Previously, the students will have completed Fibonacci's Rabbit
Problem to determine the number pattern. They will have viewed a Square
One video in which the pattern was used to solve a mystery. It may be assumed
that the students will have developed some recognition of Fibonacci's number
sequence.
Anticipatory Set:
Discuss Fibonacci numbers as they are associated with animals as well
as plants. Point out that one of the most fascinating examples of the sequence
in the animal kingdom is the remarkable spiral that characterizes some
animal growth. Explain how to construct this spiral.
Materials:
Chart paper
Pencil/colored pencils
Pine cones, a chambered nautilus, picture of the galaxy, a fern, etc.
Procedure:
Distribute chart paper, pencils
Construction of an equiangular spiral.
1.Begin with a 1-unit square.
2. Attach another 1-unit square to it.
3. Attach a 2-unit square where it fits.
4. Attach a 3-unit square where it fits.
5. In like fashion (continuing in the same counter-clockwise direction),
attach squares of 5, 8, 13, 21, and 34 units.
6. Quarter-circle arcs can be drawn connecting opposite corners of
the squares (using the sides as the radii of the arcs) in such a way that
the arcs connect sequentially.
7. Optional: each unit could be colored a different color to distinguish
it from the other units.
Assessment:
1. Students should be able to construct an equiangular spiral.
2. Students should be able to recognize the Fibonacci sequence in an
equiangular spiral.