Recently we reviewed the Pythagorean theorem with some of my students. We covered the basics of solving for an unknown side and the proof using similar triangles. This year we decided to require all of our students to have sketchbooks. One of our projects for this unit was to produce a Pythagorean Spiral. Our Pythagorean spiral started with a 45-45-90 triangle, with 1-inch legs. The hypotenuse of this triangle then forms a leg of another right triangle whose other leg is 1-inch long. The hypotenuse of the second triangle forms the leg of a third triangle whose other leg in 1-inch long, and so on. I used a standard 3x5 notecard as a straightedge and to form right angles. I marked the card 1-inch on either side of the corner I used for my right angle. Here is the spiral I made as an example for my students. I asked my youngest daughter to color it.