The Golden RatioThe Golden Ratio

Definition of Golden RatioDefinition of Golden Ratio

Golden ratioGolden ratio--Is a mathematical irrational constantIs a mathematical irrational constant

--  two quantities are in the two quantities are in the golden ratiogolden ratio if the ratio of the sum of the  if the ratio of the sum of the

quantities to the larger quantity is similar to the ratio of the larger quantities to the larger quantity is similar to the ratio of the larger

quantity to the smaller one. quantity to the smaller one. 

--a+b is to a as a is to ba+b is to a as a is to b

--denoted by phidenoted by phi

Golden Ratio Golden Ratio

Approximately 1.618

Fascinated many mathematicians, architects.

Irrational numbera+b/a= a/b = golden ratio

The Renaissance artists knew it as the The Renaissance artists knew it as the diving proportion and diving proportion and for beauty and for beauty and balance in the design of art..balance in the design of art..

The Greeks recognized it as dividing a line in the The Greeks recognized it as dividing a line in the extreme and mean ratioextreme and mean ratio beauty and balance beauty and balance in the art of architecturein the art of architecture

The Egyptians designed the pyramids.The Egyptians designed the pyramids.

The symbol of Golden RatioThe symbol of Golden Ratio

The symbol used “ Phi”

Golden Ratio in human bodyGolden Ratio in human body Our attraction to another person's body increases if that body is symmetrical Our attraction to another person's body increases if that body is symmetrical

and in proportion. and in proportion. if a face is in proportion, we are more likely to notice it and find it beautiful.if a face is in proportion, we are more likely to notice it and find it beautiful.

Scientists believe that we perceive proportional bodies to be more healthyScientists believe that we perceive proportional bodies to be more healthy..

Fibonacci Sequence is related to Fibonacci Sequence is related to the golden ratio!the golden ratio!

Fibonacci series:Fibonacci series:--appears as Indian mathematicsappears as Indian mathematics

--related to the golden ratio related to the golden ratio

NumbersNumbers

0,1,1,2,3,5,8,13,21,34,55,89..0,1,1,2,3,5,8,13,21,34,55,89..

Fibonacci sequenceFibonacci sequence

http://www.youtube.com/watch?v=eJ-KSl1Uhttp://www.youtube.com/watch?v=eJ-KSl1UR8kR8k

Golden RatioGolden Ratio

This is very effective in explanation This is very effective in explanation

http://www.youtube.com/watch?v=fmaVqkhttp://www.youtube.com/watch?v=fmaVqkR0ZXgR0ZXg

Thank you Thank you

Bibliography Bibliography

http://en.wikipedia.org/wiki/Golden_ratiohttp://en.wikipedia.org/wiki/Golden_ratio http://goldennumber.net/goldsect.htmhttp://goldennumber.net/goldsect.htm http://www.youtube.com/watch?v=eJ-KSl1http://www.youtube.com/watch?v=eJ-KSl1

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