Golden ratio

Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.
It is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment.

1. Golden Ratio Sanjeev Kumar Prajapati

2. Golden ratio

3. The GOLDEN RATIO is an irrational mathematical constant , approximately equals to  

4. The Golden Ratio is often denoted by Greek letter (Phi) So  

5. Also called as: Golden Ratio Golden Section Golden Cut Divine Proportion Divine Section Mean of Phidias Extreme and Mean Ratio Medial Section

6. Two quantities are in the Golden Ratio if the ration between the sum of those quantities and the larger one is same as the ratio between the larger one and the smaller.

8. One interesting fact about Phi is its Reciprocal It is highly unusual for the decimal integers of a number and its reciprocal to be exactly the same.  

9. A Golden rectangle is a rectangle where the ratio of its length to the width is the Golden Ratio . That is whose sides are in the ratio  

10. The Golden rectangle has the property that it can be further subdivided in to two portions of a square and a Golden rectangle . This smaller rectangle can be further subdivided into another set of smaller Golden rectangle and smaller square . And this process can be done repeatedly to produce smaller versions of squares and Golden rectangles .

11. Golden Rectangle

12. GOLDEN SPIRAL Start with the smallest one on the right corner connect the lower right corner to the upper right corner with an arc that is one fourth of a circle . Then continue your line in to the second square on the with an arc that is one fourth of a circle , we will continue this process until each square has an arc inside it , with all of them connected as a continuous line . The line should look like a Spiral when we are done .

13. Golden triangle The Golden triangle is a special isosceles triangle . The top angle is while the bottom two angles are each.  

14. GOLDEN RATIO IN NATURE

15. NAUTILUS SHELL

16. GOLDEN RATIO IN ART Many Artists who lived after Phidias have used this proportion . Leonardo Da Vinci called it the “ divine proportion ” and featured it in many of his paintings.

17. Mona Lisa’s face is a perfect Golden rectangle , according to the ratio of the width of her forehead compared to the length from the top of her head to her chin.

18. Golden ratio in the human body

19. Golden ratio in fingers

20. Golden ratio in hands

21. Golden mean gauge

22. More examples of golden sections

23. THANK YOU