The Fibonacci Sequence was introduced by Leonardo Pisano aka Fibonacci, who was an Italian mathematician during the Middle Ages. Fibonacci introduced the sequence as a solution to the Rabbit problem.
Suppose you had two rabbits, one male and one female. Every month,
the female rabbit would reproduce another pair of rabbits, a male and a
female. How many rabbits would you have after a certain amount of time?
The sequence starts out with 0 and 1 as the first two terms, and every
term after that is the sum of the preceding numbers. In my presentation,
I will use eigenvalues and eigenvectors to come up with a formula that
will give any term of the Fibonacci sequence. The material will be easier
to understand if you have taken a Linear Algebra course. However, I have
broken down the steps, so it is easy to follow along. Thank you.
This was a great presentation. I have always like Fibonacci numbers and I did a presentation on how they are used in music about one year ago. You explained each step easily so the reader can follow. I like that you included how to find eigenvalues and eigenvectors because that was always something I had to look up to figure out the answer of the larger question. You even explain how to find the determinant and the inverse. It is the small formulas I always forget. The example is well done and easy to follow. Great presentation.
I thought this was a really great presentation. I thought the math flowed very nicely, and I liked how you organized it to conclude by demonstrating that the Fibonacci formula simply boils down to the Golden Ration when you take the limit. Fibonacci numbers are really cool, and you did a great job explaining what’s behind it.
Very nice job with this presentation! You had a logical flow to the mathematics and each step seemed intuitive to follow. I like that you explained a lot of the steps you took in solving and simplifying each of the expressions, because it makes it that much easier for the reader to just trust your work and focus on the concepts since you’ve explained what you’ve done. I remember doing a project a long time ago on the Golden Ratio, so it was cool to revisit it briefly after so many years. Great job!
Every time you present I’m insanely impressed by your knowledge of the Fibonacci Sequence. I mean last time you were able to make Pythagorean triples out of them and now we have a formula to find them, like WHAAAAAT?!?! Mind = Blown. As most of the class knows, I’m horrible at linear algebra don’t know an Eigenvector from a smoke detector but I could actually follow this presentation topic. Five stars.
What a cool presentation! The Fibonacci Numbers come up frequently in many different math or computer science classes, but when I read your abstract saying that you would be using eigenvectors, eigenvalues, and other properties from Linear Algebra to find the Fibonacci sequence, I was very interested to see how that was going to work. This was such a creative way to find Fibonacci Numbers! You thoroughly went through all the steps to help make things easier to follow. Also, I really liked the information about the Rabbit problem in your abstract. I’ve never heard that before! Great job with the formatting too! I bet it was very difficult showing all of those calculations and getting the matrices just right with LaTeX! Excellent job!
I don’t know if you have thought about what you want to do in the future, but I think that you could be a very successful Linear Algebra professor! Honestly, I have taken Linear Algebra so I was able to understand your presentation, but I truly think that even someone who hasn’t taken the course will be able to understand the important concepts. Your meticulous work in describing every step really helped make this a wonderful presentation. Whether it was remembering how to find an eigenvector, or what a trace even is, to learning about the Fibonacci Sequence this presentation had it all. Well done!
I am interested in your topic because rabbit problem is similar to my presentation, “mathematical model of annual plants”. I learned Fibonacci Sequence in MAT230. But I did not know that Linear Algebra especially eigenvalues and eigenvectors can be applied to it. I am impressive that I notice how things I learned at Linear Algebra work. Also, it is probably possible to apply the knowledge of your presentation to my topic. Thank you for interesting things. Good job!
Woah! At first glance, the math in here was a little intimidating (I was never great at this whole eigenvector eigenvalue thing), but you actually did a great job of explaining everything. This is pretty useful stuff. Great job!
Wow! This is neat and shows just how much we can accomplish using our undergraduate-level linear algebra knowledge! Nothing here is ridiculously complicated, but the result it amazing! I love working with these neat recursive sequences, there’s so many neat behaviors to be observed!
Good job!