Saturday, November 8, 2014

Fibonacci Activities for Kids

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.

Beginning in the bottom left corner a 1x1 square was drawn. Adjacent to the 1x1, another 1x1 was drawn. On top of the two 1x1 squares a 2x2 square was created. The 3x3 was drawn adjacent, followed by the 5x5, and so on until the paper was filled with squares.

Next spirals were created using the same basic technique, but starting in the center and drawing the additional squares on all sides.

Fibonacci Stripes
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.)

1. The first pattern contains stripes in a repeating pattern the following units high: 1,1,2,3,5. Six different colors were used to fill in the five different strips which resulted in a pattern that appears random, yet very pleasing.

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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