Personal Connection
The Fibonacci sequence is a series of numbers that commonly appear in nature, and what we decided to do our project on. As well as having a curious mathematical concept (every number in the sequence is a sum of two of the previous numbers) we wanted to study something that was fairly relevant to biology and nature at the same time as math. The Fibonacci sequence seemed like a neat fascinating direction to go because its pattern is found in plants, animals, geological structures, and entire galaxies.
There are other math concepts that connect to nature, but the Fibonacci sequence stood out to us especially. One of the reasons was that it seems at first to be a fairly simple concept – just adding the two previous numbers to find the next. But then, once you learn about the complexities of it, it becomes much more elaborate and intriguing. Another main reason that we wanted to study the Fibonacci sequence is because of its connection to nature and biology. It is amazing the way that something so simple can apply to so many things in the natural world. Generally you don’t think of math as being particularly prevalent in nature and natural things, but the Fibonacci sequence proves otherwise. This is a mathematical concept that makes it really clear as to exactly how math can be applied in life and nature. To scientists and mathematicians alike, this theory is, in fact, relevant to life.
Math Connection
The Fibonacci Sequence is a series of numbers, where each is the sum of the previous two. The first few numbers are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… The equation for the fibonacci sequence is the recurrence relation
with basis values
These numbers also relate to the golden ratio – 1.618034... This number is found by taking each successive number and dividing it by the previous one. After a while, it will appear that the numbers settle down to this particular number – the golden ratio.
But the fibonacci sequence itself occurs frequently in nature. For example, the number of petals on a flower and the number of leaves on a plant is often a fibonacci number. In addition, this pattern of numbers occurs with the family tree of bees. Male bees only have one parent, and female bees have two. So for a male bee, if you go one generation up, there is one relative. If you go two levels up, 2 parents, 3 levels, 3 parents, 4 levels, 5 parents. And so on through the generations, always growing by fibonacci numbers. You can also see the fibonacci numbers in many plants, such as the sneezewort. If a branch has to grow for one month before it splits into two, the number of branches will always be a fibonacci number. Fibonacci numbers are also found on the number of petals on a flower, the arrangement of seeds in a flower, the arrangement of leaves on a stem, pinecones, many vegetables (like cauliflower), and much more.
So as you can see, there are many applications of the fibonacci sequence in nature. For our poster, we chose to simplify the concept to make it easier to understand and comprehend. So instead of getting into the full extent of it’s applications (spirals, family trees, and such) we simplified it to more of the number of petals, leaves, or tentacles on an object in nature. Our poster introduces the idea of the fibonacci sequence in an easy to understand, but enlightening way.
Here is a scan of some pages in my composition book. Our composition book is where we write important notes and reviews for future reference.
This page is one that I am very proud of. This is for many reasons, but one of the main ones is how organized, clear and professional it is. In my composition book, the cleanliness varies dramatically - depending on my handwriting. This is the review that is most refined. In addition to this, I did really well on this review - almost all of the questions were correct. Not only did I get them right, but I fully understood these concepts, so I am very proud of this page in my composition book.
This page from my composition is from a review of a concept that I enjoyed learning. This wasn't actually a concept that I was especially intrigued by, but I enjoyed learning it for other reasons. One of those is that we didn't really have that much time to learn this concept. While this might seem like it would make it less fun to learn, for me it make it more enjoyable because of the challenge. I like the challenge of learning a topic in a short time. And the best part is that I am comfortable with the concept, and I think that I learned it thoroughly in the time given.
