Ever since Steven Strogatz shared his go-to story about how math is beautiful, I find myself unknowingly rearranging things on pizza night.
Semicircular pizza of radius r
Approximating pizza rectangle with Area
Appreciation Geometry Photography
Math Photo: Flowery Projection
A timely combination of falling leaves and falling rain produced this lovely and unusual shadow.
This reminds me of taking the projections of curves and surfaces in space. Looking at an object’s shadows in various directions can often help you understand the nature of the object itself.
Appreciation Art
Math Art: Bird Rosetta Tiling
This lovely tiling by bird rosettas is the result of a yearly workshop for industrial design students at the Eindhoven University of Technology. You can read more about the work here.
This is another piece from the 2013 Bridges Mathematical Art Gallery.
Appreciation Photography
Math Photo: Non-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.
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.
Appreciation Numbers
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:
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.