# 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.

## 4 Comments

## John Sharp · May 4, 2014 at 10:09 am

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 · May 4, 2014 at 12:11 pm

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 · May 4, 2014 at 12:34 pm

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 · May 4, 2014 at 3:00 pm

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