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# The golden ratio

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### The golden ratio

1. 1. The Golden Ratio
2. 2. Definition of Golden Ratio <ul><li>Golden ratio </li></ul><ul><li>- Is a mathematical irrational constant </li></ul><ul><li>-   two quantities are in the  golden ratio  if the ratio of the sum of the quantities to the larger quantity is similar to the ratio of the larger quantity to the smaller one.  </li></ul><ul><li>- a+b is to a as a is to b </li></ul><ul><li>- denoted by phi </li></ul>
3. 3. Golden Ratio Approximately 1.618 Fascinated many mathematicians, architects. Irrational number a+b/a= a/b = golden ratio
4. 4. <ul><li>The Renaissance artists knew it as the diving proportion and  for beauty and balance in the design of art.. </li></ul>
5. 5. <ul><li>The Greeks recognized it as dividing a line in the extreme and mean ratio  beauty and balance in the art of architecture </li></ul>
6. 6. <ul><li>The Egyptians designed the pyramids. </li></ul>
7. 7. The symbol of Golden Ratio The symbol used “ Phi”
8. 8. Golden Ratio in human body <ul><li>Our attraction to another person's body increases if that body is symmetrical and in proportion. </li></ul><ul><li>if a face is in proportion, we are more likely to notice it and find it beautiful. </li></ul><ul><li>Scientists believe that we perceive proportional bodies to be more healthy . </li></ul>
9. 9. Fibonacci Sequence is related to the golden ratio! <ul><li>Fibonacci series: </li></ul><ul><li>- appears as Indian mathematics </li></ul><ul><li>- related to the golden ratio </li></ul>
10. 10. Numbers <ul><li>0,1,1,2,3,5,8,13,21,34,55,89.. </li></ul>
11. 11. Fibonacci sequence <ul><li>http://www.youtube.com/watch?v=eJ-KSl1UR8k </li></ul>
12. 12. Golden Ratio
13. 13. This is very effective in explanation  <ul><li>http://www.youtube.com/watch?v=fmaVqkR0ZXg </li></ul>
14. 14. Thank you 
15. 15. Bibliography <ul><li>http://en.wikipedia.org/wiki/Golden_ratio </li></ul><ul><li>http://goldennumber.net/goldsect.htm </li></ul><ul><li>http://www.youtube.com/watch?v=eJ-KSl1UR8k </li></ul>