During the learning engagements, the students are expected to:

1. Identify patterns in nature and regularities of the universe

2. Determine the importance of patterns in life.

Mathematics is all around us. As we discover more and more about our environment and our surroundings, we see that nature can be described mathematically. The beauty of a flower, the majesty of a tree and mountain, even the rocks upon which we walk can exhibit nature’s sense of symmetry and patterns. In group of four, describe orally the picture below according to how you’re perceived it.

Here the picture of a pineapple, rocks, and different flowers.

Have you ever stopped to look around and notice all the amazing shapes and patterns around us? Mathematics forms the building blocks of the natural world and can be seen in stunning ways. Here are a few examples of math in nature, but there are many other examples as well.

Fibonacci Sequence

The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. If the Fibonacci sequence is denoted F (n), where n is the first term in the sequence, the following equation obtains for n = 0, where the first two terms are defined as 0 and 1 by convention:

F (0) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ...

In some texts, it is customary to use n = 1. In that case, the first two terms are defined as 1 and 1 by default, and therefore:

F (1) = 1, 1, 2, 3, 5, 8, 13, 21, 34 ...

The Fibonacci sequence is named for Leonardo Pisano (also known as Leonardo Pisano or Fibonacci), an Italian mathematician who lived from 1170 - 1250. Fibonacci used the arithmetic series to illustrate a problem based on a pair of breeding rabbits:

"How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?" The result can be expressed numerically as: 1, 1, 2, 3, 5, 8, 13, 21, 34 ...

Fibonacci numbers are of interest to biologists and physicists because they are frequently observed in various natural objects and phenomena. The branching patterns in trees and leaves, for example, and the distribution of seeds in a raspberry are based on Fibonacci numbers.

A Sanskrit grammarian, Pingala, is credited with the first mention of the sequence of numbers, sometime between the fifth century B.C. and the second or third century A.D. Since Fibonacci introduced the series to Western civilization, it has had a high profile from time to time. In The Da Vinci Code, for example, the Fibonacci sequence is part of an important clue. Another application, the Fibonacci poem, is a verse in which the progression of syllable numbers per line follows Fibonacci's pattern.

The Fibonacci sequence is related to the golden ratio, a proportion (roughly 1:1.6) that occurs frequently throughout the natural world and is applied across many areas of human endeavor. Both the Fibonacci sequence and the golden ratio are used to guide design for architecture, websites and user interfaces, among other things.

Ever wonder why there are so many hexagons in nature?

If you have ever wandered around in nature you may have noticed how many geometric shapes there are in the world that have absolutely no design from humans. Take snail shell spirals or starfishes' bodies or the symmetry of a flower's petals; all those nature-y things are out there on their own existing in near mathematical perfection! Hexagons, in particular, are often seen in nature: bee hives are the common example, but definitely not the only. Basalt columns and insect eyes also form hexagonal patterns. But what makes hexagons so special?

Well, as it turns out, it really is all about math. A hexagon is the shape that best fills a plane with equal size units and leaves no wasted space. Hexagonal packing also minimizes the perimeter for a given area because of its 120-degree angles. With this structure, the pull of surface tension in each direction is most mechanically stable, which is why even though bees make their honey combs with circular units, the end result when the wax hardens into place is hexagonal. Want to learn more about the crazy math of nature? Watch the video!

Concentric Circles in Nature:

Another common shape in nature is a set of concentric circles. Concentric means the circles all share the same center, but have different radii. This means the circles are all different sizes, one inside the other.

A common example is in the ripples of a pond when something hits the surface of the water. But we also see concentric circles in the layers of an onion and the rings of trees that form as it grows and ages.

If you live near woods, you might go looking for a fallen tree to count the rings, or look for an orb spider web, which is built with nearly perfect concentric circles.

Math in Outer Space:

Moving away from planet earth, we can also see many of these same mathematical features in outer space.

For instance, the shape of our galaxy is a Fibonacci spiral. The planets orbit the sun on paths that are concentric. We also see concentric circles in the rings of Saturn.

But we also see a unique symmetry in outer space that is unique (as far as scientists can tell) and that is the symmetry between the earth, moon and sun that makes a solar eclipse possible.

Every two years, the moon passes between the sun and the earth in such a way that it appears to completely cover the sun. But how is this possible when the moon is so much smaller than the sun?

Because of math.

You see, the moon is approximately 400 times smaller than the sun, but it is also approximately 400 times further away.

This symmetry allows for a total solar eclipse that doesn’t seem to happen on any other planet.

Isn’t nature amazing??