the golden ratio by samanthac

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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/>

								
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