LESSON PLAN V

Purpose

Increase students' experience with and understanding of the occurrence of the Fibonacci sequence in nature.


Objectives

Students will be able to find and justify the Fibonacci sequence in natural settings.


Activities
  1. Find real life examples of Fibonacci numbers in nature. Find one each for a) flower petals, b) leaves and c) spirals.
  2. A plant called the sneezewort (Achillea ptarmica) grows in such a way that when it puts out a new shoot, that shoot has to grow two months before it is strong enough to support branching in two. If it branches every month after that at each new growing point, sketch 6 months of growth of the sneezewort. Begin with a single shoot. Find a picture of a real sneezewort.
  3. Below is a sketch of the apex of a growing plant. Mark the starting point for the first primordia at 0°. Make a table of angles at which subsequent primordia will emerge. Remember to reduce modulo 360°. Using the table values, mark off the points at which subsequent primordia will grow.

    NN*360°/ØFibonacci location
    00°-345°-15°
    1222.5°--
    285.0°.-
    3307.5°.-
    4---
    5---
    6---
    7---
    8340°.325°-355°
    9---
    10---
    11---
    12---
    13-.-
    14---
    15---
    16320°-305°-335°

    Note that the angles that are Fibonacci multiples are closest to the starting point, 0. Sketch in primordia of angular width 30° to show how spirals emerge. The first few primordia lie on the boundary of the apex. Primordia 8 displaces the one at 0 since they overlap, 9 displaces 1. Each displaces another until 16 displaces 8, making the spiral 3 deep. This arrangement will make 8 spirals. What size primordia will make 13 spirals?

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