Non-Linear Pattern Web Quest
October 19, 2008Non-Linear Pattern Web Quest
“Fibonacci” and “Phyllotaxis” and “Prime Numbers”
1. Were there ideas or concepts you were not familiar with? What were they?
I knew that the Fibonacci sequence is often described as a pattern for the population of rabbits:
Start with a single pair of rabbits. Any pair of rabbits of one generation will produce a pair for the next generation, and then another pair of rabbits for the generation after that. But then they will die. How many rabbits will be produced in the n-th generation?
The answer is the famous Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368…
http://www.lifeinitaly.com/heroes-villains/fibonacci.asp
I was unaware that Fibonacci’s actual name was Leonardo Pisano and his sequence can be found in nature’s phyllotaxis, an arrangement of leaves. The sides of pineapples, ridges of pines cones, and centers of sunflowers are examples.
2. What images did you find particularly striking?
I really liked going beyond the example of rabbits and looking at the cut away of a nautilus shell, sunflower and pinecone. I really feel that there is an artistic touch that nature employs on these items. I am mostly impressed that they can be modeled by mathematics.
3. Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?
At work I follow a non-linear pattern of time throughout the day. I have blocks of time designated for instruction, but that also have three minute intervals in between. During the middle of the day the times are slightly different to accommodate lunches.
4. How can you adapt this web quest activity for your classroom?
This web quest could be used to help students see that mathematics is truly a quest to explain what we see in nature. I think that the students would enjoy discovering the different phyllotaxis that appears in nature. If students start to see the sequence displayed in real-life then they should be more motivated to learn it.
“Fractals” and “Nature” and “Patterns”
1. Were there ideas or concepts you were not familiar with? What were they?
I knew that fractals are made of a recursive pattern and I was most familiar with the Sierpinski triangle:
I soon found that the pattern can be found in plants, animals, and lightening. All of these natural phenomenons are part of nature’s beauty.
2. What images did you find particularly striking?
Fractals are found anywhere from photographs of earth, lava, lightening, a tree, the blood vessels of a kidney, an image of the Mandelbrot set, to manmade art of a tiled floor.
3. Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?
I can picture a nonlinear pattern of my paint chipping away from my front right fender of my car and creating what seems to be a fractal pattern of rust. I can look out my window at home and see the leaves falling to the ground on a maple tree, thus showing the non-linear pattern of limbs and how the spread out and away from the trunk.
4. How can you adapt this web quest activity for your classroom?
This idea of linking what we are learning in mathematics class to what we see in nature would be a motivating activity. Students would greatly benefit from being curious about how mathematics can be used to explain something in nature.
