Math at a Rock Shop

I recently went on a Vacation to Bar Harbor in the beautiful state of Maine.  While enjoying bicycling through Acadia National Park and eating more than my fair share of lobster, I found some time to stop in the local rock shop.  Of course math was to be found absolutely everywhere!  I just knew that I couldn’t leave Maine without at least a few souvenirs so I brought the following three “math rocks” back home with me.

The first one that really stood out to me was the following piece of pyrite, also known as fools gold.

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The almost perfect rectangular solid formed by this mineral is due to its crystalline structure. FeS2structure

By Materialscientist – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=10379959

Although other crystals may have a more intricate shape that involves more complicated geometry I was struck by the simplicity of this particular mineral.

Next up I found a fossilized sea urchin.

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I like how the five-fold (72 degree rotation) symmetry of the sea urchin’s anatomy is so clearly shown in this fossil.  Each of the five marks on the side of the urchin are formed by it’s stone canals.  They can be seen in the following diagram of a sea urchin’s anatomy.

Urchin
By Alex Ries – http://abiogenisis.deviantart.com/art/Sea-Urchin-Anatomy-271355683, CC BY-SA 4.0

And last, but certainly not least, is my favorite find of the day.  A fossilized nautilus shell showing off the Fibonacci sequence and golden ratio in all of its glory.

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The colors in this particular shell are just beautiful and the spiral stands out exceptionally well.  This spiral shape can be formed by joining the corners of squares with arcs that from a quarter of a circle.  You just need to make sure that the sides of the squares have lengths corresponding to the Fibonacci sequence:

1,1,2,3,5,8,13,21,34,55,89,144,…

Starting with two 1’s for the first two terms in the sequence new ones are formed by adding together the two previous terms.  For example, the seventh term in the sequence, 13, is formed by adding together the two terms that come before it, 5 and 8.  Below is the spiral with its squares illustrated to the tenth term in the sequence.  spiral

So the next time you’re on a vacation in a new place make sure to keep an eye out for some math.  You never know where it is going to show up!