Most people are familiar with the number Pi because it can be found in so many different math problems and equations. There is, however, another irrational number like Pi. This number isn¡¦t as well known as Pi however. This number is called Phi. This number is also called the golden ratio. The golden ratio is equal to the square root of five plus one, divided by two. If you work this out it comes out as 1.618033988749895. This is also the only number that if squared, is equal to itself plus one. Mathematically speaking, Phi^2 = Phi + 1. Also if you find the reciprocal of Phi, it is equal to itself minus one, Phi^-1 = Phi ¡V 1.

The Golden Ratio is the basis for many things in nature. Even ones fingers use the Golden Ratio. First measure the length of the longest finger bone. Then measure the shorter one next to it. Finally if you divide the longer one by the shorter one, you should get a number that is close to 1.168 which is really close to the Golden Ratio. Most parts of the human body are proportional to the Golden Ratio.

The Golden Ratio can even be traced back into the times of the Romans and Pyramids. For example, the Great Pyramid of Giza, which was built in 2560 BC, is one of the earliest ways the Golden Ratio was used. The length of each side of the base is 756 feet while the height of the Pyramid when build was 481 feet. If you divide 756 by 481, you would get 1.5717 which is very close to the Golden Ratio.

Another good example of the Golden Ratio is in Athens Greece. The Parthenon, which was build during 440 BC, uses the Golden Ratio also. The spaces in between the columns are proportional to the Golden Ratio. This shows that the golden ratio has been used for a very long time.

Since the Golden Ratio is an irrational number, it cannot be written as a regular fraction. You could however, get a very close estimate. One of the easiest ways is using the Fibonacci numbers. The Fibonacci numbers is a sequence of...

...
The Golden Number
1.61803 39887 49894 84820 is by no means a number of memorization. However, it is a recognizable one. Never will you find a combination of numbers that is more significant than this one. This ratio is known as the Golden Number, or the GoldenRatio. This mystery number has been used throughout different aspects of life, such as art, architecture, and of course, mathematics. One may wonder where the...

...GoldenRatio
In mathematics, two quantities are in the goldenratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b,
Where the Greek letter phi (φ) represents the goldenratio. Its value is:
The...

...GOLDENRATIO- maths project
Index
Serial no. chapter
1 | Introduction |
2 | History |
3 | In nature |
4 | In human body |
5 | In architecture |
6 | In art |
7 | In day to day life |
8 | SIGNIFICANCE |
ACKNOWLEDGEMENT
I would like to express my special thanks of gratitude to my teacher sonali durgam on the topic goldenratio, which also helped me in doing a lot of Research and I...

...The GoldenRatio: Natures Beautiful Proportion
At first glance of the title, many may wonder: What is the GoldenRatio? There are many names the GoldenRatio has been called including the Golden Angle, the Golden Section, the Divine Proportion, the Golden Cut, the Golden Number et cetera, but what is it and how is it useful for society today? One may...

...deciphered. Until, the discovery of a natural ratio, that changed the game of beauty in all aspects. “Many of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kelper, to present day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties, called the...

...rederick smith
The GoldenRatio
March 31 2011
1. The introduction:
Hello my name is Frederick Smith, I will be speaking you about a fascinating thing that is in everything, it’s a part of you, it created you & its not just in you, its all around you. Its also in all plants and in all animals. Take for example an octopus has eight tentacles hence the name “octo’~pus, each one of its tentacles has the exact number of suckers on it and each tentacle is the same...

...A Mathematical History
of the
Golden Number
Roger Herz-Fischler
If cdc; tf dA.ll npdc; to
1tpOC;
,Axpov xui
J,1&OOV
A.Oyov Eu9sta tEtJiiiaOat AeyEtal, otav
f.1£i~ov TJlfiJla, OUt~ td J.L&i~ov
to EAattOv.
-Euclid, Elements, VI,def.3 [Euclid-Heiberg, II, 72]
Non me pare, excelso Duca, in pill suoi infiniti etTetti al presente estenderme, peroche fa carta non supliria al negro a esprimerli tutti... . -Paccioli, Divina proportione [Paccioli, 1509, Chap....

...calculate the rest of the terms the same way:
F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 |
0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 |
Segment 2: The Goldenratio
In order to define the goldenratio we need to examine the following sketch:
The line above is divided into two segments in such a way that ABAP=APPB
The ratio described above is called the goldenratio.
If we assume that AP=x units...

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