I’ve always been a doodler…and I’ve always had a fascination with the Fibonacci sequence and the golden ratio, phi. One of my favorite doodles is the logarithmic spiral. I have spent many a meeting creating a golden rectangle and continuing it out until it filled the page. In fact, I loved the spiral so much that I painted it on my office wall in bright colors when I was the principal at an elementary school. Unfortunately, the principal who took my place did not have the same aesthetic sense that I had and quickly painted over my masterpiece!
Then I saw some Vi Hart videos and have discovered many more interesting doodles that I can create based on phi. My logarithmic spiral now seems so, for lack of a better word, dated…
Here are some links to three videos on Phi, Parts 1, 2, and 3:
Another favorite video of Vi’s is Infinity Elephants, a doodle on elephants and camels and circles that has a hidden math lesson on infinite sequences and Sierpinski’s Triangle.
I found these videos on a site that highlights educational videos: Knowmia. I went to Mathematics and Algebra. There are MANY videos and subject areas (such as Geometry, Calculus…) under the Mathematics heading that I haven’t checked out yet. Most of them are by Salman Kahn and some are by Brightstone. Vi Hart is more to my liking on first look.
Back to phi…Vi pronounces “phi” as “fie”. My favorite book on phi is Mario Livio’s The Story of Phi: The World’s Most Astonishing Number. In that book, “phi” is pronounce “fee”…so fee, fie, foe, or fum…whatever it’s called, it is an amazing irrational number. But my next pressing question is: How do you pronounce Vi? Is it “vee” or “vie”…stay tuned!
By the way, as Vi Hart mentioned briefly, you can start with ANY two integers (positive or negative) as the first two numbers and the sequence will always grow so that the ratio of the “n+1″th term divided by the “n”th term will approach phi, which is approximately 1.618.
Happy doodling!…and you might just discover some math along the way!