Golden Rectangles And Golden Ratios

Before doing this research paper on the golden triangles and golden ratios many of us probably thought that this was a waste of time. That this had no nothing to do with us and our environment. Well we were wrong. Golden rectangles and golden ratios are everywhere, in paintings, in nature, ect. A rectangle is a Golden Rectangle when the ratio of the length to the width is the Golden Ratio. The Golden Ratio is equal to 1.61803398874989484820. Like in Pi, the numbers would go on for ever without repeating. Instead of using that big number we just say, the Golden Ratio is equal to 1.62. It s exact value is 1 + sqrt(5) over 2. The Golden Rectangle got it s name from the Greeks. All throughout history, this ratio was been thought to be the most pleasing to the eye. Something about it just gets your attention.

The Golden Rectangle isn t some resent invention, this comes from a long time ago. It is said that the Golden Rectangle was used 4,600 years ago to built the Great Pyramid of Giza, even before the Greeks. The Greeks used this to make many buildings, such as the Parthenon (built in 440BC for the goddess Athena). The Parthenon s exterior dimensions forms a perfect golden rectangle. The Parthenon was built on a square root of five. That means it s 5 times as long as it is wide. Phidias used the Golden Ratio in his sculptures. Someone else that used the Golden Ratio was Queen Annie Lace. She arranged her flowerettes in spiral patterns. She would put 8 flowers counterclockwise and

13 clockwise. (Notice how both 8 and 13 are Fibonacci series of numbers. The series is 1,1,2,3,5,8,13,21,34,55,89,144,ect. The rule is that after the first two numbers comes the sum of the previous two numbers. For example 1+1=2, then 1+2=3 , then 2+3=5 and so on). Pythagoras discovered that when you cut a square from a golden rectangle you end up with a similar rectangle and you can keep on cutting squares from the golden rectangle and you will still keep on getting a similar rectangle. This proves that the Golden Rectangle is everywhere because if you actually do this you will notice that it starts to

make a spiral shape and the shape starts to look like a shell or a snail.

Today, we still use the Golden Rectangle in many different ways. For example, LeCorbuster uses it to make windows and other building aspects. The United Nations building in Manhattan is L- shaped. And even thought a lot of people don t agree, it is said that the upright part of the L has a golden ratio. Also Leonardo Da Vinci used it for many of his paintings, one of them was the Mona Lisa. Leonardo called the Golden Rectangle the divine proportion because it was found in all things of the CREATION. (Remember

what I said about the snail?) Like Leonardo, many other artists used the Golden

Rectangle on many of their paintings.

In conclusion we can all agree that the Golden Ratio and the Golden Rectangle are all around us. In buildings, in insects, in everything. We just have to know how t look at things.