Page 24 - Math 21 Module_Chapter One
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The Fibonacci sequence has interesting and mysterious properties. Aside
from the fact that the sequence is very visible in nature, the ratios of the
successive Fibonacci numbers approach to the number phi (Φ), also known
as the golden ratio which is approximately equal to 1.618.
The golden ratio was first called as the Divine Proportion in the early 1500s
in Leonardo da Vinci’s work which was explored by Luca Pacioli entitled “De
Divina Proportione” in 1509.
The golden ratio (Φ) is the ratio between two numbers, a and b where
a is greater than b, if it is also the ratio between the sum and the larger of the
two numbers as in the equation below.
b a a/b
+ 3 1.5
= = = . ….
3 5 1.666666666…
5 8 1.6
8 13 1.625
13 21 1.615384615...
21 34 1.61905
34 55 1.61765
. . .
. . .
144 233 1.618055556...
233 377 1.618025751...