Wednesday, April 21, 2010

MAM Day 21: Math and nature

There may be a small population of you out there who are still skeptical that math is everywhere. You don't believe me that you use math consciously on a day to day basis or you just don't agree that everyone does do math every day.

Well, today's post in preparation for Earth Day (April 22), I'll be talking about how mathematical patterns surround us in nature! First we have to discuss two things, the Fibonacci sequence and fractalism.

Examples of mathy nature

The Fibonacci Sequence is named for Leonardo Fibonacci, an Italian mathematician who lived in the 12th and 13th centuries. The sequence begins 1, 1, 2, 3, 5, 8, 13, 21… with each consecutive number being the sum of the previous two numbers(8 = 3+5, 13 = 5+8, 21 = 8+13, etc.). The pattern continues on infinitely and occurs in nature in a number of different ways. The most obvious and easy to spot example of this is in nautilus shells.

If you look up fibonacci spirals, you'll find lots of information about the Fibonacci Sequence in the shape of a spiral. Basically, the spiral is built around squares with the Fibonacci numbers for side lengths. What starts as sides of 1, 1, then 2, 3, 5, etc. The spiral is drawn from one corner to the opposite corner, but when you stick to the Fibonacci Sequence, you'll draw a spiral that is almost exactly the same as in physical shells.

The Fibonacci numbers also occur in bone lengths in your hands! I tried measuring my middle finger and got measurements that were almost exactly the same as the picture. Awesome!

This website discusses the Fibonacci pattern in nature, with diagrams and lots of examples - rabbits, shells, plants, seed arrangements, flower petals, pine cones, even hands!

The other big math term that mathematicians use when discussing math and nature is fractalism or the study of fractals. In high school, I took a computer science class where we got to look at fractals. Man-made fractals require a special program that will graph a mathematical equation. Fractals are most simply described as a pattern or shape that reoccurs no matter how much you zoom in. The large picture of a fractal has a certain shape, but if you zoom into a small portion of the fractal, a similar if not idential shape will appear.

If you click on the picture, you can see an animation of a fractal tree

Fractals also occur in nature. Trees are a great example of fractalism. A tree trunk is basically a big branch, with main branches coming off the trunk, and even smaller branches (twigs) on the tree. If you repeat the pattern, it starts to look more and more like a real tree. If you zoom in on a section of the tree, it may look like a mini tree. I would probably guess that broccoli comes from the same principal. Smaller bits of broccoli look (and taste) just like the bigger stalks. It's fractal!

Fractals also occur in lightning, rivers, clouds, plants, mountains, and landscape. This website has great pictures of fractalism in the natural world. Check through the bottom, the cabbage fractal is pretty neat, and the lightning fractal scar is bittersweet, it looks real painful, yet beautiful at the same time.

The most famous of fractals, the Mandelbrot Set

So there we go! Even if you don't use money, don't count your calories, can't tell time with a watch, hate pop music, or even know how to count - you're experiencing math in a natural way :) You've got Fibonacci fingers after all, don't you?


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