EQUIANGULAR SPIRAL--

NATURALLY!

The Fibonacci numbers turn up in the strangest places! If you do this activity, you can see not only these interesting numbers, but also an interesting figure called an "equiangular (or logarithmic) spiral". First, you will need a sheet of graph paper with small squares:

Select one small square and color it in:

Now color in the square directly above the first one:

Moving in a clockwise direction, color in a 2 by 2 square:

Continuing in a clockwise direction, fill in a 3 by 3 square:

What size will the next square be? Where will it go?

(If you moved clockwise and made a 5 by 5 square, you were right!)

Continue this pattern as far as your paper will allow, attaching more graph paper if you wish.

Are the Fibonacci numbers here? Where do you see them?

Now for the spiral part:

Using your paper with the squares and a compass, draw an arc connecting opposite corners of the square. (The radius for each arc will be the length of the side of that square.) Sort of like this:

Try it with your paper. That is an "equiangular spiral"!

This spiral is referred to by some as the "Fibonacci spiral". Do you see why?

If that seemed easy, then try one of these CHALLENGE activities:

• EQUIANGULAR SPIRALS are not just interesting geometric constructions. They also can be found in many places in nature, like the spiral in the shell of the "chambered nautilus":



What other natural examples of this spiral shape can be found? Don't give up too easily--there are examples all around you! But if you need some help, you might try looking at Fibonacci in Nature. (See, we told you the Fibonacci numbers were here!)

• OR...Look for another kind of spiral called the ArchimedianSpiral. Do they look alike? How are they the same? How are they different?

Back to Fun with Fibonacci.