those arcs? Wikipedia lists many sorts of spirals and their general forms: Archimedean spiral � = � + � ∗ � Euler spiral Curvature of curve = reciprocal of radius ! Fermat's spiral � = � ! ! Hyperbolic spiral � = ! Logarithmic spiral � = � ∗ � !∗! And more ... 6. Make a guess about which sort of spiral the spiraling squares design is most like and explain your thoughts. If you would like to create this design on your own, we've given you a starting sheet of polar graph paper already containing 12 little squares arranged in a circle and some instructions. To complete this design you will need a pencil, compass and a straight edge. Sources: https://en.wikipedia.org/wiki/Spiral Mathematical Quilts by Diana Venters and Elaine Krajenke Ellison (1999) Key Curriculum Press Brought to you by YummyMath.com .