Math Photo: Non-Fibonacci Flooring

Fibonacci Flooring

This is the floor of the butterfly house rotunda at the Detroit Zoo.  When we entered the building, a zookeeper began chatting with us, and when he found out I was a math teacher he got very excited:  “You are going to like this!”  The zookeeper then told me that the pattern was based on the Fibonacci numbers.

I didn’t think much about the substance of his claim, and I generally don’t think much about claims involving the golden ratio that aren’t related to diagonal lengths of pentagons or rhombuses.  But after posting this under the original title Fibonacci Flooring, John Sharp’s comments made me realize that I may be unwittingly perpetuating the mythology of the golden ratio.

Following John’s lead, I checked to see if the above spiral was really a golden spiral by loading it into Desmos and seeing if I could fit a golden spiral to it.

fibonacci flooring plus desmos

Doesn’t look like it!  Thus, I have officially changed the title of this photograph to Non-Fibonacci Flooring, and I apologize if I in any way contributed to the cult of the golden ratio.  As penance, I will link readers to George Hart’s excellent video debunking of the myth of the Nautilus shell as a golden spiral.

Math Quiz — NYT Learning Network

collegeThrough Math for America, I am part of an ongoing collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here

Test Yourself — Math, April 30th, 2014

This question was inspired by the recent article What You Don’t Know About Financial Aid (but Should), and addresses the question “Approximately what percentage of income does an average family pay to send a child to college?”

Solving Pallet Equations

A recent delivery came with an unexpected bonus.

bounty box

A diagram illustrating the geometric relationship between the length and the width of the box!

pallet diagram

Of course, the equation 3w = 2l immediately came to mind.  I also noticed that the pallet could not be a square:  if 3w = l + 2w, then w = l, which would make the box itself a square-based box, which it clearly is not.

I did a quick search and found the standard pallet size to be 48 inches by 40 inches.  So my best guess is that w = 12 and l = 18.  This box has already been discarded, so I guess I’ll have to order another box to find out!

04/21/2014 — Happy Derangement Day!

Today we celebrate a Derangement Day!  Usually I call a day like today a permutation day because the digits of the day and month can be rearranged to form the year, but there’s something extra special about today’s date:

04212014

The numbers of the month and day are a derangement of the year:  that is, they are a permutation of the digits of the year in which no digit remains in its original place!

Derangements pop up in some interesting places, and are connected to many rich mathematical ideas.   The question “How many derangements of n objects are there?” is a fun and classic application of the principle of inclusion-exclusion.  Derangements also figure in to some calculations of e and rook polynomials.

So enjoy Derangement Day!  Today, it’s ok to be totally out of order.

Full Interview with Steven Strogatz Freely Available

strogatz smallMy complete interview with Steven Strogatz in the February 2014 issue of Math Horizons is now freely available.

Math Horizons makes one article from each issue freely available online, and I’m thrilled that for the February 2014 issue they chose my piece.  Professor Strogatz is an acclaimed mathematician, writer, and teacher, and I think this interview captures a small amount of his enthusiasm, insight, and brilliance in all these fields.

The full interview is available as a PDF here.  You can also find our conversation about math education in the Aftermath section of the magazine (posted online here), as well as some bonus material from our conversation here.

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