## 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.

1. John Sharp says:

I am interested in why you think this is Golden Section spiral when it plainly is not.

I wrote an article about Golden Section spirals for Nexus Network Journal.
In particular I wanted to show that the myth of the Nautilus shell being a Golden Section spiral was wrong.

Part IV of my article is at http://www.emis.de/journals/NNJ/Sharp_v4n1-pt04.html

you seem to have fallen into the group of people who say as I quoted “because a spiral is a logarithmic spiral it is a Golden Section one.”

I am surprised at what you have said since you are very good at mathematics and pointing out errors.

I perspectively altered your image as best I could and measured successive radii along a line. I find it increases by a factor of 2.2-2.5 per complete resolution

• MrHonner says:

The zookeeper told me that the design was based on the Fibonacci numbers. I didn’t think much about his claim, nor did I bother to verify it, because, to be honest, I really don’t care about any claims involving the golden ratio. This is a nice pattern, and “Fibonacci Flooring” is a fun, if inaccurate, title.

George Hart has a great video debunking the golden ratio / nautilus myth: https://www.youtube.com/watch?v=_gxC8OjoQkQ. For the record, I essentially ban this topic from student projects because of the extremely high nonsense-quotient.

• John Sharp says:

Beware of “fun” when you are using such names.
There are so many ignorant people out there that they will seize on another case and quote it.
I know you mean well, but it makes a problem for people like us trying to educate them.

Keep up the otherwise good work

• MrHonner says:

Fair enough. I have updated the post. Thanks for your thoughtful remarks, John!