I am not the only geek on this board, so I hope someone else finds this cool. But even if you are NOT a geek, I think you will appreciate how cool it is that a sequence of numbers as seemingly contrived as the Fibonacci Sequence is ALL OVER the natural world.
http://www.youtube.com/watch?v=ahXIMUkSXX0A nugget for part 2 . . . as you generate more and more terms of the Fibonacci Sequence, they just get larger and larger and go toward infinity. But the ratio of consecutive Fibonacci numbers doesn't go to infinity, or zero, and it's not random . . it approaches this one crazy irrational number we call Phi. Now it may seem silly to expect any kind of relevance to a number that again seems so clearly contrived, but instead, we see that Phi is an angle that appears all over the place in the natural world, as our friend Vi demonstrates in part 2.
http://www.youtube.com/watch?v=lOIP_Z_-0HsIf I may also make a recommendation to the parents and grandparents on the board, Vi Hart has a whole bunch of videos like this on YouTube . . . and IMO if this doesn't get them interested in mathematics, then nothing will. Nothing helps a math student more than to show them the relevance and beauty math has in the real world.
