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Sunday, July 6, 2014

The Parthenon

Though I've never been to Greece, I definitely would like to visit sometime. And for all the white sandy beaches, the exquisite food offerings, and the culture that oozes out of every pore in that country, one of the top sites on my list of things to see is the Parthenon, pictured here.

The Parthenon - photo credit: Wikimedia Commons
To most eyes (mine included, if truth be told) this building represents little more than an ancient ruin, an artifact from an era long gone, and generally, a really cool building to see, even more remarkable that it's still standing.

But from a mathematician's standpoint, some say the Parthenon is one of the great wonders of the world as it represents one of the earliest examples of builders and architects understanding dimension, perspective, and ratio. Many believe the Parthenon was built according to the Golden Ratio, or phi.

The Parthenon is considered to have been a most significant temple for the ancient Greeks, build on the hill called the Acropolis. It was a symbol of military victory, and was built to honor the city's (Athens) patron deity, Athena. It was an architectural wonder, mixing Dorian and Ionic columns, and it was decorated by sculptures, the likes of which had not been seen before.

To us, however, something even bigger lie in this building. It was built between 447 B.C. and 432 B.C. So it took fifteen years to build - not that unusual for the time. However, you may note that this period of time is around 1600-1700 years BEFORE Leonardo Pisano wrote his book about rabbits and the Fibonacci Sequence.

You see, the original dimensions (lost to us through the centuries) appear to follow a very similar pattern, as you can see in the image below. By isolating square and rectangular regions of the facade of the Parthenon, you can begin to see a Fibonacci spiral grow.
The Parthenon displays the Fibonacci spiral.
Photo credit:
Scholars have debated this, and whether it was built using the Golden Ratio or not may never truly be known. But one look at the spiral and you can see that there was something special about this building.

Taking it one step further, let's look at some relative measurements of the building. Here you can see that familiar 1.618 to 1 ratio value yet again. Remember, part of the building is no longer standing, so some of this may simply be speculation. But still, the Parthenon stands as a) one of the great architectural designs of the ancient times, and b) quite possibly the oldest-standing example of the Fibonacci sequence and Golden Ratio in the world.
Photo Credit:

Now, my question to you is this: can you find other structures, either from the ancient world, or still standing today, that reflect similar dimensions? We explored this with rectangles, but are there buildings today that just seem to 'look right'? If you find one, drop me a note and let me know about it.

Note: This will likely be the final installment looking at applications and consequences of the Fibonacci sequence. From now on, be looking for quick, simple lesson plans you can use either in your classroom or even at home with your own children to explore Fibonacci. In keeping with the spirit of my upcoming book, these lesson ideas will probably differ from much of what you find online, as those lessons tend to be geared toward middle or high school students. I would like these lessons to be applicable to elementary-aged students, and if possible even the primary grades. Obviously, such lessons will rely heavily on parent or teacher support and guidance, but could easily be used in conjunction with the book itself, allowing students to read it multiple times, each time discovering a new activity that connects their reading to their learning.

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