Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Part 3 Patterns in Nature
Mathematicians have been studying patterns in nature for centuries. In 1202 an Italian named Fibonacci investigated the breeding potential of rabbits. If the gestation period for the rabbits is one month, every rabbit survives, and one female always has a pair of bunnies (one female and one male), the resulting total numbers of rabbits for each month are as follows:
Further, he found that flower petals and shell spirals, and, spirals on fir cones, grew in a pattern described by the series 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. These are known as the Fibonacci numbers. The Web site below has some fascinating examples of Fibonacci numbers in nature:
Fibonacci numbers abound in limericks as well. For examples see http://pass.maths.org/issue10/features/syncopate/
Have you noticed that each leaflet of a fern looks strikingly similar to the whole frond, or that broccoli and cauliflower are made of up little florets that by themselves look like miniature vegetables. Or you might have noticed how a leafless branch of a tree looks like a small version of a whole tree.
Mathematicians have recognized that small parts of many natural objects look very much like the whole object. They call this phenomenon self-similarity. Mathematicians are able to recreate many of the self-similar patterns of nature by developing a rule that can be repeated over and over (i.e. an example of a mathematical rule being repeated "go distance turn 90, cut in half, turn 90, cut in half, turn 90, cut in half, turn 90" on and on and on....) Self-similar tilings are classics. This site demonstrates many of these principles.
Fractals are self-similar patterns. You may have seen images like the one below the MANDELBROT SET which has been generated by applying a mathematical rule over and over.
>> Go on to Part 4 What Does It Matter if Mathematics Can Describe the Patterns of Nature?