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Sunday, March 16, 2014

Pine cones at a Wedding?

Photo Credit: Sand Hills Wedding Expo
You might wonder what a wedding has to do with the Fibonacci Sequence. Well, nothing really. Wait - that's not totally true. A part of me wonders if I should have waited two days for my own wedding so that it would have been on 8/13, but no, my wedding was wonderful (right honey?) and the date was the perfect one for us. So what's with the wedding photo?

Let me take you back. Last December, in the depths of what turned out to be a record-breaking Midwest winter, one which saw record amounts of snow and ice, saw Lake Michigan (Lake Michigan!!!) freeze over, I flew out to Illinois to take part in my niece's wedding. It was cold - really cold. In fact, in the photo below, taken in March, 2014, Jimmy Fallon, new host of The Tonight Show, emerges from Lake Michigan after completing the Polar Plunge. Look closely in the background and you can see the walls of ice that a BULLDOZER had to break up so there was a small channel for all of the people to run into the lake. By the way, who is that RIPPED guy on the left side of the picture? Yikes!
Jimmy Fallon emerges from Lake Michigan, fully clothed in a
suit, after completing the Polar Plunge to raise money for
Special Olympics (and prove to Mayor Rahm Emanuel that
he really is a tough guy).
Photo credit:
Anyway, I was at the wedding, MC-ing the reception somewhat unexpectedly (thanks to my brother for bailing), and to my surprise, there were pine cones on the tables. Pine a Illinois (are there even pine trees in Illinois?) December. In fact, here is a picture (Photo #1) of the exact pine cone that caught my eye. I brought it home to Washington state with me.

Photo #1
The actual pine cone from the wedding reception. Sent from
Oregon, found in Illinois, and brought home to
Washington for safekeeping.
Photo credit: Tom Robinson 
Now, there is a story, and eventually I will even connect this back to Fibonacci. But please indulge me. My niece, Anna, met her husband, Jeremy, while both were visiting my brother (her uncle) in Cannon Beach, Oregon, many years ago when they were just kids, barely teenagers. Their story is complicated and hard to follow, but suffice to say that the pine cones were a gift from the Oregon part of the family as wedding decorations to commemorate their first meeting many years ago. Ok, great, so where does Fibonacci come in?

As I ate my dinner and prepared myself to run the show (reception - again, last minute fill in for my brother), I looked closely at the pine cone and started counting. Actually, I first noticed that like the pineapple, this pine cone had spirals - that its pieces (anyone know what they are called? the little things that stick out of a pine cone?) were not arranged in a straight line, but in a spiral pattern. In fact, there were multiple spirals on it, just like on a pineapple.

And so I counted. First I started from the bottom (see Photo #2) and counted counter-clockwise spirals. There were....13.

Then I counted clockwise spirals. Yep - 8. Weird, isn't it? I mean...why? Why does it always seem to be THOSE numbers? I don't know. We may never know. 

Photo #2
I know it's a little hard to count the spirals, but feel free to give it a shot.
13 rotating counter-clockwise, 8 rotating clockwise.
Photo credit: Tom Robinson

Monday, March 3, 2014


You don't have to travel to Hawaii to enjoy the sweet, decadent taste of a fresh, well.... ripe, pineapple. And what's even better is that you can experience a little bit of Fibonacci, while you enjoy a 'taste of the islands.'

Count the spirals coming out of the base of this pineapple (kind of tricky). There are exactly eight!
Photo credit: Tom Robinson

While I am not overly enamored with my picture taking skills, I did want to show you what I'm talking about. And these patterns you see here are found on just about any pineapple, whether you cut it off the stalk in Oahu or pick it up at the local grocery store. Look at the very bottom of the pineapple. This was where it was connected to the plant and was removed when harvested. In the image above, you can just make out the spiraling scales, drawn in black marker, but frustratingly hard to make out. If you count your way around the base of the pineapple, you will count exactly eight spirals. Eight is a Fibonacci number!

Truth be told, some pineapples' scales are harder to count than others, and they don't always make a nice, clean pattern. But check it out the next time you are at the store (or in Hawaii!). I bet you find the same number of spirals that I did.

Notice how these highlighted (in black marker) scales make a spiral path up the fruit in the opposite direction from the last group? Counting each of the scales from bottom to top, I found.... yep - 13 scales.
Photo credit: Tom Robinson
Now, back up from the pineapple a little bit and look at the scales spiraling the OTHER direction. You can see them in the image above circled in black marker. Counting from the bottom to the top, curving around the fruit in a spiral, I counted exactly thirteen scales - another Fibonacci number! You have to do this carefully. It turns out that not all pineapples have scales that grow in exactly a clean spiral. But keep looking - I am certain you will find what you are looking for.

I have included some better drawings and images below so you can see these patterns a little more clearly. Mahalo!
Notice the 'phyllotaxy' in this image. Yum! Actually,
you can see some of the
spirals a little more clearly here.
Photo credit:

Next time you find yourself with a pineapple at hand, use this handy guide to start counting the scales in the spirals. There are at least two distinct patterns indicated here.
Photo credit: