Doodling in Math: Spirals, Fibonacci, and Being a Plant (Three Part Series)

I chose this video because it seemed pretty relevant with our recent introduction to Strong Induction and Fibonacci Numbers. It serves as an introduction to Fibonacci Numbers and the Fibonacci Spiral and their appearances in various organisms, with particular focus on plants whose names start with “pine-“. It was interesting seeing how the number of spirals in certain plants exist in more than one direction (and in Fibonacci numbers no less). So are there any plants that violate the sanctity of this pattern?

Phi is the most irrational number? An interesting correlation between ratios of the larger over the smaller of two consecutive Fibonacci numbers exists. But, wait a contradiction arises?

Something wrong happened at the start and now we have a new type of sequence. It’s not quite a Fibonacci Sequence but very close; introducing Lucas Numbers. Also, here are instances where plants break apart from Fibonacci sequences. Okay, that answered my question.

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Are these videos relevant to the teaching I will be doing? While it is interesting to learn on our own, there is an issue where the students will not likely come across these sequences within the curriculum unless I choose to assign them some sort of project. That being said, my attention was kept, and I was borderline captivated with the presentation. There was visual evidence to prove the concepts scientifically and and additional artistic diagrams to better represent these observations. These videos are also demonstrations into how math exists outside of the textbooks, notebooks, and chalkboards as well as how we can discover and apply new knowledge. This is most certainly teaching math and I’d like to believe I have a greater understanding of Fibonacci numbers through these demonstrations.

Is there a connection between these videos and Paul Lockhart’s Lament? I could imagine so. If Lockhart wishes to expose the soul of math to students, I would go so far as to say that Vi Hart does so with these videos. She most certainly presents math in an artistic method that is seemingly fun and engaging and it’s pretty clear she’s enjoying making these videos. The only issue I might have is how would students react to seeing such a demonstration in their classrooms? Feedback is a pretty important assessment tool and I know firsthand that a comments section on the Internet is not the best place to garner such information.

I agree with what you said about how math exists without using textbooks and having someone to explain it to you. I like the question you asked if there was any plants that violate this pattern because there’s so much different plants in this world so one may never know.