What we’re reading: Fibonnaci and fractals

fractalsFractals… Quite honestly, I didn’t have any idea what they were until several books into this unit. I mean, here’s a definition:

A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. It is also known as expanding symmetry or evolving symmetry. If the replication is exactly the same at every scale, it is called a self-similar pattern. 
Yeah… there’s a reason I excelled in writing and literature and not so much in math and science.
Once I decided I didn’t want the kiddos to repeat their mother’s deficiency in the fractals arena, we plunged into a mini-unit. And guess what I discovered? Fractals are darned interesting. Seriously.
Here’s a fractal:
swedensymmetry9
And another:
swedenfractal1
And another:
swedenfractal2

Notice anything? The design repeats at different sizes. That’s a fractal. Cool, huh? Flower petals, pinecones, nautilus shells… all are fractals. Fractals in nature are everywhere.

Onto the guy who discovered this quirk: Leonardo Fibonnaci of Pisa, Italy, who lived in the 1200s. He was one of the first people to bring the Hindu-Arabic numeral system (the decimal system we use today) to Europe.

Perhaps more importantly, he solved this riddle:

Two rabbits, one male and one female, are fully grown at one month. At two months, they reproduce two baby rabbits, who then take one month to mature and one more month to mate and reproduce. Meanwhile, the original rabbits are one their second set of babies. Every month thereafter, the rabbits continue to reproduce. At the end of 12 months, how many pairs of rabbits will exist?

The answer is called the Fibonnaci Sequence, or Golden Rule. It looks like this: fibonnaci3

Month 1: 1 pair

Month 2: 1 pair

Month 3: 2 pairs

Month 4: 3 pairs

Month 5: 5 pairs

Month 6: 8 pairs

fibonnaci2Month 7: 13 pairs

And so on.

The sequence is that every month is added to the previous month: 1, 1, 2, 3, 5, 8, 13. That’s the Fibonnaci Sequence.

Since this is a reading and writing blog and not a math blog, I’ll leave the math portion at that and direct you to some books on the subject.

fibonnaci1First is a quick biography of Fibonnaci, known as “Blockhead.” “Blockhead: The Life of Fibonnaci,” by Joseph D’Agnese, is an engaging read that is very relatable to kids and does a good (if somewhat fictionalized) job of introducing students to his life and achievements.

Then are two that focus on the Fibonnaci Sequence in nature. “Growing Patterns: Fibonnaci Numbers in Nature” and “Mysterious Patterns: Finding Fractals in Nature,” both by Sarah Campbell, are great for reinforcing the concept that nature adheres to a pattern.

Happy fractal-ing!

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