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Wednesday, December 28, 2011

The Golden Ratio: A Greek Week Math Presentation

As a part of Greek Week, our 9th Graders saw a presentation today integrating the Geometry they are learning this year in Mathematics with the Greek culture they are studying in Ancient World History and the Biology they are learning in Science. The topic was the Golden Ratio. A summary of this presentation together with its supporting slides appears below.

The ancient Greeks are arguably the single largest contributors to the study of mathematics………

Particularly in the area of Geometry which all the Freshmen are studying this year.

The Greeks appreciated, studied and valued the connections between math, nature, and art. So you might be thinking “ What does math have to do with art?” Few people immediately see how math and art can be connected but I think after my presentation today you will have a greater and deeper understanding of a few mathematical ideas that were pervasive in ancient Greek art and design. Some of which is literally encoded in our bones.

The Parthenon, created by the ancient Greeks has been regarded through the ages as the pinnacle of architectural achievement. Having seen it myself in person, I can attest to its grandeur and regal presence. What is so cool is that it inspiring physical presence is created not only by its actual columns and facades but also by its openness or rather empty spaces. It sits on top of this mountain which I climbed in the heat of August so I remember it. From each opening between the columns you can see the vast and what once the splendid view of ancient Athens. The beauty of the Parthenon it no mere accident though.

See the ancient Greeks were keenly aware of a certain mathematical relationship called the golden ratio. Also known as the golden section, the golden mean, the divine proportion, golden number among other names. The ancient Greeks felt the Golden ratio held the mathematical key to beauty. They incorporated it into not only their study of math but also their art and architecture.

So what is the Golden Ratio? The Golden Ratio is a relationship between the sides of a rectangle of 1 to 1.618.

This golden ratio of 1 to 1.618 was eventually called “Phi” after the creator of the artwork of the Parthenon, a Greek man named Phidias. The first video we are going to watch will illustrate exactly what is the golden ratio and how it was used extensively in the creation of the Parthenon. Some thinkers feel there is no evidence that the Greeks actually thought of the golden ratio in their design of the Partheon but I think it is fair to say it was utilized.

See the golden ratio was not discovered by any one person. It is rather a mathematical fact that revealed itself to many people over the course of history. What is the very cool and mysterious part about the Golden ratio is its relationship to the Fibonacci sequence.

The Fibonacci sequence is a series of numbers where each term is the summation of the ones before it.
1+1 =
1+ 2=
2+3 =
3+ 5 = 8
And so on. This is nothing that interesting in itself until we look at the sequence more closely

1,1,2,3,5,8,13, ……These numbers end up being the natural dynamics of growth of many things in the world Hashem created. As the videos show, 1,1,2,3,5,8,13 is the natural growth of population of bunny rabbits, the bronchial branches in our lungs, the way many flowers grow, and on and on and on…….

When you look at the ratio of the numbers of the Fibonacci series, meaning 2/1, 3/2, 5/3 and so on you would expect the numbers to grow or be random numbers but NO they don’t!

The ratio gets closer and closer to the same number, PHI, the golden ratio.

See encoded in the sequence of numbers that explain the growth phenomena of much of our natural world is the golden ratio.

The entire presentation on the Golden Ratio appears below. Enjoy!

-Mrs. Sabrina Bernath
Math Department Chair

1 comment:

  1. Proportions are built from ratios. A "ratio" is just a comparison between two different things. For instance, someone can look at a group of people, count noses, and refer to the "ratio of men to women" in the group. Suppose there are thirty-five people, fifteen of whom are men. Then the ratio of men to women is 15 to 20 in
    ratio math.

    Notice that, in the expression "the ratio of men to women", "men" came first. This order is very important, and must be respected: whichever word came first, its number must come first. If the expression had been "the ratio of women to men", then the numbers would have been "20 to 15".

    Expressing the ratio of men to women as "15 to 20" is expressing the ratio in words. There are two other notations for this "15 to 20" ratio: