as the number of clockwise spirals is 55 and the number of counter-
clockwise spirals is 89; 89 divided by 55 = 1.618, the Divine Propor-
tion. Pinecones and pineapples illustrate similar spirals of successive
Fibonacci numbers.
PHI is also the ratio of five-sided symmetry. It can be proven by
using a basic geometrical figure, the pentagon. This five-sided figure
embodies PHI because PHI is the ratio of any diagonal to any side of
the pentagon—1.618.
Say you have a regular pentagon ABCDE with equal sides and equal
angles. You may draw a diagonal as line AC connecting any two ver-
texes of the pentagon. You can then install a total of five such lines, and
they are all of equal length. Divide the length of a diagonal AC by the
length of a side AB, and you will have an accurate numerical value for
PHI—1.618. You can draw a second diagonal line, BC inside the pen-
tagon so that this new line crosses the first diagonal at point O. What
occurs is this: Each diagonal is divided into two parts, and each part is
in PHI ratio (1.618) to the other, and to the whole diagonal—the PHI
ratio recurs every time any diagonal is divided by another diagonal.
When you draw all five pentagon diagonals, they form a five-point
star: a pentacle. Inside this star is a smaller, inverted pentagon. Each
diagonal is crossed by two other diagonals, and each segment is in PHI
ratio to the larger segments and to the whole. Also, the inverted inner
pentagon is in PHI ratio to the initial outer pentagon. Thus, PHI is
the ratio of five-sided symmetry.
Inscribe the pentacle star inside a pentagon and you have the pen-
tagram, symbol of the ancient Greek School of Mathematics founded
by Pythagoras—solid evidence that the ancient Mystery Schools knew
about PHI and appreciated the Divine Proportion’s multitude of uses
to form our physical and biological worlds.PASSAGE 2Langdon turned to face his sea of eager students. “Who can tell me
what this number is?”
A long-legged math major in back raised his hand. “That’s the num-
ber PHI.” He pronounced it fee.
“Nice job, Stettner,” Langdon said. “Everyone, meet PHI.” [... ]
“This number PHI,” Langdon continued, “one-point-six-one-eight,
is a very important number in art. Who can tell me why?” [... ]
“Actually,” Langdon said, [... ] “PHI is generally considered the most
beautiful number in the universe.” [... ] As Langdon loaded his slide
projector, he explained that the number PHI was derived from the(20)
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