The Fibonacci numbers play a significant role in nature and in art and architecture. We will first use the rectangle to lead us to some interesting applications in these areas.

We will construct a set of rectangles using the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, and 34 which will lead us to a design found in nature. You will need a ruler, protractor, and compass.

Start by drawing two, unit squares (0.5 cm is suggested) side by side. Next construct a 2-unit by 2-unit square on top of the two, unit squares. Next draw a square along the edge which borders both a unit square and the size 2 square (that is, a 3-unit square). The next square will border the 2-unit and the 3-unit squares, and each successive square will have an edge which is the sum of the two squares immediately preceding it. Continue until you have drawn a final square bordering the 13-unit and 21 unit squares.

Your construction will look like this:

Now, with your compass, starting in the unit squares, construct in each square an arc of a circle with a radius the size of the edge of each respective square (Your arcs will be quarter circles.).

This spiral construction closely approximates the spiral of a snail, nautilus, and other sea shells.

We will next consider the use by architects and artists throughout history of the "Golden Ratio" and other geometric shapes based upon these ratios.

Graphics courtesy of Dr. Ron Knott, FIMA, C.Math, MBcs,C.Eng, Dept. of Mathematical and Computing Sciences, Univerity of Surrey, UK