## Organized Chaos – Inquiry Blog

#### November 7, 2010 – Fractals… They Do Exist

Fractals can be found in all of nature’s complexity. The seemingly random branches of a tree or veins of a leaf can become simple when thought of as a fractal. Fractals can be seen in nature but aren’t found in manmade creations, because of our constant use of simple mathematics, and straight lines.

#### November 4, 2010 – Fractals

A fractal is a shape that can be divided into parts, that are similar to the whole part. Those parts are then divided again and again for an infinite number of times.

From watching part of Nova’s “Hunting the Hidden Dimension“, I found it very interesting that fractals are made of endless repetition, and that gives rise to one of the defining characteristics of a fractal, what mathematicians call self-similarity. I also thought that it is interesting that you can see and find self-similarity, or fractals, in everything from a stalk of broccoli, to the surface of the moon, to the arteries that transport blood through our bodies.

#### October 29, 2010 – The Golden Ratio

The Golden Ratio

1. What is the Golden Ratio and how does it relate to the Fibonacci sequence?

2. One interesting fact about the Golden Ratio.

3. The link to the page where you found that fact.

4. Answer the question: Do you think the Golden Ratio “naturally” occurs in nature and art/architecture or do people “force” it to be there?

#### October 28, 2010 – Facts About Fibonacci

*0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, …*

*The equation, or formula, for how this series of numbers is generated is: a(n)=a(n-2)+a(n-1) *

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The Fibonacci Series is a sequence of numbers first created by Leonardo Fibonacci in 1202. The sequence of numbers (shown above) is a recursive sequence in which, each term is related to one or more preceding term. In this case, the first two numbers in the series are one and one. To figure out each number in the sequence, you simply add the two numbers that came before it. In other words, each number of the series is the sum of the two numbers preceding it.

#### October 27, 2010

“I’m not smart, but I like to observe. Millions saw the apple fall, but Newton was the one who asked why.” – Baruch

I believe most people do not pay attention to everything around them, as we try not to overwhelm our mind and ourselves with everything that is going on around us. We observe many things everyday, however, when something catches your eye, like the sudden movement of a falling apple, some will just observe while others will inquire. Some will give it a quick thought and then move on to what they believe are more important thoughts, but others will look down at the apple, up from where it fell, and ask why. We observe many things everyday, but we really only *ask questions* about things that we think are important to us. Most of the things that we think are important to us, usually affect us in someway, and if they don’t affect us, we don’t think they really warrant our attention. However, nature is all around us and is always affecting us in some way, whether it be our mood based on the weather, or the type of air around us that we breathe. Everyday we observe many things, but we only ask questions and inquire when we think that something is important. Newton believed that the reason and apple fell was important, while others just see an apple fall and then continue on their way.

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