Renaissance Unit Study
Week 6: We played with the Fibonacci sequence to create spirals and stripes.
Leonardo Fibonacci was a Renaissance mathematician who loved to play with numbers. His legendary pattern; 1,1,2,3,5,8,13,21,34,55........ is evident in sunflowers, cabbage, pine cones, and numerous other places within nature. When two adjacent numbers in the sequence are divided together the result is the golden ratio. Designs created with the Fibonacci numbers are appealing to people. In the past we created Fibonacci spirals and explored his rabbit problem. This time we created more spirals and stripes.
The book Growing Patterns: Fibonacci Numbers in Nature contains photographs of objects from nature that contain Fibonacci numbers and spirals. Pineapples and pine cones both contain Fibonacci numbers. This book highlighted photographs with dark and light so that the spirals were visible.
Instead of beginning with a spiral, this design was created. Squares with sides length equal to Fibonacci numbers were created.
Finally we played with the numbers to see how many different stripe patterns could be created. (I plan to use these designs for future knitting projects.)
2. The blue stripes are the following units high; 5,3,2,1,1. The brown are; 1,1,2,3,5. When alternated they produce another seemingly random, yet eye catching pattern.
3. The stripes are the following units high. 1,1,1,1,1,1,2,2,2,3,3,3,5,5,5 (three consecutive Fibonacci's), colored with three colors.
4. The red and green color are each their own Fibonacci sequence, but alternated together.
5. This pattern was the most complicated and it's also my personal favorite. Each color is a 1,2,5,3,1 sequence. The colors alternate such that two stripes from each adjacent color are within each adjacent color.
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