1. The Golden Section The Divine Proportion The Golden Mean
The Golden Ratio
The Golden Section
The Divine Proportion
The Golden Mean

2. Golden ratio φ = 1 + √ 5 = 1.61803399.. 2 Golden Rectangle
Golden Triangle
φ -1 36 φ 1 72 72 1

3. Ratio of A to B is the golden ratio A = 1.618 B

5. The Great Pyramid of Giza 2560 BC
-Side lengths approximately 230m
-Base covers m^2
-Sides angled at 51.5 degrees.
1^2 + (√φ)^2 = φ^2
= 2.618 √φ φ 1 2

6. The Parthenon

7. Notre Dame

8. CN Tower Base to observation deck 342 m Base to spire 553.33 m
= = φ
342

9. B
Pentagon, each side
of length 1. A C F E D
I AF I = φ
I FD I

10. Saint Jerome Leonardo Da Vinci (1451-1519 )

11. Crucifixion (1502) Raphael

12. Ognissanti Madonna (Madonna of Glory) Giotto di Bondone (1267-1337)

13. Bathers Seurat ( )

14. Vetruvian Man Leonardo Da Vinci

15. Mona Lisa Leonardo Da Vinci

16. Golden Ratio on the Body
Height / Head to fingertips
Head to fingertips / Head to elbow
Elbow to fingertips / Elbow to wrist
Head to fingertips / Head to naval
Elbow to wrist / Length of hand

17. Fibonacci Sequence
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …..
1 / 1 = 1
2 / 1 = 2
3 / 2 = 1.5
5 / 3 =
8 / 5 = 1.6
13 / 8 = 1.625
21 / 13 =
34 / 21 =
55 / 34 = …
144 / 89 = …
Φ =

18. Ratio of Clockwise spiral to counterclockwise spirals
34 : 55, 89 : 55, 144 : 89

19. Nautilus Shell

20. Golden ratio in art, architecture & nature….believable or not?