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.

2. GOLDEN RATIO

3. The GOLDEN RATIO is an irrational
mathematical constant ,
approximately equals to
1.6180339887

4. The Golden Ratio is
often denoted by
Greek letter 𝜑 (Phi)
So 𝜑 = 1.6180339887

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. 𝜑 =
1 + 5
2
= 1.618

9. One interesting fact about Phi is its Reciprocal
1
𝜑
=
1
1.618
= 0.618
It is highly unusual for the decimal integers of a
number and its reciprocal to be exactly the same.

10. 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 1: 1.618

11. 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.

12. Golden Rectangle

13. 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 .

14. GOLDEN TRIANGLE
The Golden triangle is
a special isosceles
triangle . The top
angle is 36° while the
bottom two angles
are 72° each.

15. GOLDEN RATIO IN NATURE

16. NAUTILUS SHELL

17. 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.

18. 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.

19. GOLDEN RATIO IN THE HUMAN BODY

20. GOLDEN RATIO IN FINGERS

21. GOLDEN RATIO IN HANDS

22. GOLDEN MEAN GAUGE

24. MORE EXAMPLES OF GOLDEN
SECTIONS