I was invovled for several years with the Berkeley Math Circle, which was great fun. The founders of that group, Zvezda Stankova and Tom Rike, wrote a couple of books about how to go about organizing a math circle, containing ABOVE ALL lots and lots of interesting material to discuss. I have the first volume: https://www.amazon.com/Decade-Berkeley-Math-Circle-Mathematical/dp/082184683.... If you go to Amazon and search on math circles many books come up, and going by customer reviews there are a lot of good ones among 'em. —Dan -----Original Message-----
From: Cris Moore <moore@santafe.edu> Sent: Dec 15, 2017 12:50 PM To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] rabbits, syllables, and Fibonacci numbers
This week I did an activity at my daughters school (7th grade) talking about Fibonacci numbers, including
. rabbit genealogies . sequences of short and long syllables (1 and 2 units long) in Sanskrit poetry . domino tilings of 2xn rectangles
I challenged them to find a bijection between the rabbits after n generations and patterns n syllables long.
We then looked at ratios between successive Fibonacci numbers, and noted that they seem to be settling down. I showed them phi=(sqrt(5)+1)/2, derived the quadratic equation that it should satisfy, and showed by computing phi+1 and phi^2 that it does.
I then used phi = 1+1/phi iteratively to show them the continued fraction expansion, and showed (by example) that cutting it off at various places gives the ratios between adjacent Fibonacci numbers.
We ended with slanted diagonals in Pascal’s triangle, sunflowers, artichokes, Lucas numbers (and the fact that their asymptotic growth rate is the same), “tribonacci” numbers, and so on.
I know there are a zillion things out there on the Web of this kind — Vi Hart’s video, Math Circles http://www.mathcircles.org/wp-content/uploads/2017/10/FibAndOtherSpecNumbers... and so on. My question: is there a good, wiki-editable, collection of math activities like this, suitable for middle school and high school, with nice visuals and suggestions for teachers about what questions they should challenge students with? I want an emphasis on “why is this pattern here? is it just a coincidence, or is there a good explanation?"
(I apologize in advance, since I know I’ve asked this list similar questions before…)
thanks Cris
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