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: redalertpolitics.com

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 cones...at a wedding...in Illinois (are there even pine trees in Illinois?)...in 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

Pineapples!

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: geochembio.com

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: thinkquest.org

Fibonacci NBA Style

In honor of the NBA All-Star weekend taking place in New Orleans (home of the Pelicans), I thought I would share this interesting little prediction from last year's (2013) playoffs. It was Game 2 of the Eastern Conference Semifinals (2 is a Fibonacci number), and it took place on May 8, or 5/8/13 (all Fibonacci numbers). I won't spoil the surprise, but check out this link, where it was mathematically proven that the Bulls would win. This photo should help get you in the mood!

Photo credit: USATSI

The Bulls will totally win Game 2 because of the Fibonacci sequence

Sadly, the Heat apparently failed their high school math classes because despite all signs pointing to a big win by the Bulls (some even suggested the score would be 144-89), the Heat blew out the Bulls by a final score of 115-78, a difference of 37. And no, none of those numbers are Fibonacci numbers....

Nature by Numbers - video (3:44)

Thought you might enjoy this short but powerful video tribute to Fibonacci numbers in nature. I wish I could say I had something to do with it, but this is simply an beautiful description of Fibonacci numbers. The title is Nature by Numbers by Cristobal Vila. Enjoy!

Nature by Numbers

Fibonacci in Nature

This flower has 13 petals.
13 is a Fibonacci number!
Photo credit:
www.constructingtheuniverse.com

The Fibonacci sequence is interesting from a math standpoint...if you are into math. But if the only place to find Fibonacci was in a math class, it wouldn't be nearly as interesting as it inevitably is. So let's take a walk outside and see what's out there.

This trillium flower has three petals.
Photo credit: britton.disted.camosun.bc.ca

Where I live, it's still winter. Cold, dark, no snow surprisingly, but definitely no spring flowers yet. Still, it won't be long before our flowers are blooming in full color and I wanted to show you some examples of what I like to call 'Fibonacci flowers.' 

There are a variety of places you can see Fibonacci numbers in flowers. The simplest is in the number of petals on a bloom. Starting with the number three, you can find countless examples of flowers with three, five, eight, thirteen, and even twenty-one petals, as you will see in the photos that follow.

This flower has five petals.
Photo credit: www.bio.tamu.edu

This beautiful pink clematis has eight petals.
Photo credit: alexorbit.com

This star daisy has thirteen petals.
Photo credit: murderousmaths.com.uk

This daisy has twenty-one petals.
Photo credit: britton.disted.camosun.bc.ca

So does this one!
Photo credit: psophis.blogspot.com

Why these numbers? No one knows. It's just one of those oddities of nature that SO many flowers bloom with a Fibonacci number of petals, and not four, or seven, or twelve, for example. In all fairness, there are certainly flowers with petals that number something other than a Fibonacci number. But as winter gives way to spring, take a look around and see what you find. You just might be surprised to find Fibonacci numbers all around you!

Strange and Wonderful

Behold, the beginning of the Fibonacci sequence:

n        1     2     3     4     5     6     7     8     9     10     11     12     13     14     15 ...

F(n)   1     1     2     3     5     8    13    21    34   55    89    144    233   377   610 ...

Photo credit:
www.theoremoftheday.org

Now, here's something you may not know. Pick any two consecutive Fibonacci numbers.... let's take numbers 5 and 6. You will find the fifth Fibonacci number listed as F(5), and it's actually the number five! F(6) is 8.

Here's where it gets interesting. If you square both numbers, you will see that 5² = 25, and 8² = 64. Now add those up and you get 25 + 64 = 89. This is another Fibonacci number! But wait- there's more. WHICH Fibonacci number is it? It's the 11th....as in... 5+6 = 11. Hmm...let's try that one again.

Let's pick two consecutive Fibonacci numbers. We'll pick Fibonacci number 7 (13) and Fibonacci number 8 (21). Now, square those numbers. 13² = 169, and 21² = 441. Add those together (169 + 441) and you get ... 610 - another Fibonacci number! And which one is it? Remember, we chose F(7) and F(8).... 7 + 8 = 15, and the 15th Fibonacci number is.... 610!

What does this look like mathematically? Well, perhaps it's more than you came here for, but here goes:

F(n)² + F(n+1)² = F(n + [n+1])

When you square and then sum consecutive Fibonacci numbers, the answer you get is the Fibonacci number at the location that is the sum of the two original locations.

Whew!

Wanna see if you 'get' it? The 29th Fibonacci number is 514,229.

A Most Unusual Finding in Fibonacci - Video (9:48)

As much as I wish this was my own work, I can't claim to have even known about this phenomenon until I watched this video. If you are really into Fibonacci by now, then this is the video for you to watch! But if you consider yourself more of a casual fan of the sequence, this is still going to blow you away.

This video was produced in the UK, and is one of a vast collection of interesting mathematical tidbits. One click and you might be hooked. This one stands out to me because it talks about the Fibonacci sequence itself, and some of the hidden wonders inside it. We will spend a great deal of time in the coming weeks and months exploring places where Fibonacci numbers can be found, but I thought I would take a brief side-trip and let you look at Fibonacci numbers that lie...inside the Fibonacci sequence.

I would love to hear your thoughts or comments about this video. Maybe it will spark something in you. Maybe it will be too much for you at this part of your journey, and that's alright. But at the very least, I hope you find it entertaining and informative. And if it causes you to seek these folks' other videos, be sure to watch the one on McDonald's and the impossible quest to purchase exactly 43 Chicken McNuggets.