Golden ratio

The Golden Ratio and its Applications

1. GOLDEN RATIO Dr. R. KALAIVANAN

2. THE GOLDEN RATIO Two quantities are in the GOLDEN RATIO if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the large quantity to the smaller one.

3. FIBONACCI SPIRAL

4. APPLICATIONS OF GOLDEN RATIO Human anatomy Music Architecture Photography Solar system Logo

5. GOLDEN RATIO IN DNA DNA consists of two spirals and molecules. Between two spirals’ lengths there are 34 angstroms, and its width is 21 angstroms(21 and 34 in F ibonacci series),so it has golden ratio.

6. IN THE ASPECT RATIO OF DNA SPIRAL I t measures 34angstroms long by 21 angstroms wide-for each full cycle of its double helix spiral. 34 and 21 ,of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates phi, 1.6180339

7. Golden ratio in human brain

8. GOLDEN RATIO IN HEART RHYTHM Man’s heart is beaten uniformly. The ratio of maximum(systolic) pressure to the minimum (diastolic) pressure is equal , on the average to 1.6 that is close to the golden proportion.

9. GOLDEN RATIO IN MUSIC The black &white keys represent the ratios of musical proportion. There are 8 white keys and 5 black keys, 8:5=1.6-5:8=0.625 The black keys are in groups of 2 and 3. the series 2:3:5:8 is part of the fibonacci series. All these ratio close to ф ,which is 1.618

10. GOLDEN VIOLIN Musical instrument design is often based on phi, the golden ratio. Fibonacci and phi are used in the design of violins. even in the design of high quality speaker wire .

11. GOLDEN RATIO IN ARCHITECTURE The length of the base of the pyramid is approximately 1+1=2 The height of an isosceles traingular face is approximately phi( ф ). The height of the pyramid is approximately the square root of phi.( √ ф ) The height can then be found as √ ф - 4/ п

12. UN BUILDING

13. GOLDEN RATIO IN TAJ MAHAL The main building of the Taj Mahal was designed using the golden ratio. This is why it looks so perfect The rectangles that served as the basic outline for the exterior of the building were all in the golden proportion.

14. GOLDEN RATIO IN PHOTOGRAPHY There’s one other way to use the golden ratio to compose a photograph Instead of using the spiral, create a grid like in the rule of thirds,but one that uses a 1:1.618 ratio, instead of dividing the frame into equal parts.

15. GOLDEN RATIO IN HUMAN FACE With Golden Ratio Without Golden Ratio

16. GOLDEN RATIO IN MONA LISA

17. GOLDEN RATIO IN SOLAR SYSTEM The diameter of saturn is very close to a phi relatioship, with the diameter of its rings as illustrated by the green lines. The inner ring division is in a relationship that is very close to phi with the diameter of the rings outside the sphere of the planet illustrated by the blue lines.

18. GOLDEN RATIO BETWEEN SUN, VENUS, EARTH Venus orbits the sun in 224.695 days while earth orbits the sun in 365.242 days, creating a ratio of 8\13(both fibonacci numbers) or 0.615(roughly phi). thus conjuctions of Earth and Venus occur every 8 orbits of the earth around the sun and every 13 orbits of Venus. Mercury, on the other hand,orbits the sun in 87.968 earth days,creating a conjuction with earth every 115.88 days. thus there are 365.24/115.88 conjuction in a year or 22 conjuctios in 7 years, which is very close to phi

19. GOLDEN RATIO IN LOGO DESIGN

20. GOLDEN RATIO IN TWITTER

21. GOLDEN RATIO IN IPHONE

22. GOLDEN RATIO – GENERAL

23. GOLDEN RATIO IN PEPSI LOGO

24. GOLDEN RATIO IN TOYOTA LOGO