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What is the Golden Ratio

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					What is it?
The Golden Ratio is a special ratio that is 1:1.618. The 1.618 is the 'golden' number that is called Phi. It has a LOT of digits, but usually we just say that it is 1.618. Phi is said to be the most perfect number, and the ratio (1:1618) is supposedly the ratio that is most pleasing to the eye.

The Golden Ratio in Art
Because it is very pleasing to the eye, the Golden Ratio is used a lot in art. See how in Leonardo da Vinci’s The Annunciation the woman fits into an almost perfect golden ratio? The Golden Ratio was used in art especially during the Renaissance period. It was also used by the Greeks and the Romans. The Egyptians, who called it the ‘Sacred Ratio,’ used it in their writing and building of their pyramids. Paintings and sculptures are not the only form of art that uses the Golden Ratio. It is applied a lot in architecture, too. The Parthenon, the Greek’s famous temple to Athena, was built with a Golden Ratio.

The Golden Ratio in Nature
The Golden Ratio occurs naturally all over the place. Many aspects of the human figure involve the Golden Ratio, such as the heads and hands. Many think that the closer you are to the Golden Ratio, the more beautiful you are. In nature, the Golden Ratio can be found by measuring many things like leaves, pinecones, and flowers.

The Golden Ratio Today
Today one may find the Golden Ratio in everyday objects such as tables, couches, doors, posters, books, pencil cases, and a multitude of other things around the house as well as art and nature.

What is it?
The Golden Ratio is a special ratio that is 1:1.618. The 1.618 is the 'golden' number that is called Phi. It has a LOT of digits, but usually we just say that it is 1.618. Phi is said to be the most perfect number, and the ratio (1:1618) is supposedly the ratio that is most pleasing to the eye.

See how nice the golden rectangle (the one with the giant sparkle) looks compared to the normal rectangles? Many artists use the golden ratio to make their works of art (paintings, sculptures, etc.) look more aesthetic.

The Golden Ratio in Art
Because it is very pleasing to the eye, the Golden Ratio is used a lot in art. Here are some examples:
In Leonardo da Vinci’s The Mona Lisa¸ the painting itself is close to a golden rectangle. In his second masterpiece, The Annunciation, you may notice that the woman on the left fits into an almost perfect Golden Rectangle.

Many famous artists used the golden ratio in their art. Leonardo da Vinci used the golden ratio in many paintings, including The Annunciation, The Mona Lisa, St. Jerome and other works of art. The Golden Ratio was used especially in the Renaissance and by Greeks and Romans. The Egyptians called the golden ratio the 'Sacred Ratio.' They used it in many things, such as hieroglyphics and paintings on walls. Paintings and sculptures are not the only form of art in which you can find the Golden Ratio-it is also used quite frequently in architecture. Many Greek buildings involved the use of the Golden Ratio, including the Parthenon, the temple of Athena in Athens. The Egyptians used their ‘Sacred Ratio’ in the

building of their pyramids-the ratio of the base to the height is approximately 1.6:1. Today, the golden ratio is not only used in art, but it is also used in other things such as light switches, windows, couches, tables, doors, posters, and many other everyday objects.

The Golden Ratio in Nature
The Golden Ratio occurs naturally all over the place. Many aspects of the human figure involve the Golden Ratio, such as the heads and hands. Many think that the closer you are to the Golden Ratio, the more beautiful you are. In nature, the Golden Ratio can be found by measuring many things like leaves, pinecones, and flowers.

More than 1.618
Although we refer only to the first four digits in the Golden Ratio, it is an irrational number, so it never ends! If you would like to see the first 50,000 digits in this perfect number, please visit my extra credit website (I don’t think that my parents would be very happy if I were to print out all of those pages!)

Ratios of Every Day Objects
Here is the table from #1 of all of the objects that I measured! Item Width Length Length/width Pencil Case 13 cm 12 cm 1:1.614 Playing card 9 cm 6 ½ cm 1:1.28 Piece of Paper 21 ½ cm 28 cm 1:1.302 The Trojan War (book) 14 cm 21 cm 1:1.5 Lunchbox 17 cm 21 cm 1:1.235 Laptop battery 12 ¾ cm 5 ¼ cm 1:1.233 Algebra book 23 ½ cm 19 cm 1:1.237 Website banner 686 px 237 px 1:2.895 Backpack pocket 10 cm 9 cm 1:1.111 As you can see, the ratios of my pencil case and The Trojan War were very close to the Golden Ratio, with the playing card and the piece of paper not too different. Comparing The Trojan War to other books, it seems like a lot of books are very close to the Golden Ratio, and I don’t think that it is a coincidence!

Tricks With the Golden Ratio
I found these tricks pretty interesting! If you square the Golden Ratio and subtract one, it is equal to the golden ratio! It won't work as well if you only use the first three digits. Phi2-1=Phi

If you find the reciprocal of Phi, it is equal to Phi-1. 1/Phi+1=Phi

The End
Well, I hope that you enjoyed my Golden Ratio project. I know that I certainly did-it was very interesting and fun to find out about the Golden Ratio and how it is used in art. I’m going to start using it in my pictures right away-maybe it would make them look a bit nicer.

Work Cited
More Than 1.618. 5 Dec. 2004 <http://www.cs.arizona.edu/icon/oddsends/phi.htm> Mr. Narain’s Golden Ratio Website. 5 Dec. 2004 <http://cuip.uchicago.edu/~dlnarain/golden/> Phi: That Golden Number. 5 Dec. 2004 <http://jwilson.coe.uga.edu/emt669/Student.Folders/Frietag.Mark/Homep age/Goldenratio/goldenratio.html> The Golden Ratio. 5 Dec. 2004 <http://library.thinkquest.org/C005449/> The Golden Ratio. 5 Dec. 2004 <http://www.geocities.com/robinhuiscool/Goldenratio.html> The Golden Ratio and Aesthetics. 5 Dec. 2004 <http://pass.maths.org.uk/issue22/features/golden/>


				
DOCUMENT INFO
Description: This is an explanation and history of the golden ratio. Examples of the golden ratio abound in music and art.
Matthew Bilinsky Matthew Bilinsky
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